The works of Aristotle

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JOHN M. KELLY LIBRARY

DONATED IN MEMORY OF
DR. GEORGE HEIMAN

University of
St. Michael s College, Toronto

THE

WORKS OF ARISTOTLE

TRANSLATED INTO ENGLISH
UNDER THE EDITORSHIP

OF

W. D. ROSS, M.A., HON. LL.D. (EDIN.)

FELLOW OF ORIEL COLLEGE
FELLOW OF THE BRITISH ACADEMY

VOLUME I

CATEGORIAE AND DE INTERPRETATIONE
BY E. M. EDGHILL

ANALYTICA PRIORA
BY A. J. JENKINSON

ANALYTICA POSTERIORA
BY G. R. G. MURE

TOPICA AND DE SOPHIST1CIS ELENCHIS
BY W. A. PICKARD-CAMBR1DGE

OXFORD
AT THE CLARENDON PRESS

1928

Oxford University Press

London : Amen House, E.G. 4

Edinburgh Glasgow Leipzig Copenhagen

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Bombay Calcutta Madras Shanghai
Humphrey Milford Publisher to the UNIVERSITY

Printed in Great Britain

Special thanks are due to the Trustees of the

Jowett Copyright Fund for their assistance

towards the publication of this Volume

CATEGO RI AE

AND

DE INTERPRETATIONS

BY

E. M. EDGHILL, M.A.

EX-ASSOCIATE OF NEWNHAM COLLEGE, CAMBRIDGE

PR EFACE

THIS translation has been made from Bekker s text of
1831, any departure from which has been indicated in the
notes.

My chief authority in matters of interpretation has been
Pacius ; I have also consulted Waitz s commentary largely.

My very grateful acknowledgments are due to the
valuable criticisms and suggestions of Mr. W. D. Ross of
Oriel College and Prof. J. A. Smith of Magdalen College.

E. M. E.

B 2

CATEGORIAE

TABLE OF CONTENTS

Ch. 1. Homonyms, synonyms, and derivatives.

Ch. 2. (i) Simple and composite expressions.

(2) Things (a) predicable of a subject, (l>) present in a subject,
(c) both predicable of, and present in, a subject, (d) neither
predicable of, nor present in, a subject.

Ch. 3. (i) That which is predicable of the predicate is predicable of

the subject.

(2) The differentiae of species in one genus are not the same as
those in another, unless one genus is included in the other.

Ch. 4. The eight categories of the objects of thought.

Ch. 5. Substance.

(1) Primary and secondary substance.

(2) Difference in the relation subsisting between essential and

accidental attributes and their subject.

(3) All that which is not primary substance is either an essential

or an accidental attribute of primary substance.

(4) Of secondary substances, species are more truly substance than
genera.

(5) All species, which are not genera, are substance in the same

degree, and all primary substances are substance in the same
degree.

(6) Nothing except species and genera is secondary substance.

(7) The relation of primary substance to secondary substance and to

all other predicates is the same as that of secondary substance
to all other predicates.

(8) Substance is never an accidental attribute.

(9) The differentiae of species are not accidental attributes.

(10) Species, genus, and differentiae, as predicates, are univocal
with their subject.

(11) Primary substance is individual; secondary substance is the
qualification of that which is individual.

(12) No substance has a contrary.

(13) No substance can be what it is in varying degrees.

CATEGORIAE

(14) The particular mark of substance is that contrary qualities can

be predicated of it.

(15) Contrary qualities cannot be predicated of anything other than

substances, not even of propositions and judgements.

Ch. 6. Quantity: (i) Discrete and continuous quantity.

(2) Division of quantities, i.e. number, the spoken word, the line,
the surface, the solid, time, place, into these two classes.

(3) The parts of some quantities have a relative position, those of
others have not. Division of quantities into these two classes.

(4) Quantitative terms are applied to things other than quantity, in
view of their relation to one of the aforesaid quantities.

(5) Quantities have no contraries.

(6) Terms such as great and small are relative, not quantitative,

and moreover cannot be contrary to each other.

(7) That which is most reasonably supposed to contain a contrary

is space.

(8) No quantity can be what it is in varying degrees.

(9) The peculiar mark of quantity is that equality and inequality can

be predicated of it.

Ch. 7. Relation.

(1) First definition of relatives.

(2) Some relatives have contraries.

(3) Some relatives are what they are in varying degrees.

(4) A relative term has always its correlative, and the two are inter

dependent.

(5) The correlative is only clear when the relative is given its

proper name, and in some cases words must be coined for this
purpose.

(6) Most relatives come into existence simultaneously ; but the
objects of knowledge and perception are prior to knowledge
and perception.

(7) No primary substance or part of a primary substance is relative.

(8) Revised definition of relatives, excluding secondary substances.

(9) It is impossible to know that a thing is relative, unless we know
that to which it is relative.

Ch. 8. Quality.

(1) Definition of qualities.

(2) Different kinds of quality :

(a) habits and dispositions ;

(b) capacities ;

(c) affective qualities. [Distinction between affective qualities

and affections.]

(d) shape, &c. [Rarity, density, &c., are not qualities.]

TABLE OF CONTENTS

(3) Adjectives are generally formed derivatively from the names of

the corresponding qualities.

(4) Most qualities have contraries.

(5) If of two contraries one is a quality, the other is also a quality.

(6) A quality can in most cases be what it is in varying degrees,

and subjects can possess most qualities in varying degrees.
Qualities of shape are an exception to this rule.

(7) The peculiar mark of quality is that likeness and unlikeness is

predicable of things in respect of it.

(8) Habits and dispositions as genera are relative; as individual,
qualitative.

Ch. 9. Action and affection and the other categories described.

Ch. 10. Four classes of opposites .

(a) Correlatives.

(b) Contraries. [Some contraries have an intermediate, and some
have not.]

(c) Positives and privatives.

The terms expressing possession and privation are not the positive
and privative, though the former are opposed each to each in the same
sense as the latter.

Similarly the facts which form the basis of an affirmation or a denial
are opposed each to each in the same sense as the affirmation and
denial themselves.

Positives and privatives are not opposed in the sense in which
correlatives are opposed.

Positives and privatives are not opposed in the same sense in which
contraries are opposed.

For (i) they are not of the class which has no intermediate, nor of
the class which has intermediates.

(ii) There can be no change from one state (privation) to its
opposite.

(d} Affirmation and negation. These are distinguished from other
contraries by the fact that one is always false and the other
true. [Opposite affirmations seem to possess this mark, but
they do not.]

Ch. 11. Contraries further discussed.

Evil is generally the contrary of good, but sometimes two evils are
contrary.

When one contrary exists, the other need not exist.

Contrary attributes are applicable within the same species or genus.

Contraries must themselves be within the same genus, or within
opposite genera, or be themselves genera.

CATEGORIAE

Ch. 12. The word prior is applicable :

(a) to that which is previous in time ;

(b) to that on which something else depends, but which is not itself

dependent on it ;

(c) to that which is prior in arrangement ;

(d) to that which is better or more honourable ;

(e) to that one of two interdependent things which is the cause of

the other.

Ch. 13. The word simultaneous is used :

(a) of those things which come into being at the same time ;

(/;) of those things which are interdependent, but neither of which

is the cause of the other.
(c) of the different species of the same genus.

Ch. 14. Motion is of six kinds.

Alteration is distinct from other kinds of motion.

Definition of the contrary of motion and of the various kinds of
motion.

Ch. 15. The meanings of the term to have .

CATEGORIAE

I THINGS are said to be named equivocally when, i a
though they have a common name, the definition corre
sponding with the name differs for each. Thus, a real man
and a figure in a picture can both lay claim to the name
animal ; yet these are equivocally so named, for, though
they have a common name, the definition corresponding
with the name differs for each. For should any one define
in what sense each is an animal, his definition in the one 5
case will be appropriate to that case only.

On the other hand, things are said to be named uni-
vocally which have both the name and the definition
answering to the name in common. A man and an ox are
both animal , and these are univocally so named, inasmuch
as not only the name, but also the definition, is the same
in both cases : for if a man should state in what sense each 10
is an animal, the statement in the one case would be
identical with that in the other.

Things are said to be named derivatively , which
derive their name from some other name, but differ from
it in termination. Thus the grammarian derives his name
from the word grammar , and the courageous man from 15
the word courage .

2 Forms of speech are either simple or composite.
Examples of the latter are such expressions as the man
runs , the man wins ; of the former man , ox , runs ,
wins .

Of things themselves some are predicable of a subject, 20
and are never present in a subject. Thus man is predic
able of the individual man, and is never present in a
subject.

By being present in a subject I do not mean present
as parts are present in a whole, but being incapable of
existence apart from the said subject.

i a CATEGORIAE

Some things, again, are present in a subject, but are

25 never predicable of a subject. For instance, a certain point
of grammatical knowledge is present in the mind, but is not
predicable of any subject ; or again, a certain whiteness
may be present in the body (for colour requires a material
basis), yet it is never predicable of anything.

Other things, again, are both predicable of a subject and

l b present in a subject. Thus while knowledge is present in
the human mind, it is predicable of grammar.

There is, lastly, a class of things which are neither
present in a subject nor predicable of a subject, such as the
5 individual man or the individual horse. But, to speak
more generally, that which is individual and has the
character of a unit is never predicable of a subject. Yet in
some cases there is nothing to prevent such being present
in a subject. Thus a certain point of grammatical know
ledge is present in a subject. 1

10 When one thing is predicated of another, all that which is 3
predicable of the predicate will be predicable also of the
subject. Thus, man is predicated of the individual man ;
but animal is predicated of man ; it will, therefore, be

15 predicable of the individual man also: for the individual
man is both man and animal .

If genera are different 2 and co-ordinate, their differentiae
are themselves different in kind. Take as an instance the
genus animal and the genus knowledge . With feet ,
two-footed , winged , aquatic , are differentiae of animal ;
the species of knowledge are not distinguished by the same
differentiae. One species of knowledge does not differ from
another in being two-footed .

20 But where one genus is subordinate to another, there is
nothing to prevent their having the same differentiae : for
the greater class is predicated of the lesser, so that all the
differentiae of the predicate will be differentiae also of the
subject.

2 5 Expressions which are in no way composite signify 4

1 Omit p.fv in 1. 9 with A, B, and Waitz, and xad vnoK.fiiJ.ivov . . .
Xeyerai with B and Waitz.

2 Read T&V Irtpav yevatv in 1. 16 with Dexippus, Phil., Simpl., Waitz.

CHAPTER 4 i b

substance, quantity, quality, relation, place, time, position,
state, action, or affection. To sketch my meaning roughly,
examples of substance are man or the horse , of quantity,
such terms as two cubits long or three cubits long ,
of quality, such attributes as white , grammatical .
Double , half, greater , fall under the category of
relation ; in the market place , in the Lyceum , under 2 a
that of place ; yesterday , last year , under that of time.
Lying , sitting , are terms indicating position ; shod ,
armed , state; to lance , to cauterize , action; to be
lanced , to be cauterized , affection.

No one of these terms, in and by itself, involves an
affirmation l ; it is by the combination of such terms that 5
positive or negative statements arise. For every assertion
must, as is admitted, be either true or false, whereas
expressions which are not in any way composite, such as
man , white , runs , wins , cannot be either true or 10
false.

5 Substance, in the truest and primary and most definite
sense of the word, is that which is neither predicable of a
subject nor present in a subject ; for instance, the individual
man or horse. But in a secondary sense those things are
called substances within which, as species, the primary sub
stances are included ; also those which, as genera, include 15
the species. For instance, the individual man is included
in the species man , and the genus to which the species
belongs is animal ; these, therefore that is to say, the
species man and the genus animal are termed secondary
substances.

It is plain from what has been said that both the name
and the definition of the predicate, must be predicable of 20
the subject. For instance, man is predicated of the
individual man. Now in this case the name of the species
man is applied to the individual, for we use the term man
in describing the individual ; and the definition of man
will also be predicated of the individual man, for the
individual man is both man and animal. Thus, both the 25

1 Omit 77 <<7ro<d(m in 1. 6 with Amm., Simpl., Waitz.

2 a CATEGORIAE

name and the definition of the species are predicable of
the individual.

With regard, on the other hand, to those things which
are present in a subject, it is generally the case that neither
their name nor their definition is predicable of that in which
they are present. Though, however, the definition is never

30 predicable, there is nothing in certain cases to prevent the
name being used. For instance, white being present in a
body is predicated of that in which it is present, for a body
is called white : the definition, however, of the colour
white is never predicable of the body. 1

Everything except primary substances is either predicable
of a primary substance or present in a primary substance.

35 This becomes evident by reference to particular instances
which occur. Animal is predicated of the species man ,
therefore of the individual man, for if there were no in
dividual man of whom it could be predicated, it could not

2 b be predicated of the species man at all. Again, colour is
present in body, therefore in individual bodies, for if there
were no individual body in which it was present, it could
not be present in body at all. Thus everything except
primary substances is either predicated of primary sub-
5 stances, or is present in them, and if these last did not exist,
it would be impossible for anything else to exist.

Of secondary substances, the species is more truly
substance than the genus, being more nearly related to
primary substance. For if any one should render an account
of what a primary substance is, he would render a more
instructive account, and one more proper to the subject, by

10 stating the species than by stating the genus. Thus, he
would give a more instructive account of an individual man by
stating that he was man than by stating that he was animal,
for the former description is peculiar to the individual in

1 Qualities pure and simple are abstractions, and in their abstract
substantival form, with regard to which they are defined, do not form
the predicate of substances. We do not say X is whiteness but X is
white . It is to this latter use of the adjective that Aristotle refers when
he says that the name is sometimes applicable ; for in Greek white
ness is not only \tvKOTijs, but also TO Xev/co*/. In English evil used
in the one case as a noun, in the other as an adjective, would afford
a parallel.

CHAPTER 5 2 b

a greater degree, while the latter is too general. Again, the
man who gives an account of the nature of an individual
tree will give a more instructive account by mentioning the
species tree than by mentioning the genus plant .

Moreover, primary substances are most properly called 15
substances in virtue of the fact that they are the entities
which underlie everything else, and that everything else is
either predicated of them or present in them. Now the
same relation which subsists between primary substance and
everything else subsists also between the species and the
genus : for the species is to the genus as subject is to
predicate, since the genus is predicated of the species, 20
whereas the species cannot be predicated of the genus.
Thus we have a second ground for asserting that the species
is more truly substance than the genus.

Of species themselves, except in the case of such as are
genera, no one is more truly substance than another. We
should not give a more appropriate account of the individual
man by stating the species to which he belonged, than we 25
should of an individual horse by adopting the same method
of definition. In the same way, of primary substances, no
one is more truly substance than another ; an individual
man is not more truly substance than an individual ox.

It is, then, with good reason that of all that remains, when
we exclude primary substances, we concede to species and
genera alone the name secondary substance , for these 3
alone of all the predicates convey a knowledge of primary
substance. For it is by stating the species or the genus
that we appropriately define any individual man ; and we
shall make our definition more exact by stating the former
than by stating the latter. All other things that we state,
such as that he is white, that he runs, and so on, are 35
irrelevant to the definition. Thus it is just that these alone,
apart from primary substances, should be called substances.

Further, primary substances are most properly so called,
because they underlie and are the subjects of everything
else. Now the same relation that subsists between primary 3 a
substance and everything else subsists also between the
species and the genus to which the primary substance belongs,

3 a CATEGORIAE

on the one hand, and every attribute which is not included
within these, on the other. For these are the subjects of all
such. If we call an individual man skilled in grammar ,
the predicate is applicable also to the species and to the
5 genus to which he belongs. This law holds good in all
cases.

It is a common characteristic of all substance that it is
never present in a subject. For primary substance is neither
present in a subject nor predicated of a subject ; while, with
regard to secondary substances, it is clear from the following
arguments (apart from others) that they are not present in

jo a subject. For man is predicated of the individual man, but
is not present in any subject : for manhood is not present in
the individual man. 1 In the same way, animal is also
predicated of the individual man, but is not present in him.

15 Again, when a thing is present in a subject, though the name
may quite well be applied to that in which it is present, the
definition cannot be applied. Yet of secondary substances,
not only the name, but also the definition, applies to the
subject : we should use both the definition of the species and

20 that of the genus with reference to the individual man. Thus
substance cannot be present in a subject.

Yet this is not peculiar to substance, for it is also the case
that differentiae cannot be present in subjects. The charac
teristics terrestrial and two-footed are predicated of the
species man , but not present in it. For they are not in

25 man. Moreover, the definition of the differentia may be
predicated of that of which the differentia itself is predicated.
For instance, if the characteristic terrestrial is predicated
of the species man , the definition also of that characteristic
may be used to form the predicate of the species man :
for man is terrestrial.

The fact that the parts of substances appear to be present
in the whole, as in a subject, should not make us apprehensive

30 lest we should have to admit that such parts are not sub
stances : for in explaining the phrase being present in a
subject , we stated 2 that we meant otherwise than as parts
in a whole .

1 Cf. the definition of present in a subject , 1*24. 2 1*24.

CHAPTER 5 3 a

It is the mark of substances and of differentiae that, in
all propositions of which they form the predicate, they are
predicated univocally. For all such propositions have for
their subject either the individual or the species. It is true 35
that, inasmuch as primary substance is not predicable of
anything, it can never form the predicate of any proposition.
But of secondary substances, the species is predicated of the
individual, the genus both of the species and of the individual.
Similarly the differentiae are predicated of the species and 3 b
of the individuals. Moreover, the definition of the species
and that of the genus are applicable to the primary substance,
and that of the genus to the species. For all that is pre
dicated of the predicate will be predicated also of the
subject. Similarly, the definition of the differentiae will be 5
applicable to the species and to the individuals. But it was
stated above l that the word univocal was applied to those
things which had both name and definition in common.
It is, therefore, established that in every proposition, of
which either substance or a differentia forms the predicate,
these are predicated univocally.

All substance appears to signify that which is individual. 10
In the case of primary substance this is indisputably true,
for the thing is a unit. In the case of secondary substances,
when we speak, for instance, of man or animal , our form
of speech gives the impression that we are here also indicating
that which is individual, but the impression is not strictly 15
true ; for a secondary substance is not an individual, but
a class with a certain qualification ; for it is not one and
single as a primary substance is ; the words man , animal ,
are predicable of more than one subject.

Yet species and genus do not merely indicate quality, like
the term white ; white indicates quality and nothing
further, but species and genus determine the quality with
reference to a substance : they signify substance qualitatively 20
differentiated. The determinate qualification covers a larger
field in the case of the genus than in that of the species :
he who uses the word animal is herein using a word of
wider extension than he who uses the word man .

1 i a 6.

3 b CATEGORIAE

Another mark of substance is that it has no contrary.

2 5 What could be the contrary of any primary substance, such
as the individual man or animal ? It has none. Nor can
the species or the genus have a contrary. Yet this charac
teristic is not peculiar to substance, but is true of many
other things, such as quantity. There is nothing that forms
the contrary of two cubits long or of three cubits long ,

30 or of ten , or of any such term. A man may contend that
much is the contrary of little , or great of small , but
of definite quantitative terms no contrary exists.

Substance, again, does not appear to admit of variation
of degree. I do not mean by this that one substance cannot
be more or less truly substance than another, for it has

35 already been stated l that this is the case ; but that no single
substance admits of varying degrees within itself. For
instance, one particular substance, 2 man , cannot be more
or less man either than himself at some other time or than
some other man. One man cannot be more man than
another, as that which is white may be more or less white

4 a than some other white object, or as that which is beautiful
may be more or less beautiful than some other beautiful
object. The same quality, moreover, is said to subsist in a
thing in varying degrees at different times. A body, being-
white, is said to be whiter at one time than it was before, or,
being warm, is said to be warmer or less warm than at
5 some other time. But substance is not said to be more or
less that which it is : a man is not more truly a man at one
time than he was before, nor is anything, if it is substance,
more or less what it is. Substance, then, does not admit
of variation of degree.

10 The most distinctive mark of substance appears to be
that, while remaining numerically one and the same, it is
capable of admitting contrary qualities. From among things
other than substance, we should find ourselves unable to
bring forward any which possessed this mark. Thus, one

15 and the same colour cannot be white and black. Nor can
the same one action be good and bad : this law holds good
with everything that is not substance. But one and the self-
i 2 a n- b 22. 2 1. 37 read nvrij with A, B, C, Waitz,

CHAPTER 5 4 a

same substance, while retaining its identity, is yet capable
of admitting contrary qualities. The same individual person
is at one time white, at another black, at one time warm, 20
at another cold, at one time good, at another bad. This
capacity is found nowhere else, though it might be maintained
that a statement or opinion was an exception to the rule. 1
The same statement, it is agreed, can be both true and false.
For if the statement he is sitting is true, yet, when the 25
person in question has risen, the same statement will be
false. The same applies to opinions. For if any one thinks
truly that a person is sitting, yet, when that person has risen,
this same opinion, if still held, will be false. Yet although
this exception may be allowed, there is. nevertheless, a
difference in the manner in which the thing takes place.
It is by themselves changing that substances admit contrary 3
qualities. It is thus that that which was hot becomes cold,
for it has entered into a different state. Similarly that which
was white becomes black, and that which was bad good, by
a process of change ; and in the same way in all other cases
it is by changing that substances are capable of admitting
contrary qualities. But statements and opinions themselves
remain unaltered in all respects : it is by the alteration in 35
the facts of the case that the contrary quality comes to be
theirs. The statement he is sitting remains unaltered,
but it is at one time true, at another false, according to 4 b
circumstances. What has been said of statements applies
also to opinions. Thus, in respect of the manner in which
the thing takes place, it is the peculiar mark of substance
that it should be capable of admitting contrary qualities ;
for it is by itself changing that it does so.

If, then, 2 a man should make this exception and contend
that statements and opinions are capable of admitting
contrary qualities, his contention is unsound. For state- 5
ments and opinions are said to have this capacity, not
because they themselves undergo modification, but because
this modification occurs in the case of something else.
The truth or falsity of a statement depends on facts, and

1 Read r<av TOLOVTMV in 1. 23 with A, B, Phil., Waitz.

2 Read fy in 4 with A . B > c > Waitz.

4 b CATEGORIAE

not on any power on the part of the statement itself of
10 admitting contrary qualities. In short, there is nothing
which can alter the nature of statements and opinions.
As, then, no change takes place in themselves, these cannot
be said to be capable of admitting contrary qualities.

But it is by reason of the modification which takes place
within the substance itself that a substance is said to be
capable of admitting contrary qualities ; for a substance
admits within itself either disease or health, whiteness or
15 blackness. It is in this sense that it is said to be capable
of admitting contrary qualities.

To sum up, it is a distinctive mark of substance, that,
while remaining numerically one and the same, it is capable
of admitting contrary qualities, the modification taking
place through a change in the substance itself.

Let these remarks suffice on the subject of substance.

20 Quantity is either discrete or continuous. Moreover, some 6
quantities are such that each part of the whole has a relative
position to the other parts : others have within them no
such relation of part to part. 1

Instances of discrete quantities are number and speech ;
of continuous, lines, surfaces, solids, and, besides these, time
and place.

25 In the case of the parts of a number, there is no common
boundary at which they join. For example : two fives
make ten, but the two fives have no common boundary, but
are separate; the parts three and seven also do not join at
any boundary. Nor, to generalize, would it ever be possible
in the case of number that there should be a common

30 boundary among the parts ; they are always separate.
Number, therefore, is a discrete quantity.

The same is true of speech. That speech is a quantity
is evident : for it is measured in long and short syllables.
I mean here that speech which is vocal. Moreover, it is a
discrete quantity, for its parts have no common boundary.

1 These two divisions of quantity are not exactly co-extensive. Time,
as we see later, is a continuous quantity, yet consists of parts which
have no relative position each to each.

CHAPTER 6 4 b

There is no common boundary at which the syllables join, 35
but each is separate and distinct from the rest.

A line, on the other hand, is a continuous quantity, for it 5 a
is possible to find a common boundary at which its parts
join. In the case of the line, this common boundary is
the point ; in the case of the plane, it is the line : for the
parts of the plane have also a common boundary. Similarly
you can find a common boundary in the case of the parts of
a solid, namely either a line or a plane. 5

Space and time also belong to this class of quantities.
Time, past, present, and future, forms a continuous whole.
Space, likewise, is a continuous quantity : for the parts of a
solid occupy a certain space, and these have a common
boundary ; it follows that the parts of space also, which are 10
occupied by the parts of the solid, have the same common
boundary as the parts of the solid. Thus, not only time,
but space also, is a continuous quantity, for its parts have a
common boundary.

Quantities consist either of parts which bear a relative 15
position each to each, or of parts which do not. The parts
of a line bear a relative position to each other, for each lies
somewhere, and it would be possible to distinguish each,
and to state the position of each on the plane and to
explain to what sort of part among the rest each was
contiguous. Similarly the parts of a plane have position, 20
for it could similarly be stated what was the position of each
and what sort of parts were contiguous. The same is true
with regard to the solid and to space. But it would be
impossible to show that the parts of a number had a relative
position each to each, or a particular position, or to state 25
what parts were contiguous. Nor could this be done in the
case of time, for none of the parts of time has an abiding
existence, and that which does not abide can hardly have
position. It would be better to say that such parts had a
relative order, in virtue of one being prior to another.
Similarly with number : in counting, one is prior to two , 30
and two to three, and thus the parts of number may be
said to possess a relative order, though it would be impos
sible to discover any distinct position for each. This holds

C 2

5 a CATEGORIAE

good also in the case of speech. None of its parts has an
abiding existence : when once a syllable is pronounced, it is

35 not possible to retain it, so that, naturally, as the parts
do not abide, they cannot have position. Thus, some
quantities consist of parts which have position, and some of
those which have not.

Strictly speaking, only the things which I have mentioned
belong to the category of quantity : everything else that is
called quantitative is a quantity in a secondary sense. It
is because we have in mind some one of these quantities,
properly so called, that we apply quantitative terms to
5 b other things. We speak of what is white as large, because
the surface over which the white extends is large ; we speak
of an action or a process as lengthy, because the time
covered is long ; these things cannot in their own right
claim the quantitative epithet. For instance, should any one

5 explain how long an action was, his statement would be
made in terms of the time taken, to the effect that it lasted
a year, or something of that sort. In the same way, he
would explain the size of a white object in terms of surface,
for he would state the area which it covered. Thus the
things already mentioned, and these alone, are in their
intrinsic nature quantities ; nothing else can claim the name

10 in its own right, but, if at all, only in a secondary sense.

Quantities have no contraries. In the case of definite
quantities this is obvious ; thus, there is nothing that is the
contrary of two cubits long or of three cubits long , or of
a surface, or of any such quantities. A man might, indeed,
argue that much was the contrary of little , and great

15 of small . But these are not quantitative, but relative;
things are not great or small absolutely, they are so called
rather as the result of an act of comparison. For instance,
a mountain is called small, a grain large, in virtue of the
fact that the latter is greater than others of its kind, the

20 former less. Thus there is a reference here to an external
standard, for if the terms great and small were used
absolutely, a mountain would never be called small or a
grain large. Again, we say that there are many people in
a village, and few in Athens, although those in the city are

CHAPTER 6 5 b

many times as numerous as those in the village : or we say
that a house has many in it, and a theatre few, though those 25
in the theatre far outnumber those in the house. The terms
two cubits long, three cubits long, and so on indicate
quantity, the terms great and small indicate relation,
for they have reference to an external standard. It is,
therefore, plain that these are to be classed as relative.

Again, whether we define them as quantitative or not, 30
they have no contraries : for how can there be a contrary of
an attribute which is not to be apprehended in or by itself,
but only by reference to something external ? Again,
if great and small are contraries, it will come about
that the same subject can admit contrary qualities at one
and the same time, and that things will themselves be
contrary to themselves. For it happens at times that the 35
same thing is both small and great. For the same thing
may be small in comparison with one thing, and great in
comparison with another, so that the same thing comes to
be both small and great at one and the same time, and is
of such a nature as to admit contrary qualities at one and
the same moment. Yet it was agreed, when substance was
being discussed, that nothing admits contrary qualities at
one and the same moment. For though substance is 6 a
capable of admitting contrary qualities, yet no one is at
the same time both sick and healthy, nothing is at the
same time both white and black. Nor is there anything
which is qualified in contrary ways at one and the same time.
Moreover, if these were contraries, they would themselves
be contrary to themselves. 1 For if great is the contrary 5

1 The Greek words do not mean that the subject which possesses
the two characteristics great and small will be the contrary of
itself, but that great and small will be the contrary of themselves.
The argument may be represented as follows :
Let x = small , y great .

A is both x and y.

Now x and y are, ex hypothesi, attributes belonging to the same
class (cf. 6 a 17 ev T& UVTOI yevft : also I4 a 19-25).

. . if they both apply to the same subject, the relation between them
may be represented by the formula x = y.
. . if x is the contrary of y

x is the contrary of x
which is absurd.

. . x is not the contrary of y.

6 a CATEGORIAE

of small , and the same thing is both great and small at
the same time, then small or great is the contrary of
itself. But this is impossible. The term great , therefore,
is not the contrary of the term small , nor much of little .
And even though a man should call these terms not relative,
10 but quantitative, they would not have contraries.

It is in the case of space that quantity most plausibly
appears to admit of a contrary. For men define the term
above as the contrary of below , when it is the region at
the centre they mean by below ; and this is so, because
nothing is farther from the extremities of the universe than
15 the region at the centre. 1 Indeed, it seems that in defining
contraries of every kind men have recourse to a spatial
metaphor, for they say that those things are contraries
which, within the same class, are separated by the greatest
possible distance.

Quantity does not, it appears, admit of variation of degree.

20 One thing cannot be two cubits long in a greater degree

than another. Similarly with regard to number : what is

three is not more truly three than what is five is five ;

nor is one set of three more truly three than another set. 2

Again, one period of time is not said to be more truly time

than another. Nor is there any other kind of quantity, of

all that have been mentioned, with regard to which varia-

25 tion of degree can be predicated. The category of quantity,

therefore, does not admit of variation of degree.

The most distinctive mark of quantity is that equality
and inequality are predicated of it. Each of the aforesaid
quantities is said to be equal or unequal. For instance, one
solid is said to be equal or unequal to another ; number, too,

1 No point is farther from the circumference of a circle taken as a
whole than the centre. Cf. de Caelo, 268 b 2i.

2 6 a 22. The reading of B and Waitz is here adopted : ra rpia TO!>I>
TTti Tt ov8(v fj.a\\ov TTfVTf *] Tplo, ov8f TO T/ji a T&v Tpiwi . That of Bekker
yields no satisfactory sense. By comparison with the method adopted
by Aristotle in treating of variation of degree with regard to other
caegories, it may be surmised that the meaning here is that given in
the translation. The difficulty of the passage is not much lessened by
substituting rpia % TreVre for irt vTc fj rpia, as either reading is a very
clumsy expression of the sense : ra rpia ov8fi> paXXov rpia f) TO. ntv-rt
irtvTf. In the translation, 7rWe r? rpln is taken as equivalent in sense
to orrep (<niv.

CHAPTER 6 6 a

and time can have these terms applied to them, 1 as indeed
can all those kinds of quantity that have been mentioned. 30

That which is not a quantity can by no means, it would
seem, be termed equal or unequal to anything else. One
particular disposition or one particular quality, such as
whiteness, is by no means compared with another in terms
of equality and inequality but rather in terms of similarity.
Thus it is the distinctive mark of quantity that it can be
called equal and unequal. 35

7 Those things arc called relative, which, being either said
to be of something else or related to something else, arc
explained by reference to that other thing. 2 For instance,
the word superior is explained by reference to something
else, for it is superiority over something else that is meant.
Similarly, the expression double has this external refer
ence, for it is the double of something else that is meant.
So it is with everything else of this kind. There are, 6 b
moreover, other relatives, e. g. habit, disposition, perception,
knowledge, and attitude. 3 The significance of all these is
explained by a reference to something else and in no other
way. Thus, a habit is a habit of something, knowledge is 5
knowledge of something, attitude is the attitude of something.
So it is with all other relatives that have been mentioned.
Those terms, then, are called relative, the nature of which
is explained by reference to something else, the preposition
of or some other preposition being used to indicate the
relation. Thus, one mountain is called great in comparison
with another ; for the mountain claims this attribute by
comparison ivith something. Again, that which is called

1 Read in 1. 29, before /era ^peifor, *rm apidpos KOI laos K<U livicros Xeyfra/,
with A, B, C, and Waitz.

2 Aristotle reckons as relative (l) terms which in Greek have a
genitive depending on them (oa-a frepcw tlvm \iytrai) and (2) terms
which naturally call for a prepositional phrase depending on them (fj
onaxTovv aXXwr rrpos (Ttpov). Since there is no one form in English
answering to the Greek use of the genitive, the distinction has been
somewhat paraphrased in the translation : but it must not be forgotten
that the distinction is taken primarily from the usage of the Greek
language.

3 Just as the genus knowledge is relative, while the particular
branches of it are not (see u a 2o), so habit and attitude require
particularization ; otherwise they are relative.

6 b CATEGORIAE

10 similar must be similar to something else, and all other such
attributes have this external reference. It is to be noted
that lying and standing and sitting are particular attitudes,
but attitude is itself a relative term. To lie, to stand, to be
seated, are not themselves attitudes, but take their name
from the aforesaid attitudes.

15 It is possible for relatives to have contraries. Thus virtue
has a contrary, vice, these both being relatives ; knowledge,
too, has a contrary, ignorance. But this is not the mark of
all relatives ; double and triple have no contrary, nor
indeed has any such term.

20 It also appears that relatives can admit of variation of
degree. For like and unlike , equal and unequal , have
the modifications more and less applied to them, and each
of these is relative in character : for the terms like and
unequal 1 bear a reference to something external. Yet,
again, it is not every relative term that admits of variation

25 of degree. No term such as double admits of this modi
fication. All relatives have correlatives : by the term slave
we mean the slave of a master; by the term master , the

30 master of a slave ; by double , the double of its half\ by
half, the half of its doubk ; by greater , greater than that
which is less ; by less , less than that which is greater.

So it is with every other relative term ; but the case
we use to express the correlation differs in some instances.
Thus, by knowledge we mean knowledge of the knowable ;
by the knowable, that which is to be apprehended by know-

35 ledge ; by perception, perception 0/~the perceptible ; by the
perceptible, that which is apprehended by perception.

Sometimes, however, reciprocity of correlation does not
appear to exist. This comes about when a blunder is made,
and that to which the relative is related is not accurately
stated. If a man states that a wing is necessarily relative to
a bird, the connexion between these two will not be reci
procal, for it will not be possible to say that a bird is a bird
by reason of its wings. The reason is that the original

1 6 b 23. The reading of B and Waitz : TO re yap opoiov rivl O/JLOLOV
\cycrat, Ka\ TO avivov rivi ilviaov. This has more inherent probability
than, and equal authority with, that of Bekker.

CHAPTER 7 7 a

statement was inaccurate, for the wing is not said to be 7 a
relative to the bird qua bird, since many creatures besides
birds have wings, but qua winged creature. If, then, the
statement is made accurate, the connexion will be reciprocal,
for we can speak of a wing having reference necessarily to a
winged creature, and of a winged creature as being such
because of its wings.

Occasionally, perhaps, it is necessary to coin words, if no 5
word exists by which a correlation can adequately be
explained. If we define a rudder as necessarily having
reference to a boat, our definition will not be appropriate,
for the rudder does not have this reference to a boat qua
boat, as there are boats which have no rudders. Thus we 10
cannot use the terms reciprocally, for the word boat can
not be said to find its explanation in the word rudder .
As there is no existing word, our definition would perhaps
be more accurate if we coined some word like ruddered
as the correlative of rudder . If we express ourselves
thus accurately, at any rate the terms are reciprocally
connected, for the ruddered thing is ruddered in virtue
of its rudder. So it is in all other cases. A head will be 15
more accurately defined as the correlative of that which is
headed , than as that of an animal, for the animal does not
have a head qua animal, since many animals have no head.

Thus we may perhaps most easily comprehend that to
which a thing is related, when a name does not exist, if,
from that which has a name, we derive a new name, and
apply it to that with which the first is reciprocally connected,
as in the aforesaid instances, when we derived the word 20
winged from wing and ruddered from rudder .

All relatives, then, if properly defined, have a correlative.
I add this condition because, if that to which they are related
is stated at haphazard and not accurately, the two are not
found to be interdependent. Let me state what I mean 25
more clearly. Even in the case of acknowledged correla
tives, and where names exist for each, there will be no
interdependence if one of the two is denoted, not by that
name which expresses the correlative notion, but by one of
irrelevant significance. The term slave , if defined as

7 a CATEGORIAE

related, not to a master, but to a man, or a biped, or any
thing of that sort, is not reciprocally connected with that in

30 relation to which it is defined, for the statement is not exact.
Further, if one thing is said to be correlative with another,
and the terminology used is correct, then, though all irrele
vant attributes should be removed, and only that one attri
bute left in virtue of which it was correctly stated to be cor
relative with that other, the stated correlation will still exist.
If the correlative of the slave is said to be the master ,

?o then, though all irrelevant attributes of the said master ,
such as biped , receptive of knowledge , human , should
be removed, and the attribute master alone left, the stated
correlation existing between him and the slave will remain the
same, for it is of a master that a slave is said to be the slave.

7 b On the other hand, if, of two correlatives, one is not correctly
termed, then, when all other attributes are removed and
that alone is left in virtue of which it was stated to be
correlative, the stated correlation will be found to have
disappeared.

For suppose the correlative of the slave should be said
to be the man , or the correlative of the wing the bird ;
5 if the attribute master be withdrawn from the man , the
correlation between the man and the slave will cease to
exist, for if the man is not a master, the slave is not a slave.
Similarly, if the attribute winged be withdrawn from the
bird , the wing will no longer be relative; for if the so-
called correlative is not winged, it follows that the wing
has no correlative.

10 Thus it is essential that the correlated terms should be
exactly designated ; if there is a name existing, the state
ment will be easy ; if not, it is doubtless our duty to
construct names. When the terminology is thus correct, it
is evident that all correlatives are interdependent.

15 Correlatives are thought to come into existence simul
taneously. This is for the most part true, as in the case
of the double and the half. The existence of the half
necessitates the existence of that of which it is a half.
Similarly the existence of a master necessitates the existence
of a slave, and that of a slave implies that of a master ; these

CHAPTER 7 7 b

are merely instances of a general rule. Moreover, they
cancel one another ; for if there is no double it follows that 20
there is no half, and vice versa ; this rule also applies to all
such correlatives. Yet it does not appear to be true in all
cases that correlatives come into existence simultaneously.
The object of knowledge would appear to exist before
knowledge itself, for it is usually the case that we acquire
knowledge of objects already existing ; it would be difficult, 25
if not impossible, to find a branch of knowledge the begin
ning of the existence of which was contemporaneous with
that of its object.

Again, while the object of knowledge, if it ceases to exist,
cancels at the same time the knowledge which was its
correlative, the converse of this is not true. It is true that
if the object of knowledge does not exist there can be no
knowledge : for there will no longer be anything to know.
Yet it is equally true that, if the knowledge of a certain 30
object does not exist, the object may nevertheless quite
well exist. Thus, in the case of the squaring of the circle,
if indeed that process is an object of knowledge, though it
itself exists as an object of knowledge, yet the knowledge
of it has not yet come into existence. Again, if all animals
ceased to exist, there would be no knowledge, but there
might yet be many objects of knowledge.

This is likewise the case with regard to perception : for the 35
object of perception is, it appears, prior to the act of percep
tion. If the perceptible is annihilated, perception also will
cease to exist; but the annihilation of perception does not
cancel the existence of the perceptible. For perception im
plies a body perceived and a body in which perception takes
place. Now if that which is perceptible is annihilated, it
follows that the body is annihilated, for the body is a percep
tible thing ; and if the body does not exist, it follows that 8 a
perception also ceases to exist. Thus the annihilation of
the perceptible involves that of perception.

But the annihilation of perception does not involve that
of the perceptible. For if the animal is annihilated, it
follows that perception also is annihilated, but perceptibles 5
such as body, heat, sweetness, bitterness, and so on, will
remain.

8 a CATEGORIAE

Again, perception is generated at the same time as the
perceiving subject, for it comes into existence at the same
time as the animal. But the perceptible surely exists
before x perception ; for fire and water and such elements,

10 out of which the animal is itself composed, exist before the
animal is an animal at all, and before perception. Thus it
would seem that the perceptible exists before perception.

It may be questioned whether it is true that no substance
is relative, as seems to be the case, or whether exception is
to be made in the case of certain secondary substances. 2

15 With regard to primary substances, it is quite true that there
is no such possibility, for neither wholes nor parts of primary
substances are relative. The individual man or ox is not
defined with reference to something external. Similarly

20 with the parts : a particular hand or head is not defined as
a particular hand or head of a particular person, but as the
hand or head of a particular person. It is true also, for the
most part at least, in the case of secondary substances ;
the species man and the species ox are not defined with
reference to anything outside themselves. Wood, again, is
only relative in so far as it is some one s property, not in so
far as it is wood. It is plain, then, that in the cases men-

25 tioned substance is not relative. But with regard to some
secondary substances there is a difference of opinion ; thus,
such terms as head and hand 3 are defined with reference
to that of which the things indicated are a part, and so it
comes about that these appear to have a relative character. 4
Indeed, if our definition of that which is relative was

30 complete, it is very difficult, if not impossible, to prove that
no substance is relative. If, however, our definition was
not complete, if those things only are properly called relative
in the case of which relation to an external object is a
necessary condition of existence, perhaps some explanation
of the dilemma may be found.

1 Omit <*ov ff in 1. 9 with B, Phil., and Waitz.

2 So far Aristotle has stated, and adhered to, the generally received
definition of relatives ; he now improves upon it.

3 Sc. : when the species are meant.

4 In accordance with this, Aristotle speaks of wing as a relative
term in the earlier part of the chapter.

CHAPTER 7 8 a

The former definition does indeed apply to all relatives,
but the fact that a thing is explained with reference to some
thing else does not make it essentially relative. 1

From this it is plain that, if a man definitely apprehends 35
a relative thing, he will also definitely apprehend that to
which it is relative. Indeed this is self-evident : for if a
man knows that some particular thing is relative, assuming
that we call that a relative in the case of which relation to
something is a necessary condition of existence, he knows 8 b
that also to which it is related. For if he does not know at
all that to which it is related, he will not know whether or
not it is relative. This is clear, moreover, in particular
instances. If a man knows definitely that such and such
a thing is double , he will also forthwith know definitely 5
that of which it is the double. For if there is nothing
definite of which he knows it to be the double, he does not
know at all that it is double. Again, if he knows that
a thing is more beautiful, it follows necessarily that he will
forthwith definitely know that also than which it is more
beautiful. He will not merely know indefinitely that it is
more beautiful than something which is less beautiful, for 10
this would be supposition, not knowledge. For if he does
not know definitely that than which it is more beautiful, he
can no longer claim to know definitely that it is more
beautiful than something else which is less beautiful : for it
might be that nothing was less beautiful. It is, therefore,
evident that if a man apprehends some relative thing
definitely, he necessarily knows that also definitely to
which it is related.

Now the head, the hand, and such things are substances, 15
and it is possible to know their essential character definitely,
but it does not necessarily follow that we should know that
to which they are related. It is not possible to know
forthwith whose head or hand is meant. Thus these are
not relatives, and, this being the case, it would be true to 20
say that no substance is relative in character. It is perhaps
a difficult matter, in such cases, to make a positive statement

1 ov firjv TOVTI I (A 2 , C, Phil., and Waitz) ye fVri TO (A 2 , B, C, Phil., and
Waitz) Trpor TI, in 1. 34.

8 b CATEGORIAE

without more exhaustive examination, but to have raised
questions with regard to details is not without advantage.

25 By quality I mean that in virtue of which people are said 8
to be such and such.

Quality is a term that is used in many senses. One sort
of quality let us call habit or disposition V Habit differs
from disposition in being more lasting and more firmly
established. The various kinds of knowledge and of virtue
are habits, for knowledge, even when acquired only in

30 a moderate degree, is, it is agreed, abiding in its character
and difficult to displace, unless some great mental upheaval
takes place, through disease or any such cause. The virtues,
also, such as justice, self-restraint, and so on, are not easily
dislodged or dismissed, so as to give place to vice.

35 By a disposition, on the other hand, we mean a condition
that is easily changed and quickly gives place to its
opposite. Thus, heat, cold, disease, health, and so on are
dispositions. For a man is disposed in one way or another
with reference to these, but quickly changes, becoming

g a cold instead of warm, ill instead of well. So it is with all
other dispositions also, unless through lapse of time a
disposition has itself become inveterate and almost im
possible to dislodge : in which case we should perhaps go
so far as to call it a habit.

It is evident that men incline to call those conditions
habits which are of a more or less permanent type and
5 difficult to displace ; for those who are not retentive of
knowledge, but volatile, are not said to have such and such
a habit as regards knowledge, yet they are disposed, we
may say, either better or worse, towards knowledge. Thus
habit differs from disposition in this, that while the latter
is ephemeral, the former is permanent and difficult to
alter.

10 Habits are at the same time dispositions, but dispositions
arc not necessarily habits. For those who have some

1 The term habit itself is relative, but particular habits are quali
ties ; as also virtues and vices. ei? means habit and state ;
sometimes the one, sometimes the other, English word gives the sense
better ; but it is, perhaps, best to reserve the word state for the
category so called.

CHAPTER 8 9 a

specific habit may be said also, in virtue of that habit, to be
thus or thus disposed ; but those who are disposed in some
specific way have not in all cases the corresponding habit.

Another sort of quality is that in virtue of which, for
example, we call men good boxers or runners, or healthy
or sickly: in fact it includes all those terms which refer to 15
inborn capacity or incapacity. Such things are not predi
cated of a person in virtue of his disposition, but in virtue
of his inborn capacity or incapacity to do something with
ease or to avoid defeat of any kind. Persons are called
good boxers or good runners, not in virtue of such and
such a disposition, but in virtue of an inborn capacity to 20
accomplish something with ease. Men are called healthy
in virtue of the inborn capacity of easy resistance to those
unhealthy influences that may ordinarily arise ; unhealthy,
in virtue of the lack of this capacity. Similarly with regard
to softness and hardness. Hardness is predicated of a 25
thing because it has that capacity of resistance which
enables it to withstand disintegration ; softness, again, is
predicated of a thing by reason of the lack of that capacity.

A third class within this category is that of affective
qualities and affections. 1 Sweetness, bitterness, sourness,
are examples of this sort of quality, together with all that
is akin to these ; heat, moreover, and cold, whiteness, and 30
blackness are affective qualities. It is evident that these
are qualities, for those things that possess them are them
selves said to be such and such by reason of their presence.
Honey is called sweet because it contains sweetness ; the
body is called white because it contains whiteness ; and so
in all other cases.

The term affective quality is not used as indicating 35
that those things which admit these qualities are affected in
any way. Honey is not called sweet because it is affected Q b
in a specific way, nor is this what is meant in any other
instance. Similarly heat and cold are called affective
qualities, not because those things which admit them are
affected. What is meant is that these said qualities are 5

1 Here Aristotle seems to call Trddij TroiorrjTfs, but later he dis
tinguishes them.

g b CATEGORIAE

capable of producing an affection in the way of percep
tion. For sweetness has the power of affecting the sense of
taste ; heat, that of touch ; and so it is with the rest of these
qualities.

Whiteness and blackness, however, and the other colours,

10 are not said to be affective qualities in this sense, but because
they themselves are the results of an affection. 1 It is plain
that many changes of colour take place because of affections.
When a man is ashamed, he blushes ; when he is afraid, he
becomes pale, and so on. So true is this, that when a man

15 is by nature liable to such affections, arising from some
concomitance of elements in his constitution, it is a probable
inference that he has the corresponding complexion of skin.
For the same disposition of bodily elements, which in the
former instance was momentarily present in the case of an
access of shame, might be a result of a man s natural
temperament, so as to produce the corresponding colouring
also as a natural characteristic. All conditions, therefore,

20 of this kind, if caused by certain permanent and lasting
affections, are called affective qualities. For pallor and
duskiness of complexion are called qualities, inasmuch as
we are said to be such and such in virtue of them, not only
if they originate in natural constitution, but also if they

25 come about through long disease or sunburn, and are
difficult to remove, or indeed remain throughout life. For
in the same way we are said to be such and such because of
these.

Those conditions, however, which arise from causes which
may easily be rendered ineffective or speedily removed, are
called, not qualities, but affections : for we are not said to be

30 such and such in virtue of them. The man whc blushes
through shame is not said to be a constitutional blusher,
nor is the man who becomes pale through fear said to be
constitutionally pale. He is said rather to have been
affected. Thus such conditions are called affections, not
qualities.

1 The colours seen in inanimate objects are presumably to be called
affective qualities in the former sense of the word, because they affect
the eye.

CHAPTER 8 9 b

In like manner there are affective qualities and affections
of the soul. That temper with which a man is born and 35
which has its origin in certain deep-seated affections is
called a quality. I mean such conditions as insanity, lo a
irascibility, and so on : for people are said to be mad or
irascible in virtue of these. Similarly those abnormal
psychic states which are not inborn, but arise from the
concomitance of certain other elements, and are difficult to
remove, or altogether permanent, are called qualities, for in 5
virtue of them men are said to be such and such.

Those, however, which arise from causes easily rendered
ineffective are called affections, not qualities. Suppose that
a man is irritable when vexed : he is not even spoken of as a
bad-tempered man, when in such circumstances he loses his
temper somewhat, but rather is said to be affected. Such
conditions are therefore termed, not qualities, but affections. 10

The fourth sort of quality is figure and the shape that
belongs to a thing ; and besides this, straightness and
curvedness and any other qualities of this type ; each of
these defines a thing as being such and such. Because it is
triangular or quadrangular a thing is said to have a specific
character, or again because it is straight or curved ; T in fact 1 5
a thing s shape in every case gives rise to a qualification
of it.

Rarity and density, roughness and smoothness, seem to be
terms indicating quality : yet these, it would appear, really
belong to a class different from that of quality. For it is
rather a certain relative position of the parts composing the
thing thus qualified which, it appears, is indicated by each
of these terms. A thing is dense, owing to the fact that its 20
parts are closely combined with one another ; rare, because
there are interstices between the parts ; smooth, because its
parts lie, so to speak, evenly ; rough, because some parts
project beyond others.

There may be other sorts of quality, but those that are 25
most properly so called have, we may safely say, been

enumerated.

1 Read ry yap rpiy&vov . . . TO> evdv in 11. 14. 15 with Waitz.

645-24-1 D

io a CATEGORIAE

These, then, are qualities, and the things that take their
name from them as derivatives, or are in some other way
dependent on them, are said to be qualified in some specific
way. 1 In most, indeed in almost all cases, the name of that

30 which is qualified is derived from that of the quality. Thus
the terms whiteness , grammar , justice , give us the
adjectives white . grammatical , just , and so on.

There are some cases, however, in which, as the quality
under consideration has no name, it is impossible that those
possessed of it should have a name that is derivative. For
instance, the name given to the runner or boxer, who is so

35 called in virtue of an inborn capacity, is not derived from
lo b that of any quality ; for those capacities have no name
assigned to thern^. In this, the inborn capacity is distinct
from the science, with reference to which men are called, e.g.,
boxers or wrestlers. Such a science is classed as a disposi
tion ; it has a name, and is called boxing or wrestling
as the case may be, and the name given to those disposed
in this way is derived from that of the science.
5 Sometimes, even though a name exists for the quality,
that which takes its character from the quality has a name
that is not a derivative. For instance, the upright man
takes his character from the possession of the quality of
integrity, but the name given him is not derived from the
word integrity . Yet this does not occur often.

We may therefore state that those things are said to be

10 possessed of some specific quality which have a name derived
from that of the aforesaid quality, or which are in some
other way dependent on it.

One quality may be the contrary of another ; thus justice
is the contrary of injustice, whiteness of blackness, and so on.
The things, also, which are said to be such and such in virtue
of these qualities, may be contrary the one to the other ;
for that which is unjust is contrary to that which is just,

15 that which is white to that which is black. This, however,
is not always the case. Red, yellow, and such colours,
though qualities, have no contraries.

1 The words TO notuv and ra rroid are, however, often used in this
chapter as equivalent to Trotor^y : cf. io b 2o Trmbv ; SiKaioa-vvij.

CHAPTER 8 io l

If one of two contraries is a quality, the other will also
be a quality. This will be evident from particular instances,
if we apply the names used to denote the other categories ;
for instance, granted that justice is the contrary of injustice
and justice is a quality, injustice will also be a quality : 20
neither quantity, nor relation, nor place, nor indeed any other
category but that of quality, will be applicable properly to
injustice. So it is with all other contraries falling under the
category of quality. 2 r

Qualities admit of variation of degree. Whiteness is
predicated of one thing in a greater or less degree than of
another. This is also the case with reference to justice.
Moreover, one and the same thing may exhibit a quality in
a greater degree than it did before : if a thing is white, it
may become whiter.

Though this is generally the case, there are exceptions.
For if we should say that justice admitted of variation of 30
degree, difficulties might ensue, and this is true with regard
to all those qualities which arc dispositions. There are
some, indeed, who dispute the possibility of variation here.
They maintain that justice and health cannot very well
admit of variation of degree themselves, but that people 35
vary in the degree in which they possess these qualities,
and that this is the case with grammatical learning and all n a
those qualities which are classed as dispositions. However
that may be, it is an incontrovertible fact that the things
which in virtue of these qualities are said to be what they
are vary in the degree in which they possess them ; for one
man is said to be better versed in grammar, or more healthy
or just, than another, and so on.

The qualities expressed by the terms triangular and =,
quadrangular do not appear to admit of variation of degree,
nor indeed do any that have to do with figure. For those
things to which the definition of the triangle or circle is
applicable are all equally triangular or circular. Those, on
the other hand, to which the same definition is not applic
able, cannot be said to differ from one another in degree ;
the square is no more a circle than the rectangle, for to 10
neither is the definition of the circle appropriate. In short,

D 2

n a CATEGORIAE

if the definition of the term proposed is not applicable to
both objects, they cannot be compared. Thus it is not all
qualities which admit of variation of degree.

15 Whereas none of the characteristics I have mentioned are
peculiar to quality, the fact that likeness and unlikeness can
be predicated with reference to quality only, gives to that
category its distinctive feature. One thing is like another
only with reference to that in virtue of which it is such and
such ; thus this forms the peculiar mark of quality.

20 We must not be disturbed because it may be argued that,
though proposing to discuss the category of quality, we
have included in it many relative terms. We did say that
habits and dispositions were relative. In practically all
such cases the genus is relative, the individual not. Thus
knowledge, as a genus, is explained by reference to some-

2=; thing else, for we mean a knowledge of something. But
particular branches of knowledge are not thus explained.
The knowledge of grammar is not relative to anything
external, nor is the knowledge of music, but these, if relative
at all, are relative only in virtue of their genera ; thus

30 grammar is said to be the knoivledge of something, not the
grammar of something ; similarly music is the knoivledge of
something, not the music of something.

Thus individual branches of knowledge are not relative.
And it is because we possess these individual branches of
knowledge that we are said to be such and such. It is these
that we actually possess : we are called experts because
we possess knowledge in some particular branch. Those

35 particular branches, therefore, of knowledge, in virtue of
which we are sometimes said to be such and such, are them
selves qualities, and are not relative. Further, if anything
should happen to fall within both the category of quality
and that of relation, there would be nothing extraordinary
in classing it under both these heads.

n b Action and affection both admit of contraries and also 9
of variation of degree. Heating is the contrary of cooling,
being heated of being cooled, being glad of being vexed.
Thus they admit of contraries. They also admit of varia-

5 tion of degree : for it is possible to heat in a greater or less

CHAPTER 9 n b

degree ; also to be heated in a greater or less degree. Thus
action and affection also admit of variation of degree. So
much, then, is stated with regard to these categories.

We spoke, moreover, of the category of position when we
were dealing with that of relation, and stated that such
terms derived their names from those of the corresponding
attitudes.

As for the rest, time, place, state, since they are easily 10
intelligible, I say no more about them than was said at the
beginning, that in the category of state are included such
states as shod , armed , in that of place in the Lyceum
and so on, as was explained before.

10 The proposed categories have, then, been adequately 15
dealt with.

We must next explain the various senses in which the
term opposite is used. Things are said to be opposed in
four senses : (i) as correlatives to one another, (ii) as con
traries to one another, (iii) as privatives to positives, (iv) as
affirmatives to negatives.

Let me sketch my meaning in outline. An instance of
the use of the word opposite with reference to correlatives
i.s afforded by the expressions double and half; with ao
reference to contraries by bad and good . Opposites in
the sense of privatives and positives are blindness
and sight ; in the sense of affirmatives and negatives, the
propositions he sits , he does not sit .

(i) Pairs of opposites which fall under the category of
relation are explained by a reference of the one to the other,
the reference being indicated by the preposition of or by 25
some other preposition. Thus, double is a relative term,
for that which is double is explained as the double of some
thing. Knowledge, again, is the opposite of the thing
known, in the same sense; and the thing known also is
explained by its relation to its opposite, knowledge. For 30
the thing known is explained as that which is known by
something; that is, by knowledge. Such things, then, as
are opposite the one to the other in the sense of being
correlatives are explained by a reference of the one to the
other.

n b CATEGORIAE

(ii) Pairs of oppositcs which arc contraries are not in any
way interdependent, but are contrary the one to the other.

35 The good is not spoken of as the good of the bad, but as
the contrary of the bad, nor is white spoken of as the white
of the black, but as the contrary of the black. These two
I2 a types of opposition are therefore distinct. Those contraries
which are such that the subjects in which they are naturally
present, or of which they are predicated, must necessarily
contain either the one or the other of them, have no inter
mediate, but those in the case of which no such necessity
obtains, always have an intermediate. Thus disease and
5 health are naturally present in the body of an animal, and
it is necessary that either the one or the other should be
present in the body of an animal. Odd and even, again,
are predicated of number, and it is necessary that the one
or the other should be present in numbers. Now there is
no intermediate between the terms of either of these two
pairs. On the other hand, in those contraries with regard

10 to which no such necessity obtains, we find an intermediate.
Blackness and whiteness are naturally present in the body,
but it is not necessary that either the one or the other should
be present in the body, inasmuch as it is not true to say that
everybody must be white or black. Badness and goodness,

15 again, are predicated of man, and of many other things, but
it is not necessary that either the one quality or the other
should be present in that of which they are predicated : it
is not true to say that everything that may be good or bad
must be either good or bad. These pairs of contraries have
intermediates : the intermediates between white and black
are grey, sallow, and all the other colours that come between ;
the intermediate between good ond bad is that which is
neither the one nor the other.

20 Some intermediate qualities have names, such as grey
and sallow and all the other colours that come between
white and black ; in other cases, however, it is not easy to
name the intermediate, but we must define it as that which
is not either extreme, as in the case of that which is neither

25 good nor bad, neither just nor unjust.

(iii) Privatives and positives have reference to the

CHAPTER 10 I2 a

same subject. Thus, sight and blindness have reference to
the eye. It is a universal rule that each of a pair of
opposites of this type has reference to that to which the
particular positive is natural. We say that that which is
capable of some particular faculty or possession has suffered
privation when the faculty or possession in question is in 30
no way present in that in which, and at the time at which,
it should naturally be present. We do not call that tooth
less which has not teeth, or that blind which has not sight,
but rather that which has not teeth or sight at the time
when by nature it should. For there are some creatures
which from birth are without sight, or without teeth, but
these are not called toothless or blind.

To be without some faculty or to possess it is not the 35
same as the corresponding * privative or positive . Sight
is a positive , blindness a privative , but to possess
sight is not equivalent to sight , to be blind is not
equivalent to blindness . Blindness is a privative , to be
blind is to be in a state of privation, but is not a privative .
Moreover, if blindness were equivalent to being blind ,
both would be predicated of the same subject ; but though 40
a man is said to be blind, he is by no means said to be
blindness.

To be in a state of possession is, it appears, the opposite I2 b
of being in a state of privation , just as positives and
privatives themselves are opposite. There is the same
type of antithesis in both cases ; for just as blindness is
opposed to sight, so is being blind opposed to having sight. 5

That which is affirmed or denied is not itself affirmation
or denial. By affirmation we mean an affirmative pro
position, by denial a negative. Now, those facts which
form the matter of the affirmation or denial are not proposi
tions ; yet these two are said to be opposed in the same 10
sense as the affirmation and denial, for in this case also the
type of antithesis is th same. For as the affirmation is
opposed to the denial, as in the two propositions he sits ,
he does not sit , so also the fact which constitutes the
matter of the proposition in one case is opposed to that in
the other, his sitting, that is to say, to his not sitting. j=;

I2 b CATEGOR1AR

It is evident that positives and privatives are not
opposed each to each in the same sense as relatives. The
one is not explained by reference to the other ; sight is not
sight of blindness, nor is any other preposition used to
indicate the relation. Similarly blindness is not said to be

20 blindness of sight, but rather, privation of sight. Relatives,
moreover, reciprocate ; if blindness, therefore, were a rela
tive, there would be a reciprocity of relation between it and
that with which it was correlative. But this is not the case.

25 Sight is not called the sight of blindness.

That those terms which fall under the heads of positives
and privatives are not opposed each to each as contraries,
either, is plain from the following facts : Of a pair of con
traries such that they have no intermediate, one or the
other must needs be present in the subject in which they

?,o naturally subsist, or of which they are predicated ; for it is
those, as we proved, 1 in the case of which this necessity
obtains, that have no intermediate. Moreover, we cited
health and disease, odd and even, as instances. But those
contraries which have an intermediate are not subject to
any such necessity. It is not necessary that every substance,
receptive of such qualities, should be either black or white,
cold or hot, for something intermediate between these

3? contraries may very well be present in the subject. We
proved, moreover, that those contraries have an interme
diate in the case of which the said necessity does not obtain. -
Yet when one of the two contraries is a constitutive property
of the subject, as it is a constitutive property of fire to be
hot, of snow to be white, it is necessary dcterminately that
one of the two contraries, not one or the other, should be

40 present in the subject ; 3 for fire cannot be cold, or snow
black. Thus, it is not the case here that one of the two
must needs be present in every subject receptive of these
I3 a qualities, but only in that subject of which the one forms a
constitutive property. Moreover, in such cases it is one
member of the pair determinately. and not either the one or
the other, which must be present.

1 Cf. n b 38. 2 <>vTf . . . ft(KTtK<, 11. 33-7, is parenthetical.

3 Si. : although they have intermediates.

CHAPTER 10 13*

In the case of positives and privatives , on the other
hand, neither of the aforesaid statements holds good. For
it is not l necessary that a subject receptive of the qualities
should always have either the one or the other ; that which 5
has not yet advanced to the state when sight is natural is
not said either to be blind or to see. Thus positives and
privatives do not belong to that class of contraries which
consists of those which have no intermediate. On the other
hand, they do not belong either to that class which consists
of contraries which have an intermediate. For under cer
tain conditions it is necessary that either the one or the
other should form part of the constitution of every appro
priate subject. For when a thing has reached the stage
when it is by nature capable of sight, it will be said either 10
to see or to be blind, and that in an indeterminate sense,
signifying that the capacity may be either present or absent ;
for it is not necessary either that it should see or that it
should be blind, but that it should be either in the one state
or in the other. Yet in the case of those contraries which
have an intermediate we found that it was never necessary
that either the one or the other should be present in every
appropriate subject, but only that in certain subjects one of
the pair should be present, and that in a determinate sense.
It is, therefore, plain that positives and privatives are 15
not opposed each to each in either of the senses in which
contraries are opposed.

Again, in the case of contraries, it is possible that there
should be changes from either into the other, while the
subject retains its identity, unless indeed one of the con
traries is a constitutive property of that subject, as heat is
of fire. For it is possible that that which is healthy should 20
become diseased, that which is white, black, that which is
cold, hot, that which is good, bad, that which is bad, good.
The bad man, if he is being brought into a better way of
life and thought, may make some advance, however slight,
and if he should once improve, even ever so little, it is plain 2-^
that he might change completely, or at any rate make very
great progress ; for a man becomes more and more easily
1 Read wrt in 1. 4 with B, C, and Waitz.

I3 a CATEGORIAE

moved to virtue, however small the improvement was at
first. It is, therefore, natural to suppose that he will make
yet greater progress than he has made in the past ; and as
this process goes on, it will change him completely and estab-

;,o lish him in the contrary state, provided he is not hindered
by lack of time. In the case of positives and privatives ,
however, change in both directions is impossible. There
may be a change from possession to privation, but not from
privation to possession. The man who has become blind

35 does not regain his sight ; the man who has become bald
does not regain his hair ; the man who has lost his teeth
does not grow a new set.

J 3 (iv) Statements opposed as affirmation and negation
belong manifestly to a class which is distinct, for in this
case, and in this case only, it is necessary for the one opposite
to be true and the other false.

Neither in the case of contraries, nor in the case of
correlatives, nor in the case of positives and privatives ,
is it necessary for one to be true and the other false.
5 Health and disease are contraries : neither of them is true
or false. Double and half are opposed to each other as
correlatives : neither of them is true or false. The case is
the same, of course, with regard to positives and priva-

10 tives such as sight and blindness . In short, where there
is no sort of combination of words, truth and falsity have
no place, and all the opposites we have mentioned so far
consist of simple words.

At the same time, when the words which enter into
opposed statements are contraries, these, more than any
other set of opposites, would seem to claim this character
istic. Socrates is ill is the contrary of Socrates is well .

15 but not even of such composite expressions is it true to say
that one of the pair must always be true and the other
false. For if Socrates exists, one will be true and the other
false, but if he does not exist, both will be false ; for neither
Socrates is ill nor Socrates is well is true, if Socrates
does not exist at all.

23 In the case of positives and privatives , if the subject
does not exist at all, neither proposition is true, but even if

CHAPTER 10 I3 b

the subject exists, it is not always the fact that one is true
and the other false. For Socrates has sight is the oppo
site of Socrates is blind in the sense of the word opposite
which applies to possession and privation. Now if Socrates
exists, it is not necessary that one should be true and the
other false, for when he is not yet able to acquire the power
of vision, both are false, as also if Socrates is altogether 25
non-existent.

But in the case of affirmation and negation, whether the
subject exists or not, one is always false and the other true.
For manifestly, if Socrates exists, one of the two proposi
tions Socrates is ill , Socrates is not ill , is true, and the 30
other false. This is likewise the case if he does not exist ; for
if he does not exist, to say that he is ill is false, to say that he
is not ill is true. Thus it is in the case of those opposites
only, which are opposite in the sense in which the term is
used with reference to affirmation and negation, that the
rule holds good, that one of the pair must be true and
the other false. 35

II That the contrary of a good is an evil is shown by induc
tion : the contrary of health is disease, of courage, cowardice,
and so on. But the contrary of an evil is sometimes a 14*
good, sometimes an evil. For defect, which is an evil, has
excess for its contrary, this also being an evil, and the
mean, which is a good, is equally the contrary of the one
and of the other. It is only in a few cases, however, that
we see instances of this : in most, the contrary of an evil is 5
a good.

In the case of contraries, it is not always necessary that if
one exists the other should also exist : for if all become
healthy there will be health and no disease, and again, if-
everything turns white, there will be white, but no black.
Again, since the fact that Socrates is ill is the contrary 10
of the fact that Socrates is well, and two contrary conditions
cannot both obtain in one and the same individual at the same
time, both these contraries could not exist at once : for if
that Socrates was well was a fact, then that Socrates was ill
could not possibly be one.

i4 b CATEGORIAE

are said to be simultaneous in nature. I mean those
species which are distinguished each from each by one

35 and the same method of division. Thus the winged species
is simultaneous with the terrestrial and the water
species. These are distinguished within the same genus,
and are opposed each to each, for the genus animal has
the winged , the ( terrestrial , and the water species, and
no one of these is prior or posterior to another ; on the
contrary, all such things appear to be simultaneous in
I5 a nature. Each of these also, the terrestrial, the winged, and
the water species, can be divided again into subspecies.
Those species, then, also will be simultaneous in point of
nature, which, belonging to the same genus, are dis
tinguished each from each by one and the same method of
differentiation.

? But genera are prior to species, for the sequence of their
being cannot be reversed. If there is the species water-
animal , there will be the genus animal , but granted the
being of the genus animal , it does not follow necessarily
that there will be the species water-animal .

Those things, therefore, are said to be simultaneous in
nature, the being of each of which involves that of the other,
while at the same time neither is in any way the cause of

10 the other s being ; those species, also, which are dis
tinguished each from each and opposed within the same
genus. Those things, moreover, are simultaneous in the
unqualified sense of the word which come into being at
the same time.

There are six sorts of movement : generation, destruction, 14
increase, diminution, alteration, and change of place.

15 It is evident in all but one case that all these sorts of
movement are distinct each from each. Generation is
distinct from destruction, increase and change of place from
diminution, and so on. But in the case of alteration it may
be argued that the process necessarily implies one or other

20 of the other five sorts of motion. This is not true, for we
may say that all affections, or nearly all, produce in us an
alteration which is distinct from all other sorts of motion,
for that which is affected need not suffer either increase or

CHAPTER 14 15"

diminution or any of the other sorts of motion. Thus altera
tion is a distinct sort of motion ; for, if it were not, the 25
thing altered would not only be altered, but would forth
with necessarily suffer increase or diminution or some one of
the other sorts of motion in addition ; which as a matter of
fact is not the case. Similarly that which was undergoing
the process of increase or was subject to some other sort of
motion would, if alteration were not a distinct form of motion,
necessarily be subject to alteration also. But there are
-some things which undergo increase but yet not alteration.
The square, for instance, if a gnomon is applied to it, under- 30
goes increase but not alteration, 1 and so it is with all other
figures of this sort. Alteration and increase, therefore, arc
distinct.

Speaking generally, rest is the contrary of motion. But I5 b
the different forms of motion have their own contraries in
other forms ; thus destruction is the contrary of generation,
diminution of increase, rest in a place, of change of place.
As for this last, change in the reverse direction would seem
to be most truly its contrary ; thus motion upwards is the 5
contrary of motion downwards and vice versa.

In the case of that sort of motion which yet remains, of
those that have been enumerated, it is not easy to state
what is its contrary. It appears to have no contrary,
unless one should define the contrary here also either as
rest in its quality or as change in the direction of the
contrary quality , just as we defined the contrary of change 10
of place either as rest in a place or as change in the reverse
direction. For a thing is altered when change of quality
takes place ; therefore either rest in its quality or change
in the direction of the contrary quality may be called the
contrary of this qualitative form of motion. In this way
becoming white is the contrary of becoming black ; there is 15
alteration in the contrary direction, since a change of a
qualitative nature takes place.

15 The term to have is used in various senses. In the
first place it is used with reference to habit or disposition or

1 As in the figure p 1. the square remains a square, though in
creased in area by the addition of the gnomon.

I5 b CATEGORIAE

any other quality, for we are said to have a piece of know
ledge or a virtue. Then, again, it has reference to quantity,

20 as. for instance, in the case of a man s height ; for he is
said to have a height of three cubits or four cubits. It is
used, moreover, with regard to apparel, a man being said to
have a coat or tunic ; or in respect of something which
we have on a part of ourselves, as a ring on the hand : or in
respect of something which is a part of us. as hand or foot.
The term refers also to content, as in the case of a vessel
and wheat, or of a jar and wine ; a jar is said to have

25 wine, and a corn-measure wheat. The expression in such
cases has reference to content. Or it refers to that which
has been acquired ; we are said to have a house or a field.
A man is also said to have a wife, and a wife a husband,
and this appears to be the most remote meaning of the

30 term, for by the use of it we mean simply that the husband
lives with the wife.

Other senses of the word might perhaps be found, but the
most ordinary ones have all been enumerated.

DE INTERPRETATIONS

TABLE OF CONTENTS

Ch. 1. (i) The spoken word is a symbol of thought.

(2) Isolated thoughts or expressions are neither true nor false.

(3) Truth and falsehood are only attributable to certain com

binations of thoughts or of words.

Ch. 2. (i) Definition of a noun.

(2) Simple and composite nouns.

(3) Indefinite nouns.

(4) Cases of a noun.

Ch. 3. (i) Definition of a verb.

(2) Indefinite verbs.

(3) Tenses of a verb.

(4) Verbal nouns and adjectives.

Ch. 4. Definition of a sentence.

Ch. 5. Simple and compound propositions.

Ch. 6. Contradictory propositions.

Ch. 7. (i) Universal, indefinite, and particular affirmations and
denials.

(2) Contrary as opposed to contradictory propositions.

(3) In contrary propositions, of which the subject is universal

or particular, the truth of the one proposition implies the
falsity of the other, but this is not the case in indefinite
propositions.

Ch. 8. Definition of single propositions.

Ch. 9. Propositions which refer to present or past time must be
either true or false : propositions which refer to future time must
be either true or false, but it is not determined which must be true
and which false.

Ch. 10. (i) Diagrammatic arrangement of pairs of affirmations and
denials, (a) without the complement] of the verb to be , (b) with
the complement of the verb to be , (c) with an indefinite noun for
subject.

(2) The right position of the negative.

(3) Contraries can never both be true, but subcontraries may both

be true.

E 2

TABLE OF CONTENTS

(4) In particular propositions, if the affirmative is false, the contrary
is true ; in universal propositions, if the affirmative is false, the
contradictory is true.

(5) Propositions consisting of an indefinite noun and an indefinite
verb are not denials.

(6) The relation to other propositions of those which have an indefi

nite noun as subject.

(7) The transposition of nouns and verbs makes no difference to the

sense of the proposition.

Ch. 11. (i) Some seemingly simple propositions are really compound.

(2) Similarly some dialectical questions are really compound.

(3) The nature of a dialectical question.

(4) When two simple propositions having the same subject are true,

it is not necessarily the case that the proposition resulting from
the combination of the predicates is true.

(5) A plurality of predicates which individually belong to the same

subject can only be combined to form a simple proposition when
they are essentially predicable of the subject, and when one is
not implicit in another.

(6) A compound predicate cannot be resolved into simple predicates

when the compound predicate has within it a contradiction in
terms, or when one of the predicates is used in a secondary sense.

Ch. 12. (i) Propositions concerning possibility, impossibility, contin
gency, and necessity.
(2) Determination of the proper contradictories of such propositions.

Ch. 13. (i) Scheme to show the relation subsisting between such
propositions.

(2) Illogical character of this scheme proved.

(3) Revised scheme.

(4) That which is said to be possible may be (a] always actual,

(b) sometimes actual and sometimes not, (c) never actual.

Ch. 14. Discussion as to whether a contrary affirmation or a denial
is the proper [contrary of an affirmation, either universal or
particular.

DE INTERPRETATIONS

1 FIRST we must define the terms noun and verb , then i6 a
the terms f denial and affirmation , then proposition and

sentence .

Spoken words are the symbols of mental experience and
written words are the symbols of spoken words. Just as 5
all men have not the same writing, so all men have not the
same speech sounds, but the mental experiences, which
these directly symbolize, are the same for all, as also are
those things of which our experiences are the images. This
matter has, however, been discussed in my treatise about
the soul, for it belongs to an investigation distinct from
that which lies before us. 1

As there are in the mind thoughts which do not involve
truth or falsity, and also those which must be either true or 10
false, so it is in speech. For truth and falsity imply com
bination and separation. Nouns and verbs, provided no
thing is added, are like thoughts without combination or
separation; man and white , as isolated terms, are not 15
yet either true or false. In proof of this, consider the word
goat-stag . It has significance, but there is no truth or
falsity about it, unless is or is not is added, either in the
present or in some other tense.

2 By a noun we mean a sound significant by convention,
which has no reference to time, and of which no part is ao
significant apart from the rest. In the noun Fairsteed ,
the part steed has no significance in and by itself, as in
the phrase fair steed . Yet there is a difference between
simple and composite nouns ; for in the former the part

is in no way significant, in the latter it contributes to the 25
meaning of the whole, although it has not an independent

1 Great difficulty has been found in discovering any passage of the
De Anima to which this can refer. Maier is probably right in holding
that this sentence should come after the next two (after dX?#fs-, 1. 13),
and refers to De An. 43o a 26-8.

i6 a DE INTERPRETATIONS

meaning. Thus in the word pirate-boat the word boat
has no meaning except as part of the whole word-. 1

The limitation by convention was introduced because
nothing is by nature a noun or name it is only so when
it becomes a symbol ; inarticulate sounds, such as those
which brutes produce, are significant, yet none of these
constitutes a noun.

9,0 The expression not-man is not a noun. There is in
deed no recognized term by which we may denote such an
expression, for it is not a sentence or a denial. Let it then
be called an indefinite noun. 2

The expressions of Philo , to Philo , and so on, con-

l6 b stitute not nouns, but cases of a noun. The definition of

these cases of a noun is in other respects the same as that

of the noun proper, but, when coupled with is , was , or

will be , they do not, as they are, form a proposition either

true or false, and this the noun proper always does, under

^these conditions. Take the words of Philo is or of Philo

is not ; these words do not, as they stand, form either

5 a true or a false proposition.

A verb is that which, in addition to its proper meaning, 3
carries with it the notion of time. No part of it has any
independent meaning, and it is a sign of something said
of something else.

I will explain what I mean by saying that it carries with
it the notion of time. Health is a noun, but is healthy
is a verb ; for besides its proper meaning it indicates the
present existence of the state in question.
10 Moreover, a verb is always a sign of something said of
something else, i. e. of something either predicable of or
present in some other thing.

Such expressions as is not-healthy , is not-ill , I do not
describe as verbs ; for though they carry the additional
note of time, and always form a predicate, there is no
specified name for this variety ; but let them be called

1 i.e. as in the case of a chemical compound, so in that of compound
words, the elements, being amalgamated into one whole, cease to
have their own particular character and significance.

2 Omit on . . . fir/ wrot, 11. 32, 33, with A, B, and Waitz. These
words have probably been introduced from b 15.

CHAPTER 3 i6 b

indefinite verbs, since they apply equally well to that which 15
exists and to that which does not.

Similarly he was healthy , he will be healthy , are not
verbs, but tenses of a verb ; the difference lies in the fact
that the verb indicates present time, while the tenses of the
verb indicate those times which lie outside the present.

Verbs in and by themselves are substantival and have
significance, for he who uses such expressions arrests the 20
hearer s mind, and fixes his attention ; but they do not,
as they stand, express any judgement, either positive or
negative. For neither are to be and not to be and the
participle being significant of any fact, 1 unless something
is added ; for they do not themselves indicate anything, but
imply a copulation, of which we cannot form a conception a 5
apart from the things coupled.

4 A sentence is a significant portion of speech, 2 some parts
of which have an independent meaning, that is to say, as an
utterance, though not as the expression of any positive
judgement. 3 Let me explain. The word human has
meaning, but does not constitute a proposition, either posi
tive or negative. It is only when other words are added
that the whole will form an affirmation or denial. But if 3
we separate one syllable of the word human from the
other, it has no meaning ; similarly in the word mouse ,
the part -ouse has no meaning in itself, but is merely
a sound. In composite words, indeed, the parts contribute
to the meaning of the whole ; yet, as has been pointed out, 4
they have not an independent meaning.

Every sentence has meaning, not as being the natural I7 a
means by which a physical faculty is realized, but, as we
have said, by convention. Yet every sentence is not a pro
position ; only such are propositions as have in them either
truth or falsity. Thus a prayer is a sentence, but is neither
true nor false.

1 The words to be and not to be are here regarded in their
strictly copulative sense.

2 Omit Kara ffwdrjKrjv in 1. 26 with B, C, Amm., Boeth., and Waitz.
? Omit r) dir6<pa<ns in 1. 28 with B, C, Amm., and Waitz.

4 Cf. l6 a 22-26.

I7 a DE INTERPRETATIONE

5 Let us therefore dismiss all other types of sentence but
the proposition, for this last concerns our present inquiry,
whereas the investigation of the others belongs rather to the
study of rhetoric or of poetry. 1

The first class of simple propositions is the simple affirma- 5
tion, the next, the simple denial ; all others are only one by
conjunction.

10 Every proposition must contain a verb or the tense of
a verb. The phrase which defines the species man , if no
verb in present, past, or future time be added, is not a pro
position. It may be asked how the expression a footed
animal with two feet can be called single ; for it is not the
circumstance that the words follow in unbroken succession
that effects the unity. This inquiry, however, finds its
place in an investigation foreign to that before us. 2

JS We call those propositions single which indicate a single
fact, or the conjunction of the parts of which results in
unity : those propositions, on the other hand, are separate
and many in number, which indicate many facts, or whose
parts have no conjunction.

Let us, moreover, consent to call a noun or a verb an
expression only, and not a proposition, since it is not
possible for a man to speak in this way when he is express
ing something, in such a way as to make a statement,
whether his utterance is an answer to a question or an act
of his own initiation.

20 To return : of propositions one kind is simple, i. e. that
which asserts or denies something of something, the other
composite, i.e. that which is compounded of simple proposi
tions. A simple proposition is a statement, with meaning,
as to the presence of something in a subject or its absence,
in the present, past, or future, according to the divisions
of time.

2 5 An affirmation is a positive assertion of something about 6
something, a denial a negative assertion.

1 Ci.Poet. i456 b ii.

2 Cf. Met. Z. 12, H.6. Read nv . . . t orni 1, 14 in brackets, with a
comma following.

CHAPTER 6 17*

Now it is possible both to affirm and to deny the presence
of something which is present or of something which is not,
and since these same affirmations and denials are possible
with reference to those times which lie outside the present,
it would be possible to contradict any affirmation or denial. 30
Thus it is plain that every affirmation has an opposite
denial, and similarly every denial an opposite affirmation.

We will call such a pair of propositions a pair of contra
dictories. Those positive and negative propositions are
said to be contradictory which have the same subject and
predicate. The identity of subject and of predicate must 35
not be equivocal . Indeed there are definitive qualifica
tions besides this, which we make to meet the casuistries
of sophists.

7 Some things are universal, others individual. By the
term universal I mean that which is of such a nature as to
be predicated of many subjects, by individual that which
is not thus predicated. Thus man is a universal, Callias 40
an individual.

Our propositions necessarily sometimes concern a uni- ij b
versal subject, sometimes an individual.

If, then, a man states a positive and a negative proposi
tion of universal character with regard to a universal,
these two propositions are contrary . By the expression 5
1 a proposition of universal character with regard to a uni
versal , such propositions as every man is white , no
man is white are meant. When, on the other hand, the
positive and negative propositions, though they have regard
to a universal, are yet not of universal character, they will
not be contrary, albeit the meaning intended is sometimes
contrary. 1 As instances of propositions made with regard
to a universal, but not of universal character, we may take
the propositions man is white , man is not white . Man 10
is a universal, but the proposition is not made as of
universal character ; for the word every does not make
the subject a universal, but rather gives the proposition a

1 Read a comma after fKaa-rov 1. i, a colon after Znao-rov 1. 3, and
place Xe yw . . . ovdels av6pa>-nos \evKos, 11. 5, 6, in brackets, followed by
a colon. Bonitz has thus cleared up the construction of the sentence.

,b

i? D DE INTERPRETATIONS

universal character. If, however, both predicate and sub
ject are distributed, the proposition thus constituted is
contrary to truth ; no affirmation will, under such circum-
15 stances, be true. The proposition every man is every
animal is an example of this type.

An affirmation is opposed to a denial in the sense which
I denote by the term contradictory , when, while the
subject remains the same, the affirmation is of universal
character and the denial is not. The affirmation every
man is white is the contradictory of the denial not every
man is white , or again, the proposition no man is white
is the contradictory of the proposition some men are white . 1
20 But propositions are opposed as contraries when both the
affirmation and the denial are universal, as in the sentences
every man is white , no man is white , every man is
just , no man is just .

We see that in a pair of this sort both propositions
cannot be true, but the contradictories of a pair of contraries
can sometimes both be true with reference to the same
25 subject ; for instance not every man is white and some
men are white are both true. Of such corresponding
positive and negative propositions as refer to universals and
have a universal character, 2 one must be true and the other
false. This is the case also when the reference is to in
dividuals, as in the propositions Socrates is white , Socrates
is not white .

When, on the other hand, the reference is to universals,
but the propositions are not universal, it is not always the
30 case that one is true and the other false, for it is possible to
state truly that man is white and that man is not white and
that man is beautiful and that man is not beautiful ; for if a
man is deformed he is the reverse of beautiful, also if he is
progressing towards beauty he is not yet beautiful.

This statement might seem at first sight to carry with it

1 A contraries E

Every man is white = A"!

No man is white = E I according to
Some men are white = I f the usual log-
Not every man is white = Oj lcal foniiul a-

- Strictly one of which has a universal character .

CHAPTER 7 I7 b

a contradiction, owing to the fact that the proposition man 35
is not white appears to be equivalent to the proposition
no man is white . This, however, is not the case, nor are
they necessarily at the same time true or false.

It is evident also that the denial corresponding to a single
affirmation is itself single ; for the denial must deny just
that which the affirmation affirms concerning the same
subject, and must correspond with the affirmation both in
the universal or particular character of the subject and i8 a
in the distributed or undistributed sense in which it is
understood.

For instance, the affirmation Socrates is white has its
proper denial in the proposition c Socrates is not white .
If anything else be negatively predicated of the subject or
if anything else be the subject though the predicate remain
the same, the denial will not be the denial proper to that
affirmation, but one that is distinct.

The denial proper to the affirmation every man is white
is not every man is white ; that proper to the affirmation 5
some men are white is no man is white , while that
proper to the affirmation man is white is man is not
white .

We have shown further that a single denial is contradic
torily opposite to a single affirmation and we have explained
which these are ; we have also stated that contrary are
distinct from contradictory propositions and which the
contrary are ; also that with regard to a pair of opposite 10
propositions it is not always the case that one is true and
the other false. 1 We have pointed out, moreover, what the
reason of this is and under what circumstances the truth of
the one involves the falsity of the other.

8 An affirmation or denial is single, if it indicates some one
fact about some one subject ; it matters not whether the
subject is universal and whether the statement has a
universal character, or whether this is not so. Such single

1 By the words d\r)6!]s fj ^evBrjs, as Waitz explains, Aristotle means
avrtyao-is, n]v fj.(v dei trover a d\T)6f], T!]V de \l/fv8ij. The subcontraries,
that is, contradictories of the contraries, may both be true. Cf.

i8 a DE INTERPRETATIONE

propositions are : every man is white , not every man is
1 5 white ; man is white , man is not white ; no man
is white , some men are white ; provided the word white
has one meaning. If, on the other hand, one word has two
meanings which do not combine to form one, the affirma
tion is not single. 1 For instance, if a man should establish
the symbol garment as significant both of a horse and of
20 a man, the proposition garment is white would not be a
single affirmation, nor its opposite a single denial. For it is
equivalent to the proposition horse and man are white ,
which, again, is equivalent to the two propositions horse is
white , man is white . If, then, these two propositions
have more than a single significance, and do not form
a single proposition, it is plain that the first proposition
25 either has more than one significance or else has none; for a
particular man is not a horse.

This, then, is another instance of those propositions of
which both the positive and the negative forms may be true
or false simultaneously.

In the case of that which is or which has taken place, 9
propositions, whether positive or negative, must be true or
false. Again, in the case of a pair of contradictories, either
when the subject is universal and the propositions are of a
3 universal character, 2 or when it is individual, as has been
said, 3 one of the two must be true and the other false ;
whereas when the subject is universal, but the propositions
are not of a universal character, there is no such necessity.
We have discussed this type also in a previous chapter. 4

When the subject, however, is individual, and that which
is predicated of it relates to the future, the case is altered. 5

1 Omit ov&t dir6<f>a<ns pia in 1. 19 with B, Amm., and Waitz.

2 Aristotle means that if you start with a universal proposition (A
or E) and take the corresponding negation (by which he means O or
I), one must be true and the other false.

3 Cf. 17^26-9. " Cf. I7 b 29-37.

5 In this chapter, as Pacius points out, Aristotle deals with four
possible theories as to contradictory propositions concerning the
future : (i) that both are true ; this he refutes, 18*34-9, by implication ;
(2) that one is true and the other false determinately ; this he deals
with at length; (3) that both are false ; this he dismisses, l8 b 16-25 ;
(4) that one is true and the other false, indeterminately ; this last he
commends, I9 a 23~ b 4.

CHAPTER 9 i8 a

For if all propositions whether positive or negative l arc
either true or false, then any given predicate must either 35
belong to the subject or not, so that if one man affirms that
an event of a given character will take place and another
denies it, it is plain that the statement of the one will
correspond with reality and that of the other will not.
For the predicate cannot both belong and not belong to
the subject at one and the same time with regard to the
future.

Thus, if it is true to say that a thing is white, it must i8 b
necessarily be white ; if the reverse proposition is true, it
will of necessity not be white. Again, if it is white, the
proposition stating that it is white was true ; if it is not
white, the proposition to the opposite effect was true. And
if it is not white, the man who states that it is is making
a false statement ; and if the man who states that it is white
is making a false statement, it follows that it is not white.
It may therefore be argued that it is necessary that affirma
tions or denials must be either true or false.

Now if this be so, nothing is or takes place fortuitously, 5
either in the present or in the future, and there are no real
alternatives ; everything takes place of necessity and is
fixed. For either he that affirms that it will take place or
he that denies this is in correspondence with fact, whereas
if things did not take place of necessity, an event might
just as easily not happen as happen ; for the meaning of
the word fortuitous with regard to present or future events
is that reality is so constituted that it may issue in either of
two opposite directions.

Again, if a thing is white now, it was true before to say 10
that it would be white, so that of anything that has taken
place it was always true to say it is or it will be . But
if it was always true to say that a thing is or will be, it is
not possible that it should not be or not be about to be,
and when a thing cannot not come to be, it is impossible

1 In i8 a 34, 38 Bekker reads Kai, but it seems better to adhere to the
reading fj, which is that of B, C, Amm., and Waitz, since the phrase
occurs in a 29, 4 in the same sense: i.e. propositions, whether
positive or negative.

i8 b DE INTERPRETATION

that it should not come to be, and when it is impossible
that it should not come to be, it must come to be. All,

15 then, that is about to be must of necessity take place. It
results from this that nothing is uncertain or fortuitous, for
if it were fortuitous it would not be necessary.

Again, to say that neither the affirmation nor the denial
is true, maintaining, let us say, that an event neither will
take place nor will not take place, is to take up a position
impossible to defend. In the first place, though facts should
prove the one proposition false, the opposite would still be

20 untrue. 1 Secondly, if it was true to say that a thing was
both white and large, both these qualities must necessarily
belong to it ; and if they will belong to it the next day, 2
they must necessarily belong to it the next day. 3 But if an
event is neither to take place nor not to take place the next
day, the element of chance will be eliminated. 4 For ex
ample, it would be necessary that a sea-fight should neither

25 take place nor fail to take place on the next day.

These awkward results and others of the same kind
follow, if it is an irrefragable law that of every pair of
contradictory propositions, whether they have regard to
universals and are stated as universally applicable, or whether
they have regard to individuals, one must be true and the

30 other false, and that there are no real alternatives, but that
all that is or takes place is the outcome of necessity.
There would be no need to deliberate or to take trouble,
on the supposition that if we should adopt a certain course,
a certain result would follow, while, if we did not, the result
would not follow. For a man may predict an event ten
thousand years beforehand, and another may predict the

35 reverse ; that which was truly predicted at the moment in
the past will 5 of necessity take place in the fullness of time.

1 sc. ex hypothesi: and thus the Law of Excluded Middle would
be violated .

2 Or : if it was true to say that they would belong to it ; and
below : if it was true to say that an event . . . . Possibly Pacius is
right in his contention that ci\r)df)s ?/v emtlv on should be understood
after el 8e in both cases.

3 l8 b 23 read v^dp^tiv eis avpiov with A, B, Amm., and Waitz.

4 sc. and thus this suggestion does not prove any amendment on
the first .

sc. on our hypothesis .

CHAPTER 9 i8 b

Further, it makes no difference whether people have or
have not actually made the contradictory statements. For
it is manifest that the circumstances are not influenced by
the fact of an affirmation or denial on the part of anyone.
For events will not take place or fail to take place because
it was stated that they would or would not take place, nor
is this any more the case if the prediction dates back ten
thousand years or any other space of time. Wherefore, if 19*
through all time the nature of things was so constituted
that a prediction about an event was true, then through all
time it was necessary that that prediction should find fulfil
ment ; and with regard to all events, 1 circumstances have
always been such that their occurrence is a matter of
necessity. For that of which someone has said truly that
it will be, cannot fail to take place ; and of that which takes 5
place, it was always true to say that it would be.

Yet this view leads to an impossible conclusion ; for we
see that both deliberation and action are causative with
regard to the future, and that, to speak more generally, in
those things which are not continuously actual there is a
potentiality in either direction. Such things may either be 10
or not be ; events also therefore may either take place or
not take place. There are many obvious instances of this.
It is possible that this coat may be cut in half, and yet it
may not be cut in half, but wear out first. In the same way,
it is possible that it should not be cut in half; unless this 15
were so, it would not be possible that it should wear out
first. So it is therefore with all other events which possess
this kind of potentiality. It is therefore plain that it is not
of necessity that everything is or takes place ; but in some
instances there are real alternatives, in which case the
affirmation is no more true and no more false than the
denial ; while some exhibit a predisposition and general 20
tendency in one direction or the other, and yet can issue in
the opposite direction by exception. 2

Now that which is must needs be when it is, and that
which is not must needs not be when it is not. Yet it can-

1 sc. on our hypothesis .

2 Bonitz has pointed out that opd^v 1. j-ToiavTt]i> 1. 18 is paren
thetical, <f)avp6v beginning the apodosis of the main sentence.

I9 a DE INTERPRETATIONS

not be said without qualification that all existence and
non-existence is the outcome of necessity. Eor there is a

^5 difference between saying that that which is, when it is,
must needs be, and simply saying that all that is must
needs be, and similarly in the case of that which is not. In
the case, also, of two contradictory propositions this holds
good. Everything must either be or not be, whether in the
present or in the future, but it is not always possible to
distinguish and state determinately which of these alterna
tives must necessarily come about.

30 Let me illustrate. A sea-fight must either take place
to-morrow or not, but it is not necessary that it should take
place to-morrow, neither is it necessary that it should not
take place, yet it is necessary that it either should or should
not take place to-morrow. Since propositions correspond
with facts, it is evident that when in future events there is
a real alternative; and a potentiality in contrary directions,
the corresponding affirmation and denial have the same
character.

35 This is the case with regard to that which is not always
existent or not always non-existent. One of the two pro
positions in such instances must be true and the other
false, but we cannot say determinately that this or that is
false, but must leave the alternative undecided. One may
indeed be more likely to be true than the other, but it cannot
be either actually true or actually false. It is therefore
igb plain that it is not necessary that of an affirmation and a
denial one should be true and the other false. 1 For in
the case of that which exists potentially, but not actually,
the rule which applies to that which exists actually does
not hold good. The case is rather as we have indicated.

5 An affirmation is the statement of a fact with regard to 10
a subject, and this subject is either a noun or that which has
no name ; the subject and predicate in an affirmation must
each denote a single thing. I have already explained 2 what
is meant by a noun and by that which has no name ; for
I stated that the expression not-man was not a noun, in
the proper sense of the word, but an indefinite noun, denoting

1 sc. (\(frtopuTfj.f i/cos- determinately .
. 2 Cf. i6 a i9, 30.

CHAPTER 10 ig b

as it does in a certain sense a single thing. Similarly the
expression does not enjoy health is not a verb proper, but
an indefinite verb. Every affirmation, then, and every denial, 10
will consist of a noun and a verb, either definite or indefinite.

There can be no affirmation or denial without a verb ;
for the expressions is , will be , was , ( is coming to be ,
and the like are verbs according to our definition, since be
sides their specific meaning they convey the notion of time.

Thus the primary affirmation and denial are as follows :
man is , man is not . Next to these, there are the propo- 15
sitions : not-mart is , not-man is not . Again we have the
propositions : every man is , every man is not , all that
is not-man is , all that is not-man is not . The same classi
fication holds good with regard to such periods of time as lie
outside the present.

When the verb is is used as a third element in the
sentence, there can be positive and negative propositions
of two sorts. 1 Thus in the sentence man is just the verb 20
is is used as a third element, call it verb or noun, which
you will. Four propositions, 2 therefore, instead of two can
be formed with these materials. Two of the four, as
regards their affirmation and denial, correspond in their
logical sequence with the propositions which deal with a
condition of privation; 3 the other two do not correspond
with these. 4

1 Waitz argues that the use of the word Trpoo-KarqyopeZrat implies
that the verb to be is not here regarded as a copula, i.e. that the
sentence earl Sixmos avdfxoTros should be translated there is a just
man . As a matter of fact, however, when interpreted as strictly
indefinite, the proposition man is just means exactly the same as
the proposition there is a just man . An objection to Waitz s con
tention is that Aristotle expressly refuses to define the function of
tori in these propositions, but calls it 6 ropa 77 p/jpa. It is difficult to
see why it should not be defined as pr^a, if it were being used in its
independent sense. Besides this, in the form of proposition adopted
by Waitz just man is one term ; the whole therefore consists not of
three elements, but of two.

2 Four propositions, not four pairs of propositions. The objection
to Grote s rendering lies in the fact that while he translates rerrapa
here as four pairs , he makes r p-eV 8vo mean one pair (i. e. the second
pair of the first quaternion) and ra 8e Suo another single pair (i.e. the
second pair of the second quaternion, of which OVK iivOpanros is the
subject).

3 In the subjoined table to which Aristotle refers, D follows from A
and I> from C and the sequence is the same as it would be if unjust
were substituted for not-just .

4 Let c represent the proposition man is unjust and d the proposi-

DE INTERPRETATIONS

I mean that the verb is is added either to the term
2 5 just or to the term not-just , 1 and two negative proposi
tions are formed in the same way. Thus we have the four
propositions. Reference to the subjoined table will make
matters clear :

A. Affirmation. Man is just.

B. Denial. Man is not just.

D. Denial. Man is not not-just. C. Affirmation. Man is not-just.

Here is and is not are added either to just* or to not-

3 just . This then is the proper scheme for these propositions,

as has been said in the Analytics? The same rule holds

good, if the subject is distributed. Thus we have the table :

A . Affirmation. Every man is just. B . Denial. Not every man is just.

D . Denial.

Not every man is
[not-just.

C . Affirmation.

Every man is
[not-just.

35 Yet here it is not possible, in the same way as in the former
case, that the propositions joined in the table by a diagonal
line should both be true ; though under certain circumstances
this is the case. 3

We have thus set out two pairs of opposite propositions ;

tion man is not unjust . D and C correspond with d and c, A and
B do not.

1 I9 b 25-30. Waitz reads OI^PCOTTW for StKtu w and owe avQpumui for
ot> SiKcdti) and maintains that in both cases SIKCU W is understood before
uv6f)(a7ra> and that this has in some MSS. caused the easier reading
StKcu w, ou Si/ctti to supplant the true. The omission of 8iKaia> between
OL> and avdpwTTcp is obviously impossible, and there is no other way of
taking the words, should that reading be adopted. To those, however,
who consider eWi to be the copula in all these propositions, there can
be no question as to the reading, Sixain and ou diiia> being necessary
to the argument.

2 Analytica Priora, 5i b 36~52 a i7.

3 D and B may both be true.

CHAPTER 10 ig b

there are moreover two other pairs, 1 if a term be conjoined 2
with not-man , the latter forming a kind of subject. Thus :
A". Not-man is just. B". Not-man is not just.

D". Not-man is not not-just. C". Not-man is not-just.

This is an exhaustive enumeration of all the pairs of opposite 2O a
propositions that can possibly be framed. This last group
should remain distinct from those which preceded it, since
it employs as its subject the expression not-man .

When the verb is does not fit the structure of the
sentence (for instance, when the verbs walks , enjoys
health are used), that scheme applies, which applied when
the word is was added.

Thus we have the propositions: every man enjoys health , 5
every man does-not-enjoy-health , all that is not-man en
joys health , all that is not-man does-not-enjoy-health .

We must not in these propositions use the expression
not every man . The negative must be attached to the
word man , for the word every does not give to the
subject a universal significance, but implies that, as a subject,
it is distributed. This is plain from the following pairs : 10
* man enjoys health , man does not enjoy health ; not-
man enjoys health , not-man does not enjoy health .
These propositions differ from the former in being indefinite
and not universal in character. Thus the adjectives every
and no have no additional significance except that the
subject, whether in a positive or in a negative sentence, is
distributed. The rest of the sentence, therefore, will in each
case be the same. 15

Since the contrary of the proposition every animal is
just is no animal is just , it is plain that these two proposi-

1 Here 8vo must mean two pairs, whereas TCI fiev Sv<> in 1. 23 means
two propositions. This irregularity is not impossible, and the use of
the feminine here (aiTi$<rei? being understood) as opposed to the
neuter above makes all the difference.

2 Read Trpoo-Tcdevrns in 1. 38 with A, B, C, Amm., and Waitz.

F 2

20 a DK INTERPRETATIONE

tions will never both be true at the same time or with
reference to the same subject. Sometimes, however, the
contradictories of these contraries will both be true, as in
the instance before us : the propositions not every animal
is just and some animals are just are both true.

20 Further, the proposition no man is just follows from the
proposition every man is not-just and the proposition
not every man is not-just , which is the opposite of every
man is not-just , follows from the proposition some men
are just ; for if this be true, there must be some just men.
It is evident, also, that when the subject is individual, if a
question is asked and the negative answer is the true one,

25 a certain positive proposition is also true. Thus, if the
question were asked Is Socrates wise? and the negative
answer were the true one, the positive inference Then
Socrates is unwise is correct. But no such inference is
correct in the case of universals, but rather a negative
proposition. For instance, if to the question Is every man
wise ? the answer is no , the inference Then every man
is unwise is false. But under these circumstances the

30 inference Not every man is wise is correct. This last is
the contradictory, the former the contrary. 1 Negative ex
pressions, 2 which consist of an indefinite noun or predicate,
such as not-man or not-just , may seem to be denials con
taining neither noun nor verb in the proper sense of the
words. But they are not. For a denial must always be

. ,5 either true or false, and he that uses the expression not-
man , if nothing more be added, is not nearer but rather
further from making a true or a false statement than he who
uses the expression man . :J

The propositions : everything that is not man is just , and
the contradictory of this, are not equivalent to any of the
other propositions; on the other hand, the proposition
everything that is not man is not just is equivalent to the

40 proposition nothing that is not man is just .

1 sc. to that which would form the positive answer to the question .

2 ai . . . ai TiKfi^evai agrees loosely with the succeeding nn-o^acreir,
although the noun is not really applicable.

3 Presumably because the indefinite noun has less complete meaning
than the noun proper.

CHAPTER 10 20 b

The conversion of the position of subject and predicate in 2O b
a sentence involves no difference in its meaning. Thus we
say man is white and white is man V If these were not
equivalent, there would be more than one contradictory to
the same proposition, whereas it has been demonstrated 2
that each proposition has one proper contradictory and one
only. For of the proposition man is white the appropriate
contradictory is man is not white , and of the proposition 5
white is man , if its meaning be different, the contradictory
will either be white is not not-man or white is not man .
Now the former of these is the contradictory of the proposi
tion white is not-man , and the latter of these is the
contradictory of the proposition man is white ;" thus there
will be two contradictories to one proposition.

It is evident, therefore, that the inversion of the relative 10
position of subject and predicate does not affect the sense
of affirmations and denials.

II There is no unity about an affirmation or denial which,
either positively or negatively, predicates one thing of
many subjects, or many things of the same subject, unless
that which is indicated by the many is really some one
thing.

I do not apply this word one to those things which, 15
though they have a single recognized name, yet do not
combine to form a unity. Thus, man may be an animal,
and biped, and domesticated, but these three predicates
combine to form a unity. On the other hand, the predicates
white , man , and walking do not thus combine. Neither,
therefore, if these three form the subject of an affirmation,
nor if they form its predicate, is there any unity about that 20
affirmation. In both cases the unity is linguistic, but not real.

1 Aristotle has in mind the case where the inversion is purely
rhetorical, man remaining grammatical subject.

2 Cf. I7 b s8.

s Aristotle really begs the question here, when he states that white
is not man is the denial of man is white . Pacius explains that
man is not white and man is white are in exactly the same relation
each to each as white is not man and man is white , and that there
fore white is not man and man is not white are identical. This
seems fair, but is in itself sufficient to prove the point at issue at once.
The argument of the whole, therefore, is unnecessarily complicated.

2o b DE INTERPRETATIONS

If therefore the dialectical question is a request for an
answer, i. e. either for the admission of a premiss or for the
admission of one of two contradictories and the premiss is
itself always one of two contradictories the answer to such
a question as contains the above predicates cannot be a single

25 proposition. 1 For as I have explained in the Topics? the
question is not a single one, even if the answer asked for is
true.

At the same time it is plain that a question of the form
what is it ? is not a dialectical question, for a dialectical
questioner must by the form of his question give his opponent
the chance of announcing one of two alternatives, whichever
he wishes. He must therefore put the question into a more

30 definite form, and inquire, e. g., whether man has such and
such a characteristic or not.

Some combinations of predicates are such that the separate
predicates unite to form a single predicate. Let us consider
under what conditions this is and is not possible. We may
either state in two separate propositions that man is an
animal and that man is a biped, or we may combine the
two, and state that man is an animal with two feet. Similarly
we may use man and white as separate predicates, or

35 unite them into one. Yet if a man is a shoemaker and is
also good, we cannot construct a composite proposition and
say that he is a good shoemaker. For if, whenever two
separate predicates truly belong to a subject, it follows that
the predicate resulting from their combination also truly
belongs to the subject, many absurd results ensue. For
instance, a man is man and white. Therefore, if predicates
may always be combined, he is a white man. Again, if the
predicate white belongs to him, then the combination
of that predicate with the former composite predicate will
be permissible. Thus it will be right to say that he is a

1 Aristotle has shown that the affirmation which contains more than
one predicate is not single : he here proves the same about the
dialectical question of the same type, and its answer. Incidentally he
refutes the argument that the reason why the question and answer are
not single lies in the fact that the question is alternative in form,
pointing out that a dialectical question is always implicitly alternative
even if the second part is not expressed.

a Topica, viii. 7; Soph. El. i69 a 6, 175^39 sq^-j l8l a 36 sqq.

CHAPTER ii 2 o b

white white man and so on indefinitely. Or, again, we may 40
combine the predicates musical , white , and walking ,
and these may be combined many times. 1 Similarly we 2i a
may say that Socrates is Socrates and a man, and that
therefore he is the man Socrates, or that Socrates is a man
and a biped, and that therefore he is a two-footed man. 2
Thus it is manifest that if a man states unconditionally that 5
predicates can always be combined, many absurd con
sequences ensue.

We will now explain what ought to be laid down.

Those predicates, and terms forming the subject of pre
dication, which are accidental either to the same subject
or to one another, do not combine to form a unity. Take 10
the proposition man is white of complexion and musical .
Whiteness and being musical do not coalesce to form a unity,
for they belong only accidentally to the same subject. Nor
yet, if it were true to say that that which is white is musical,
would the terms musical and white form a unity, for it
is only incidentally that that which is musical is white ; the
combination of the two will, therefore, not form a unity.

Thus, again, whereas, if a man is both good and a shoe
maker, we cannot combine the two propositions and say
simply that he is a good shoemaker, we are, at the same
time, able to combine the predicates animal and biped
and say that a man is an animal with two feet, for these 15
predicates are not accidental.

Those predicates, again, cannot form a unity, of which
the one is implicit in the other : thus we cannot combine
the predicate white again and again with that which
already contains the notion white , nor is it right to call a
man an animal-man or a two-footed man; for the notions
animal and biped are implicit in the word man . On
the other hand, it is possible to predicate a term simply of

1 Omit ds unfipov in 1. 2 with B, C, Amm., and Waitz.

2 2i a 3, 4. The reading of A, B, Amm.: i.e. en 6 ^axpdrrjs

ScuKpaTr)! KOL <u #peo7ros, KOL ScoKpurr;? avdp&Tros KOI el avOpwros Kal fiiTrouy,
KOI avdpuiTos diTrovs, is here chosen, since that of C, which Bekker
adopts, does not seem to give any satisfactory sense, and is not
intrinsically more likely to be correct.

3 Omit 6 in 1. 14 with C.

2i a DE INTERPRETATIONS

any one instance, and to say that some one particular man
20 is a man or that some one white man is a white man.

Yet this is not always possible : indeed, when in the
adjunct there is some opposite which involves a contradiction,
the predication of the simple term is impossible. Thus it is
not right to call a dead man a man. When, however, this
is not the case, it is not impossible.

Yet the facts of the case might rather be stated thus :
when some such opposite elements are present, resolution is
25 never possible, but when they are not present, resolution is
nevertheless not always possible. Take the proposition
Homer is so-and-so , say a poet ; does it follow that
Homer is, or does it not? The verb is is here used of
Homer only incidentally, the proposition being that Homer
is a poet, not that he is, in the independent sense of the word.
Thus, in the case of those predications which have within
30 them no contradiction when the nouns are expanded into
definitions, and wherein the predicates belong to the subject 1
in their own proper sense and not in any indirect way, the
individual may be the subject of the simple propositions as
well as of the composite. But in the case of that which is
not, it is not true to say that because it is the object of
opinion, it is ; for the opinion held about it is that it is not,
not that it is.

As these distinctions have been made, we must consider 12
35 the mutual relation of those affirmations and denials which
assert or deny possibility or contingency, impossibility or
necessity : for the subject is not without difficulty.

We admit that of composite expressions those are
contradictory each to each which have the verb to be in
its positive and negative form respectively. Thus the
contradictory of the proposition man is is man is not ,
2i b not not-man is , and the contradictory of man is white is
man is not white , not man is not-white . For otherwise,
since either the positive or the negative proposition is true
of any subject, it will turn out true to say that a piece of
wood is a man that is not white. 2

1 Reading K.arr]yope iraL in 1. 30.

2 It is plain that if two propositions are contradictory, either one or

CHAPTER 12 2i b

Now if this is the case, in those propositions which do 5
not contain the verb to be the verb which takes its place
will exercise the same function. Thus the contradictory of
man walks is man does not walk , not not-man walks ;
for to say man walks is merely equivalent to saying man
is walking .

If then this rule is universal, the contradictory of it may 10
be is it may not be , not it cannot be . 1

Now it appears that the same thing both may and may
not be ; for instance, everything that may be cut or may
walk may also escape cutting and refrain from walking ; and
the reason is that those things that have potentiality in this
sense are not always actual. In such cases, both the positive 15
and the negative propositions will be true ; for that which is
capable of walking or of being seen has also a potentiality
in the opposite direction.

But since it is impossible that contradictory propositions
should both be true of the same subject, it follows that it
may not be is not the contradictory of it may be . For
it is a logical consequence of what we have said, either that
the same predicate can be both applicable and inapplicable
to one and the same subject at the same time, or that it is 20
not by the addition of the verbs be and not be , respect
ively, that positive and negative propositions are formed.
If the former of these alternatives must be rejected, we
must choose the latter.

The contradictory, then, of it may be is it cannot be .
The same rule applies to the proposition it is contingent
that it should be ; the contradictory of this is it is not
contingent that it should be . The similar propositions, 25
such as it is necessary and it is impossible , may be dealt
with in the same manner. For it comes about that just as
in the former instances the verbs is and is not were
added to the subject-matter of the sentence white and
man , so here that it should be and that it should not be

the other predicate must belong to any subject. Thus, since the pro
position a piece of wood is a white man is not true, the contradictory
of this proposition must be true.

1 fl . . . ftwarbv tlvai a 38- b 12 forms one sentence, . . . avdpamov
b 3-5 and oL 8ey . . . fia8iovTa flvat b 9, lo being parentheses within it.
So Bonitz.

2i b DE INTERPRETATION

30 are the subject-matter and is possible , is contingent , are
added. These indicate that a certain thing is or is not
possible, just as in the former instances is and is not 1
indicated that certain things were or were not the case. 1

The contradictory, then, of it may not be is not it
cannot be , but it cannot not be , and the contradictory of
it may be is not it may not be , but it cannot be .
35 Thus the propositions it may be and it may not be
appear each to imply the other : for, since these two proposi
tions are not contradictory, the same thing both may and may
not be. But the propositions < it may be and it cannot
be can never be true of the same subject at the same time.
22 a for they are contradictory. Nor can the propositions it
may not be and it cannot not be be at once true of the
same subject.

The propositions which have to do with necessity are
governed by the same principle. The contradictory of it is
necessary that it should be is not it is necessary that it
should not be , but l it is not necessary that it should be ,
5 and the contradictory of it is necessary that it should not
be is it is not necessary that it should not be .

Again, the contradictory of it is impossible that it should
be is not it is impossible that it should not be but it is
not impossible that it should be , and the contradictory of
1 it is impossible that it should not be is it is not impossible
that it should not be .

To generalize, we must, as has been stated, define the

clauses that it should be and that it should not be as the

subject-matter of the propositions, and in making these terms -

10 into affirmations and denials we must combine them with

that it should be and that it should not be respectively.

We must consider the following pairs as contradictory

propositions :

It may be. It cannot be.

It is contingent. It is not contingent.
It is impossible. It is not impossible.
It is necessary. It is not necessary.
It is true. It is not true.

1 Omit the comma in 1. 31 with Maier.

2 sc. possible, contingent, impossible, necessary.

CHAPTER 13 22 B

13 Logical sequences follow in due course when we have
arranged the propositions thus. From the proposition it 15
may be l it follows that it is contingent, and the relation is
reciprocal. It follows also that it is not impossible and not
necessary.

From the proposition it may not be or it is contingent
that it should not be it follows that it is not necessary that
it should not be and that it is not impossible that it should
not be. From the proposition it cannot be or it is not
contingent it follows that it is necessary that it should not
be and that ft is impossible that it should be. From the 20
proposition it cannot not be or it is not contingent that
it should not be it follows that it is necessary that it should
be and that it is impossible that it should not be.

Let us consider these statements by the help of a table :
A. It may be. E. It cannot be.

It is contingent. It is not contingent. 25

It is not impossible that it It is impossible that it

should be. should be.

It is not necessary that it It is necessary that it

should be. should not be. 2

C. It may not be. D. It cannot not be.

It is contingent that it It is not contingent that it

should not be. should not be.

It is not impossible that It is impossible that it 3

it should not be. should not be.

It is not necessary that It is necessary that it

it should not be. should be.

Now the propositions it is impossible that it should be
and it is not impossible that it should be are consequent
upon the propositions it may be , it is contingent , and it
cannot be , it is not contingent , the contradictories upon
the contradictories. But there is inversion. The negative

1 Read Swarw in a 15, 17, 19, 20, 34, 36, b 18, 24, and eVSexo/^eVw in
a 17, 19, 21, with A, B, and, in most cases, C.

2 Aristotle here gives the wrong denial to OVK uvnyKaiov emu. Pacius
explains that he is here following former logicians, in order to expose
their false reasoning. In 22 b 10 he points out the flaw and in 22 b 22
gives the correct table, exchanging the position of OVK avayKaiov
and OVK avayKaiov p.fj flvai.

22 a DE INTERPRETATIONS

of the proposition it is impossible is consequent upon the
35 proposition it may be and the corresponding positive in
the first case upon the negative in the second. For it is
impossible is a positive proposition and it is not impos
sible is negative.

We must investigate the relation subsisting between these
propositions and those \vhich predicate necessity. That
there is a distinction is clear. In this case, contrary proposi
tions follow respectively from contradictory propositions,
and the contradictory propositions belong to separate
sequences. For the proposition it is not necessary that
it should be is not the negative of it is necessary that it
22 should not be , for both these propositions may be true of
the same subject ; for when it is necessary that a thing should
not be, it is not necessary that it should be. The reason
why the propositions predicating necessity do not follow in
the same kind of sequence as the rest, lies in the fact that
the proposition it is impossible is equivalent, when used
with a contrary subject, to the proposition it is necessary .
5 For when it is impossible that a thing should be, it is
necessary, not that it should be, but that it should not be,
and when it is impossible that a thing should not be, it is
necessary that it should be. Thus, if the propositions
predicating impossibility or non-impossibility follow with
out change of subject from those predicating possibility or
non-possibility, those predicating necessity must follow with
the contrary subject ; for the propositions it is impossible
and it is necessary are not equivalent, but, as has been
said, inversely connected.

10 Yet perhaps it is impossible that the contradictory pro
positions predicating necessity should be thus arranged.
For when it is necessary that a thing should be, it is possible
that it should be. (For if not, the opposite follows, since
one or the other must follow ; so, if it is not possible, it is
impossible, and it is thus impossible that a thing should be,
which must necessarily be ; which is absurd.)

Yet from the proposition it may be it follows that it is
15 not impossible, and from that it follows that it is not neces
sary ; it comes about therefore that the thing which must

CHAPTER 13 22*

necessarily be need not be ; which is absurd. But again,
the proposition it is necessary that it should be does not
follow from the proposition it may be , nor does the proposi
tion it is necessary that it should not be . For the pro
position it may be implies a twofold possibility, while, if
either of the two former propositions is true, the twofold
possibility vanishes. For if a thing may be. it may also not 20
be, but if it is necessary that it should be or that it should
not be, one of the two alternatives will be excluded. It
remains, therefore, that the proposition it is not necessary
that it should not be follows from the proposition it may
be . For this is true also of that which must neces
sarily be.

Moreover the proposition it is not necessary that it
should not be is the contradictory of that which follows
from the proposition it cannot be ; for it cannot be 25
is followed by it is impossible that it should be and by
it is necessary that it should not be , and the contradictory
of this is the proposition it is not necessary that it should
not be . Thus in this case also contradictory propositions
follow contradictory in the way indicated, and no logical
impossibilities occur when they are thus arranged.

It may be questioned whether the proposition it may be
follows from the proposition it is necessary that it should
be . If not, the contradictory must follow, namely that it 3
cannot be, or, if a man should maintain that this is not the
contradictory, then the proposition it may not be .

Now both of these are false of that which necessarily is.
At the same time, it is thought that if a thing may be cut
it may also not be cut, if a thing may be it may also not
be, and thus it would follow that a thing which must
necessarily be may possibly not be ; which is false. It is 35
evident, then, that it is not always the case that that
which may be or may walk possesses also a potentiality in
the other direction. There are exceptions. In the first
place we must except those things which possess a poten
tiality not in accordance with a rational principle, as fire
possesses the potentiality of giving out heat, that is, an
irrational capacity. Those potentialities which involve a

22 b DE INTERPRETATIONS

rational principle are potentialities of more than one result,
23 a that is, of contrary results ; those that are irrational are not
always thus constituted. As I have said, fire cannot both
heat and not heat, neither has anything that is always
actual any twofold potentiality. Yet some 1 even of those
potentialities which are irrational admit of opposite results.
5 However, thus much has been said to emphasize the truth
that it is not every potentiality which admits of opposite
results, even where the word is used always in the same
sense.

But in some cases the word is used equivocally. For the
term possible is ambiguous, being used in the one case
with reference to facts, to that which is actualized, as when
a man is said to find walking possible because he is actually
walking, and generally when a capacity is predicated
10 because it is actually realized ; in the other case, with
reference to a state in which realization is conditionally
practicable, as when a man is said to find walking possible
because under certain conditions he would walk. This last
sort of potentiality belongs only to that which can be in
motion, the former can exist also in the case of that which
has not this power. Both of that which is walking and is
actual, and of that which has the capacity though not
necessarily realized, it is true to say that it is not impossible
that it should walk (or, in the other case, that it should be),
15 but while we cannot predicate this latter kind of potentiality
of that which is necessary in the unqualified sense of the
word, we can predicate the former.

Our conclusion, then, is this : that since the universal is
consequent upon the particular, that which is necessary
is also possible, though not in every sense in which the
word may be used. 2

We may perhaps state that necessity and its absence are

1 Aristotle alludes to the twofold potentiality possessed by inanimate
things, in virtue of which they may be either affected or not affected,
as, e.g., a cloak may be either cut or not cut.

2 Just as, if the species may be predicated of a certain thing, the
genus or universal may also be predicated, so, if necessity is predicated
of an event, possibility may also be predicated, provided that sense of
the word which includes the negative possibility be rejected.

CHAPTER 13 23"

the initial principles of existence and non-existence, and
that all else must be regarded as posterior to these. 20

It is plain from what has been said that that which is
of necessity is actual. Thus, if that which is eternal is prior,
actuality also is prior to potentiality. 1 Some things are
actualities without potentiality, namely, the primary sub
stances ; 2 a second class consists of those things which are
actual but also potential, whose actuality is in nature prior
to their potentiality, though posterior in time ; 3 a third 25
class comprises those things which are never actualized, but
are pure potentialities. 4

14 The question arises whether an affirmation finds its
contrary in a denial or in another affirmation ; whether the
proposition every man is just finds its contrary in the pro
position no man is just , or in the proposition every man is
unjust . Take the propositions Callias is just , Callias 30
is not just , Callias is unjust ; we have to discover which
of these form contraries.

Now if the spoken word corresponds with the judgement
of the mind, and if, in thought, that judgement is the con
trary of another, which pronounces a contrary fact, in the
way, for instance, in which the judgement every man is
just pronounces a contrary to that pronounced by the
judgement every man is unjust , the same must needs hold 3 -
good with regard to spoken affirmations.

But if, in thought, it is not the judgement which pro
nounces a contrary fact that is the contrary of another,
then one affirmation will not find its contrary in another,
but rather in the corresponding denial. We must therefore
consider which true judgement is the contrary of the false,
that which forms the denial of the false judgement or that
which affirms the contrary fact.

1 The argument is this : the necessary is actual,

the necessary is also a first principle, i.e. eternal,
that which is eternal is prior,
. . the actual is prior to the potential.

2 i.e. God and the intelligences that move the heavenly bodies.
Cf. Met. A. 6 and 6. 1050 3-19.

3 i.e. TO ffrdaprd. Cf. Met. e. iO49 b 10-1050* 23.

4 Aristotle means such things as a maximal number, a minimal
magnitude, or a void; cf. Met. 0. 1048 9-17.

23 a DE INTERPRETATIONE

40 Let me illustrate. There is a true judgement concerning
that which is good, that it is good ; another, a false judge
ment, that it is not good ; and a third, which is distinct,
23 b that it is bad. Which of these two is contrary to the true ?
And if they are one and the same, which mode of expres
sion forms the contrary ?

It is an error to suppose that judgements are to be defined
as contrary in virtue of the fact that they have contrary
subjects ; for the judgement concerning a good thing, that
it is good, and that concerning a bad thing, that it is bad,
5 may be one and the same, and whether they are so or not,
they both represent the truth. Yet the subjects here are
contrary. But judgements are not contrary because they have
contrary subjects, but because they are to the contrary effect.
Now if we take the judgement that that which is good is
good, and another that it is not good, and if there are at
the same time other attributes, which do not and cannot
belong to the good, we must nevertheless refuse to treat as
the contraries of the true judgement those which opine
that some other attribute subsists which does not subsist,

TO as also those that opine that some other attribute does not
subsist which does subsist, for both these classes of judge
ment are of unlimited content. 1

Those judgements must rather be termed contrary to
the true judgements, in which error is present. Now these
judgements are those which are concerned with the starting
points of generation, and generation is the passing from one
extreme to its opposite ; 2 therefore error is a like transition.

J.5 Now that which is good is both good and not bad. The
first quality is part of its essence, the second accidental ;
for it is by accident that it is not bad. But if that true
judgement is most really true, which concerns the subject s
intrinsic nature, then that false judgement likewise is most
really false, which concerns its intrinsic nature. Now the
judgement that that which is good is not good is a false
judgement concerning its intrinsic nature, the judgement

1 sc. whereas there can be only one contrary.

2 For this sense of the word avriKei^vov cf. Met. A. 10.

CHAPTER 14 23

that it is bad is one concerning that which is accidental.
Thus the judgement which denies the truth of the true 20
judgement is more really false than that which positively
asserts the presence of the contrary quality. But it is the
man who forms that judgement which is contrary to the true
who is most thoroughly deceived, for contraries are among
the things which differ most widely within the same class. 1
If then of the two judgements one is contrary to the true
judgement, but that which is contradictory is the more
truly contrary, then the latter, it seems, is the real contrary. 2
The judgement that that which is good is bad is composite. 25
For presumably the man who forms that judgement must at
the same time understand that that which is good is not good.

Further, the contradictory is either always the contrary
or never ; therefore, if it must necessarily be so in all other
cases, our conclusion in the case just dealt with would seem
to be correct. Now where terms have no contrary, that 30
judgement is false, which forms the negative of the true;
for instance, he who thinks a man is not a man forms a
false judgement. If then in these cases the negative is the
contrary, then the principle is universal in its application.

Again, the judgement that that which is not good is not
good is parallel with the judgement that that which is good
is good. Besides these there is the judgement that that
which is good is not good, parallel with the judgement
that that which is not good is good. Let us consider, 35
therefore, what would form the contrary of the true judge
ment that that which is not good is not good. The
judgement that it is bad would, of course, fail to meet
the case, since two true judgements are never contrary and
this judgement might be true at the same time as that with

1 Cf. Cat. 6 a i;.

2 The argument of this passage is, shortly, this :

Error consists in the transition in thought from one judgement to
its opposite extreme.

The idea not good 1 is further removed from good than the idea
bad . . . complete error consists in the transition from the judgement
that that which is good is good to the judgement that it is not good.

But (repeating the statement ot>8f/u ai> dercov . . . a\X" ev Serais Wh ??
aTTaTTj) it is the man who holds the contrary judgement to the true who
suffers most completely from error.

. . not good is the contrary of good .

23 b DE INTERPRETATION

which it is connected. For since some things which are not
good are bad, both judgements may be true. Nor is the
judgement that it is not bad the contrary, for this too might
be true, since both qualities might be predicated of the same
40 subject. It remains, therefore, that of the judgement con
cerning that which is not good, that it is not good, the

24 a contrary judgement is that it is good ; for this is false. In
the same way, moreover, the judgement concerning that
which is good, that it is not good, is the contrary of the
judgement that it is good.

It is evident that it will make no difference if we univer
salize the positive judgement, for the universal negative
5 judgement will form the contrary. For instance, the con
trary of the judgement that everything that is good is
good is that nothing that is good is good. For the judge
ment that that which is good is good, if the subject be
understood in a universal sense, is equivalent to the judge
ment that whatever l is good is good, and this is identical
with the judgement that everything that is good is good.
We may deal similarly with judgements concerning that
which is not good.

24 If therefore this is the rule with judgements, and if
spoken affirmations and denials are judgements expressed
in words, it is plain that the universal denial is the con
trary of the affirmation about the same subject. Thus
the propositions everything good is good , every man is
good , have for their contraries the propositions nothing
5 good is good , no man is good . The contradictory propo
sitions, on the other hand, are not everything good is good ,
not every man is good .

It is evident, also, that neither true judgements nor true
propositions 2 can be contrary the one to the other. For
whereas, when two propositions are true, a man may state
both at the same time without inconsistency, contrary
propositions are those which state contrary conditions,
and contrary conditions cannot subsist at one and the
same time in the same subject.

1 Omit 6 in 1. 7 with C and Amm.

" Read avrtycKriv in 1. 7 with Amm. and \Vaitz.

ANALYTICA PRIORA

BY

A. J. JENKINSON, M.A.

FELLOW AND TUTOR OF BRASENOSE COLLEGE

PREFACE

THIS translation is based upon the text of Bekker. The
notes show where I have deviated from it. I have obtained
much help from the translation and commentary of Pacius,
and especially with regard to the text from the edition of
the Organon by Waitz. But my greatest obligations are
due to Mr. W. D. Ross, who has placed his knowledge of
Aristotle s thought and language so freely at my disposal
that any merit which this work may have belongs to him
rather than to me.

A. J. J.

B 2

CONTENTS

BOOK I

A. Structure of the Syllogism.

i. PRELIMINARY DISCUSSIONS.
CHAP.

1. Subject and scope of the Analytics. Certain definitions and

divisions.

2. Conversion of pure propositions.

3. Conversion of necessary and contingent propositions.

2. EXPOSITION OF THE THREE FIGURES.

4. Pure syllogisms in the first figure.

5. Pure syllogisms in the second figure.

6. Pure syllogisms in the third figure.

7. Common properties of the three figures.

8. Syllogisms with two necessary premisses.

9. Syllogisms with one pure and one necessary premiss in the

first figure.

10. Syllogisms with one pure and one necessary premiss in the

second figure.

11. Syllogisms with one pure and one necessary premiss in the

third figure.

12. Comparison of pure and necessary conclusions.

13. Preliminary discussion of the contingent.

14. Syllogisms in the first figure with two contingent premisses.

15. Syllogisms in the first figure with one contingent and one pure

premiss.

1 6. Syllogisms in the first figure with one contingent and one

necessary premiss.

17. Syllogisms in the second figure with two contingent premisses.

1 8. Syllogisms in the second figure with one contingent and one

pure premiss.

19. Syllogisms in the second figure with one contingent and one

necessary premiss.

20. Syllogisms in the third figure with two contingent premisses.

21. Syllogisms in the third figure with one contingent and one

pure premiss.

22. Syllogisms in the third figure with one contingent and one

necessary premiss.

CONTENTS

3. SUPPLEMENTARY DISCUSSIONS.
CHAP.

23. Every syllogism is in one of the three figures, is completed

through the first figure, and reducible to a universal mood
of the first figure.

24. Quality and quantity of the premisses of the syllogism.

25. Number of the terms, propositions, and conclusions.

26. The kinds of proposition to be established or disproved in

each figure.

B. Mode of discovery of arguments.
i. GENERAL.

27. Rules for categorical syllogisms, applicable to all problems.

28. Rules for categorical syllogisms, peculiar to different problems.

29. Rules for reductio ad iinpossibile, hypothetical syllogisms, and

modal syllogisms.

30. 2. PROPER TO THE SEVERAL SCIENCES AND ARTS.

31. 3. DIVISION.

C. Analysis (i) of arguments into figures and moods of

syllogism.

32. Rules for the choice of premisses, terms, middle term, figure.

33. Quantity of the premisses.

34. Concrete and abstract terms.

35. Expressions for which there is no one word.

36. The nominative and the oblique cases.

37. The various kinds of attribution.

38. Repetition of the same term.

39. Substitution of equivalent expressions.

40. The definite article.

41. Interpretation of certain expressions.

42. Analysis of composite syllogisms.

43. Analysis of definitions.

44. Analysis of arguments per impossibile and of other hypo

thetical syllogisms.

45. Analysis (2) of syllogisms in one figure into another.

46. Is not A and is not-A .

CONTENTS

BOOK II

Properties and defects of syllogism ; arguments akin to
syllogism.

A. PROPERTIES.
CHAP.

i. The drawing of more than one conclusion from the same

premisses.
2-4. The drawing of true conclusions from false premisses in the

three figures.

5-7. Circular proof in the three figures.
8-10. Conversion in the three figures.
11-13. Keductio ad impossibile in the three figures.

14. Comparison of reductio ad impossibile and ostensive proof.

15. Reasoning from opposites.

B. DEFECTS.

1 6. Petitio principii.

17. False Cause.

1 8. Falsity of conclusion due to falsity in one or more premisses.

19. How to impede opposing arguments and conceal one s own.

20. When refutation is possible.

2 1 . Error.

C. ARGUMENTS AKIN TO SYLLOGISM.

22. Rules for conversion and for the comparison of desirable and

undesirable objects.
Induction.
Example.

25. Reduction.

26. Objection.

27. Enthymeme.

ANALYTICA PRIORA
BOOK I

WE must first state the subject of our inquiry and the 24*
faculty to which it belongs : its subject is demonstration
and the faculty that carries it out demonstrative science.
We must next define a premiss, a term, and a syllogism,
and the nature of a perfect and of an imperfect syllogism ;
and after that, the inclusion or non-inclusion of one term in
another as in a whole, and what we mean by predicating
one term of all, or none, of another. 15

A premiss then is a sentence affirming or denying one
thing of another. This is either universal or particular or
indefinite. By universal I mean the statement that some
thing belongs to all or none of something else ; by particular
that it belongs to some or not to some or not to all ; by
indefinite that it does or does not belong, without any mark
to show whether it is universal or particular, e.g. contraries 20
are subjects of the same science , or pleasure is not good .
The demonstrative premiss differs from the dialectical,
because the demonstrative premiss is the assertion of one of
two contradictory statements (the demonstrator does not
ask for his premiss, but lays it down), whereas the dialectical
premiss depends on the adversary s choice between two 25
contradictories. But this will make no difference to the
production of a syllogism in either case; for both the
demonstrator and the dialectician argue syllogistically after
stating that something does or does not belong to some
thing else. Therefore a syllogistic premiss without qualifica
tion will be an affirmation or denial of something concerning
something else in the way we have described ; it will be
demonstrative, if it is true and obtained through the first 3
principles of its science ; while a dialectical premiss is the
giving of a choice between two contradictories, when a man
is proceeding by question, but when he is syllogizing it

24 b ANALYTICA PRIORA

is the assertion of that which is apparent and generally
admitted, as has been said in the Topics^ The nature then
of a premiss and the difference between syllogistic, demon
strative, and dialectical premisses, may be taken as sufficiently

15 defined by us in relation to our present need, but will be
stated accurately in the sequel. 2

I call that a term into which the premiss is resolved,

i. e. both the predicate and that of which it is predicated,

being being added and not being removed, or vice versa.

A syllogism is discourse in which, certain things being

stated, something other than what is stated follows of

20 necessity from their being so. I mean by the last phrase
that they produce the consequence, and by this, that no
further term is required from without in order to make the
consequence necessary.

I call that a perfect syllogism which needs nothing other
than what has been stated to make plain what necessarily
follows ; a syllogism is imperfect, if it needs either one or

25 more propositions, which are indeed the necessary conse
quences of the terms set down, but have not been expressly
stated as premisses.

That one term should be included in another as in a whole
is the same as for the other to be predicated of all of the
first. And we say that one term is predicated of all of
another, whenever no instance of the subject can be found
of which the other term cannot be asserted : to be predi-

3 cated of none must be understood in the same way.

25* Every premiss states that something either is or must be 2
or may be the attribute of something else ; of premisses of
these three kinds some are affirmative, others negative, in
respect of each of the three modes of attribution ; again
some affirmative and negative premisses are universal,
5 others particular, others indefinite. It is necessary then
that in universal attribution the terms of the negative
premiss should be convertible, e.g. if no pleasure is good,
then no good will be pleasure; the terms of the affirmative

1 ioo a 29, 104*8.

2 The nature of demonstrative premisses is discussed in the Post.
An.; that of dialectical premisses in the Topics.

BOOK I. 2 25*

must be convertible, not however universally, but in part,
e. g. if every pleasure is good, some good must be pleasure ;
the particular affirmative must convert in part (for if some 10
pleasure is good, then some good will be pleasure) ; but the
particular negative need not convert, for if some animal is
not man, it does not follow that some man is not animal.

First then take a universal negative with the terms
A and B. If no B is A, neither can any A be B. For if 15
some A (say C) were B, it would not be true that no B
is A ; for C is a B. But if every B is A, then some A
is B. For if no A were B, then no B could be A. But
we assumed that every B is A. Similarly too, if the premiss 20
is particular. For if some B is A, then some of the As
must be B. For if none were, then no B would be A.
But if some B is not A, there is no necessity that some
of the As should not be B ; e.g. let B stand for animal
and A for man. Not every animal is a man ; but every 25
man is an animal.

3 The same manner of conversion will hold good also in
respect of necessary premisses. The universal negative
converts universally ; each of the affirmatives converts into
a particular. If it is necessary that no B is A, it is necessary 3
also that no A is B. For if it is possible that some A is B,
it would be possible also that some B is A. If all or some B
is A of necessity, it is necessary also that some A is B : for
if there were no necessity, neither would some of the Bs be A
necessarily. But the particular negative does not convert, 35
for the same reason which we have already stated. 1

In respect of possible premisses, since possibility is used
in several senses (for we say that what is necessary and what
is not necessary and what is potential is possible), affirma
tive statements will all convert in a manner similar to those 4
described. 2 For if it is possible that all or some B is A, it
will be possible that some A is B. For if that were not 25
possible, then no B could possibly be A. This has been
already proved/ 5 But in negative statements the case is
different. Whatever is said to be possible, either because B

1 11. 12, 22-6. 2 In 11. 7-13. S a 20-2.

25 b ANALYTICA PRIORA

necessarily is A, 1 or because B is not necessarily A, admits
5 of conversion like other negative statements, e.g. if one
should say, it is possible that man is not horse, or that no
garment is white. For in the former case the one term
necessarily does not belong to the other ; in the latter there
is no necessity that it should : and the premiss converts like
other negative statements. For if it is possible for no man

10 to be a horse, it is also admissible for no horse to be a man ;
and if it is admissible for no garment to be white, it is also
admissible for nothing white to be a garment. For if any
white thing must be a garment, then some garment will
necessarily be white. This has been already proved. 2 The
particular negative also must be treated like those dealt
with above. 3 But if anything is said to be possible because

15 it is the general rule and natural (and it is in this way we
define the possible), the negative premisses can no longer
be converted like the simple negatives ; the universal nega
tive premiss does not convert, and the particular does. This
will be plain when we speak about the possible. 4 At present
we may take this much as clear in addition to what has been

20 said : the statement that it is possible that no B is A or
some B is not A is affirmative in form : for the expression
is possible ranks along with is , and is makes an affirma
tion always and in every case, whatever the terms to which
it is added in predication, e. g. it is not-good or it is not-
white or in a word it is not-this . But this also will be

25 proved in the sequel. 5 In conversion these premisses will
behave like the other affirmative propositions.

After these distinctions we now state by what means, 4
when, and how every syllogism is produced ; subsequently (1
we must speak of demonstration. Syllogism should be
discussed before demonstration, because syllogism is the
30 more general : the demonstration is a sort of syllogism,
but not every syllogism is a demonstration.

Whenever three terms are so related to one another that
the last is contained in the middle as in a whole, and the

1 Omit /JT; in 1. 4 with A, B, Phil., and Waitz. 2 a 14-17.

: In a 12. 4 cc. 13, 17. 6 c. 46.

6 In the Posterior Analytics.

BOOK I. 4 25 b

middle is either contained in, or excluded from, the first
as in or from a whole, the extremes must be related by
a perfect syllogism. I call that term middle which is itself 35
contained in another and contains another in itself: in
position also this comes in the middle. By extremes
I mean both that term which is itself contained in another
and that in which another is contained. If l A is predicated
of all B, and B of all C, A must be predicated of all C: we
have already explained 2 what we mean by predicated of 40
all . Similarly :i also, if A is predicated of no B, and B of 26 a
all C, it is necessary that no C will be A.

But 4 if the first term belongs to all the middle, but the
middle to none of the last term, there will be no syllogism
in respect of the extremes ; for nothing necessary follows
from the terms being so related ; for it is possible that the
first should belong either to all or to none of the last, so 5
that neither a particular nor a universal conclusion is
necessary. But if there is no necessary consequence, there
cannot be a syllogism by means of these premisses. As an
example of a universal affirmative relation between the
extremes we may take the terms animal, man, horse; of a
universal negative relation, the terms animal, man, stone.
Nor 5 again can a syllogism be formed when neither the
first term belongs to any of the middle, nor the middle to 10
any of the last. As an example of a positive relation
between the extremes take the terms science, line, medicine :
of a negative relation science, line, unit.

If then the terms are universally related, it is clear in this
figure when a syllogism will be possible and when not, and
that if a syllogism is possible the terms must be related as 15
described, and if they are so related there will be a syllogism.

But if one term is related universally, the other in part
only, to its subject, there must be a perfect syllogism
whenever universality is posited with reference to the major
term either affirmatively or negatively, and particularity
with reference to the minor term affirmatively : but whenever 20

1 Barbara, major A, minor A. 2 24^28.

3 Celarent, major E, minor A. 4 Major A, minor E.

r> Major E, minor E.

26 a ANALYTICA PRIORA

the universality is posited in relation to the minor term,
or the terms are related in any other way, a syllogism is
impossible. I call that term the major in which the middle
is contained and that term the minor which comes under
the middle. Let l all B be A and some C be B. Then if
predicated of all means what was said above, 2 it is necessary

25 that some C is A. And 3 if no B is A, but some C is B, it is
necessary that some C is not A. (The meaning of predi
cated of none has also been defined. 4 ) So there will be a
perfect syllogism. This holds good also if the premiss BC*
should be indefinite, provided that it is affirmative: for we
shall have the same syllogism whether the premiss is
indefinite or particular.

30 But if the universality is posited with respect to the minor
term either affirmatively or negatively, a syllogism will not
be possible, whether the major premiss is- positive or nega
tive, indefinite or particular : e. g. (; if some B is or is not A,
and all C is B. As an example of a positive relation between

35 the extremes take the terms good, state, wisdom : of a nega
tive relation, good, state, ignorance. Again 7 if no C is ,
but some B is or is not A, or not every B is A, there cannot
be a syllogism. Take the terms white, horse, swan : white,
horse, raven. The same terms may be taken also if the
premiss BA is indefinite.

26 b Nor when the major premiss is universal, whether affirma
tive or negative, and the minor premiss is negative and
particular, can there be a syllogism, whether the minor
premiss be indefinite or particular: e.g. 8 if all B is A, and
some C is not B, or if not all C is B. For the major term
may be predicable both of all and of none of the minor,
5 to some of which the middle term cannot be attributed.
Suppose the terms are animal, man, white : next take some
of the white things of which man is not predicated swan

1 Darii. 2 24 28. s Ferio. " 24 30.

The Aristotelian formula for the proposition, AB, in which B
represents the subject and A the predicate (A belongs to B), has
been retained throughout, because in most places this suits the context
better than the modern formula in which A represents the subject and
B the predicate. fi Major / or O, minor A.

7 Major / or O, minor E. 8 Major A, minor O,

BOOK I. 4 2 6 l

and snow : animal is predicated of all of the one, but of
none of the other. Consequently there cannot be a syllogism.
Again l let no B be A, but let some C not be B. Take the 10
terms inanimate, man. white : then take some white things of
which man is not predicated swan and snow : the term in
animate is predicated of all of the one, of none of the other.

Further since it is indefinite to say some C is not B y and
it is true that some C is not />, whether no C is B, or not all 15
C is B, and since if terms are assumed such that no C is B,
no syllogism follows (this has already been stated 2 ), it is
clear that this arrangement of terms" will not afford a
syllogism : otherwise one would have been possible with
a universal negative minor premiss. A similar proof may 20
also be given if the universal premiss 4 is negative."

Nor can there in any way be a syllogism if both the rela
tions of subject and predicate are particular, either positively
or negatively, or the one negative and the other affirmative, 6
or one indefinite and the other definite, or both indefinite.
Terms common to all the above are animal, white, horse : 25
animal, white, stone.

It is clear then from what has been said that if there is
a syllogism in this figure with a particular conclusion, the
terms must be related as we have stated : if they are related
otherwise, no syllogism is possible anyhow. It is evident
also that all the syllogisms in this figure are perfect (for
they are all completed by means of the premisses originally 30
taken) and that all conclusions are proved by this figure,
viz. universal and particular, affirmative and negative. Such
a figure I call the first.

5 Whenever the same thing belongs to all of one subject,
and to none of another, or to all of each subject or to none 35
of either, I call such a figure the second ; by middle term in
it I mean that which is predicated of both subjects, by
extremes the terms of which this is said, by major
extreme that which lies near the middle, by minor that
which is further away from the middle. The middle term

1 Major E, minor O. - a 2. " Major A, minor O.

4 i.e. the major premiss. 5 Major E, minor O.

" //, OO, IO, Of.

27 a ANALYTICA PRIORA

27* stands outside the extremes, and is first in position. A
syllogism cannot be perfect anyhow in this figure, but it may
be valid whether the terms are related universally or not.

If then the terms are related universally a syllogism will
be possible, whenever the middle belongs to all of one
subject and to none of another (it does not matter which has
5 the negative relation), but in no other way. Let M be
predicated of no N, but of all O. Since, then, the negative
relation is convertible, ^V will belong to no M : but M was
assumed to belong to all O : consequently ^V will belong to
no O. 1 This has already been proved. 2 Again if M belongs
10 to all JV, but to no O, then ^Vwill belong to no 0? For if
M belongs to no O, O belongs to no M : but M (as was said)
belongs to all N : O then will belong to no N \ for the first
figure has again been formed. But since the negative
relation is convertible, ^V will belong to no O. Thus it will
be the same syllogism that proves both conclusions.
15 It is possible to prove these results also by reduction ad
impossibile.

It is clear then that a syllogism is formed when the terms
are so related, but not a perfect syllogism ; for necessity is
not perfectly established merely from the original premisses ;
others also are needed.

But if M is predicated of every N and O, there cannot be

a syllogism. Terms to illustrate a positive relation between

the extremes are substance, animal, man ; a negative

20 relation, substance, animal, number substance being the

middle term.

Nor is a syllogism possible when M is predicated neither
of any N nor of any O, Terms to illustrate a positive
relation are line, animal, man : a negative relation, line,
animal, stone.

It is clear then that if a syllogism is formed when the terms
are universally related, the terms must be related as we
25 stated at the outset : 4 for if they are otherwise related no
necessary consequence follows.

1 Cesare. 2 25 b 4O.

3 Camestres. Read ovSe TW & TO N in 1. 10 with A 2 , Waitz, and
perhaps Philoponus.

4 1.3-

BOOK I. 5 27 a

If the middle term is related universally to one of the
extremes, a particular negative syllogism must result
whenever the middle term is related universally to the
major whether positively or negatively, and particularly to
the minor and in a manner opposite to that of the universal
statement : by an opposite manner I mean, if the
universal statement is negative, the particular is affirmative : 30
if the universal is affirmative, the particular is negative. For
if M belongs to no .V, but to some O, it is necessary that jV
does not belong to some O. 1 For since the negative statement
is convertible, A 7 will belong to no M: but M was admitted to
belong to some O : therefore N will not belong to some O : 35
for the result is reached by means of the first figure. Again
if M belongs to all N, but not to some O, it is necessary
that N does not belong to some O : - for if .V belongs
to all (9, and M is predicated also of all N, M must belong
to all : but we assumed that M does not belong to some 2y b
O. And if M belongs to all N but not to all O, we shall
conclude that N does not belong to all O : the proof is the
same as the above. But if M is predicated of all (9, but not
of all N, there will be no syllogism. Take the terms
animal, substance, raven ; animal, white, raven. Nor will 5
there be a conclusion when M is predicated of no O, but of
some .V. Terms to illustrate a positive relation between the
extremes are animal, substance, unit : a negative relation,
animal, substance, science.

If then the universal statement is opposed to the particular,
we have stated when a syllogism will be possible and when 10
not : but if the premisses are similar in form, I mean both
negative or both affirmative, a syllogism will not be possible
anyhow. First let them be negative, and let the major
premiss be universal, e. g. let M belong to no .V, and not to
some O. It is possible then for TV to belong either to all O or 15
to no O. Terms to illustrate the negative relation are black,
snow, animal. But it is not possible to find terms of which the
extremes are related positively and universally, if M belongs
to some O, and does not belong to some O. For if .V
belonged to all O, but M to no N, then M would belong to
1 Festino. 2 Baroco. ^

645-24.3 C

27 b ANALYTICA PRIORA

no O : but we assumed that it belongs to some O. In this
20 way then it is not admissible to take terms : our point must
be proved from the indefinite nature of the particular state
ment. For since it is true that M does not belong to some O,
even if it belongs to no O, and since if it belongs to no O
a syllogism is (as we have seen 1 ) not possible, clearly it will
not be possible now either.

Again let the premisses be affirmative, and let the major
premiss as before be universal, e. g. let M belong to all ^V
25 and to some O. It is possible then for TV to belong to all
O or to no O. Terms to illustrate the negative relation
are white, swan, stone. But it is not possible to take terms
to illustrate the universal affirmative relation, for the reason
already stated : 2 the point must be proved from the indefinite
nature of the particular statement. But if the minor pre-
30 miss is universal, and M belongs to no O, and not to some
A 7 , it is possible for N to belong either to all O or to no O.
Terms for the positive relation are white, animal, raven : for
the negative relation, white, stone, raven. If the premisses
are affirmative, terms for the negative relation are white,
animal, snow ; for the positive relation, white, animal, swan.
Evidently then, whenever the premisses are similar in form,
35 and one is universal, the other particular, a syllogism cannot
be formed anyhow. Nor is one possible if the middle term
belongs to some of each of the extremes, or does not belong
to some of either, or belongs to some of the one, not to some
of the other, or belongs to neither universally/ or is related
to them indefinitely. Common terms for all the above are
white, animal, man : white, animal, inanimate.
28 a It is clear then from what has been said that if the terms
are related to one another in the way stated, a syllogism
results of necessity ; and if there is a syllogism, the terms
must be so related. But it is evident also that all the
syllogisms in this figure are imperfect : for all are made
5 perfect by certain supplementary statements, which either
are contained in the terms of necessity or are assumed as

1 a 2I. 2 1. IS.

3 An alternative and clearer expression for does not belong to some
of either .

BOOK I. 5 28 a

hypotheses, i. e. when we prove per impossibile. And it is
evident that an affirmative conclusion is not attained by
means of this figure, but all are negative, whether universal
or particular.

6 But if one term belongs to all, and another to none, of a 10
third, or if both belong to all, or to none, of it, I call such a
figure the third ; by middle term in it I mean that of which
both the predicates are predicated, by extremes I mean the
predicates, by the major extreme that which is further from
the middle, by the minor that which is nearer to it. The
middle term stands outside the extremes, and is last 15
in position. A syllogism cannot be perfect in this figure
either, but it may be valid whether the terms are related
universally or not to the middle term.

If they are universal, whenever both P and R belong to all
5, it follows that P will necessarily belong to some R. 1
For, since the affirmative statement is convertible. 5 will
belong to some R : consequently since P belongs to all S, 20
and 5 to some R, P must belong to some R : for a syllogism
in the first figure is produced. It is possible to demonstrate
this also per impossibile and by exposition. For if both P
and R belong to all 5, should one of the 5s, e.g. N t be taken,
both P and R will belong to this, and thus P will belong to 25
some R.

If R belongs to all S, and P to no S, there will be
a syllogism to prove that P will necessarily not belong
to some A . 2 This may be demonstrated in the same way
as before by converting the premiss A 5. :1 It might be
proved also per impossibile, as in the former cases. But if 30
R belongs to no S, P to all S, there will be no syllogism.
Terms for the positive relation are animal, horse, man : for
the negative relation animal, inanimate, man.

Nor can there be a syllogism when both terms are asserted
of no 6 . Terms for the positive relation are animal, horse,
inanimate ; for the negative relation man, horse, inanimate 35
inanimate being the middle term.

It is clear then in this figure also when a syllogism will

1 Darapti. 2 Felapton. 3 See note 26* 29.

C 2

28 a ANALYTICA PRIORA

be possible and when not, if the terms are related universally.
For whenever both the terms are affirmative, there will be a
syllogism to prove that one extreme belongs to some of the
other ; but when they are negative, no syllogism will
28 b be possible. But when one is negative, the other affirmative,
if the major is negative, the minor affirmative, there will be
a syllogism to prove that the one extreme does not belong
to some of the other: but if the relation is reversed,
no syllogism will be possible.

5 If one term is related universally to the middle, the other
in part only, when both are affirmative there must be
a syllogism, no matter which of the premisses is universal.
For if R belongs to all .S, P to some S, P must belong to
some R. 1 For since the affirmative statement is convertible

10 6" will belong to some P : consequently since R belongs to
all S, and 5 to some P, R must also belong to some P :
therefore P must belong to some R.

Again if R belongs to some S, and P to all S, P must
belong to some R. z This may be demonstrated in the same
way as the preceding. And it is possible to demonstrate it
also per impossibile and by exposition, as in the former

1.5 cases. But if one term is affirmative, the other negative,
and if the affirmative is universal, a syllogism will be possible
whenever the minor term is affirmative. For if R belongs
to all S, but P does not belong to some S, it is necessary
that P does not belong to some R. z For if P belongs to
all R, and R belongs to all S* then P will belong to all S :

20 but we assumed that it did not. Proof is possible also
without reduction ad impossibile, if one of the ^s be
taken to which P does not belong.

But whenever the major is affirmative, no syllogism will
be possible, e.g. if P belongs to all ^S", and R does not belong
to some vS\ Terms for the universal affirmative relation are
animate, man, animal. For the universal negative relation

25 it is not possible to get terms, if /x* belongs to some S, and
does not belong to some S. For if P belongs to all S,
and R to some S, then P will belong to some R : but we

1 Disamis. 2 Datisi.

3 Bocardo. * Comma after 2 in 1. 19.

BOOK I. 6 28*

assumed : that it belongs to no R. We must put the
matter as before. 2 Since the expression it does not belong
to some is indefinite, it maybe used truly of that also which
belongs to none. But if R belongs to no S, no syllogism is 30
possible, as has been shown. 3 Clearly then no syllogism will
be possible here.

But if the negative term is universal, whenever the major
is negative and the minor affirmative there will be a syllogism.
For if P belongs to no S, and R belongs to some S, P will
not belong to some R : 4 for we shall have the first figure
again, if the premiss RS is converted. 35

But when the minor is negative, there will be no syllogism.
Terms for the positive relation are animal, man, wild : for
the negative relation, animal, science, wild the middle in
both being the term wild.

Nor is a syllogism possible when both are stated in the
negative, but one is universal, the other particular. When
the minor is related universally to the middle, take the terms 29*
animal, science, wild ; animal, man, wild. When the major
is related universally to the middle, take as terms for
a negative relation raven, snow, white. For a positive
relation terms cannot be found, if R belongs to some ^>, and
does not belong to some S. For if P belongs to all R, and 5
R to some S, then P belongs to some 6" : but we assumed
that it belongs to no 5. Our point, then, must be proved
from the indefinite nature of the particular statement.

Nor is a syllogism possible anyhow, if each of the extremes
belongs to some of the middle, or does not belong, or one
belongs and the other does not to some of the middle, or
one belongs to some of the middle, the other not to all, or
if the premisses are indefinite. Common terms for all are
animal, man, white : animal, inanimate, white. 10

It is clear then in this figure also when a syllogism will
be possible, and when not ; and that if the terms are as stated,
a syllogism results of necessity, and if there is a syllogism,
the terms must be so related. It is clear also that all the

1 i.e. in supposing the universal negative relation between the
extremes.

2 27 b 20. s 28 a 30. * Ferison.

2Q a ANALYTICA PRIORA

15 syllogisms in this figure are imperfect (for all are made
perfect by certain supplementary assumptions), and that it
will not be possible to reach a universal conclusion by means
of this figure, whether negative or affirmative.

It is evident also that in all the figures, whenever a proper 7

20 syllogism does not result, if both the terms are affirmative
or negative nothing necessary follows at all, but if one
is affirmative, the other negative, and if the negative is
stated universally, a syllogism always results relating the
minor l to the major term, 2 e. g. if A belongs to all or some
B, and B belongs to no C: for if the premisses are converted

25 it is necessary that C does not belong to some A. 3 Similarly
also in the other figures : a syllogism always results by
means of conversion. It is evident also that the substitution
of an indefinite for a particular affirmative will effect the
same syllogism in all the figures.

-o It is clear too that all the imperfect syllogisms are made
perfect by means of the first figure. For all are brought to
a conclusion either ostensively or per impossibile. In both
ways the first figure is formed : if they are made perfect
ostensively, because (as we saw) all are brought to a conclu
sion by means of conversion, and conversion produces the

35 first figure : if they are proved per impossibile^ because
on the assumption of the false statement the syllogism
comes about by means of the first figure, e.g. in the
last figure, if A and B belong to all C, it follows that A
belongs to some B : for if A belonged to no B, and B belongs
to all C, ~A would belong to no C: but (as we stated) it
belongs to all C. Similarly also with the rest.
2g b It is possible also to reduce all syllogisms to the universal
syllogisms in the first figure. Those in the second figure
are clearly made perfect by these, though not all in the same
way ; the universal syllogisms are made perfect by convert-
5 ing the negative premiss, each of the particular syllogisms
by reduction ad impossibile. In the first figure particular
syllogisms are indeed made perfect by themselves, but it is
possible also to prove them by means of the second figure.

1 As predicate. 2 As subject. 3 Fesapo, Fresison.

BOOK I. 7 2Q l

reducing them ad impossibile, e. g. if A belongs to all B,
and B to some C, it follows that A belongs to some C. For
if it belonged to no C, and belongs to all B, then B will
belong to no C\ this we know by means of the second figure. 10
Similarly also demonstration will be possible in the case of
the negative. For if A belongs to no B, and B belongs to
some C, A will not belong to some C : for if it belonged to
all C, and belongs to no B, then B will belong to no C: and
this (as we saw) is the middle figure. Consequently, since 15
all syllogisms in the middle figure can be reduced to universal
syllogisms in the first figure, and since particular syllogisms
in the first figure can be reduced to syllogisms in the middle
figure, it is clear that particular syllogisms J can be reduced
to universal syllogisms in the first figure. Syllogisms in the
third figure, if the terms are universal, are directly made 20
perfect by means of those syllogisms ; 2 but, when one
of the premisses is particular, by means of the particular
syllogisms in the first figure : and these (we have seen) may
be reduced to the universal syllogisms in the first figure :
consequently also the particular syllogisms in the third figure
may be so reduced. It is clear then that all syllogisms may
be reduced to the universal syllogisms in the first figure. 25

We have stated then how syllogisms which prove that
something belongs or does not belong to something else are
constituted, both how syllogisms of the same figure are
constituted in themselves, and how syllogisms of different
figures are related to one another.

g Since there is a difference according as something belongs,
necessarily belongs, or may belong to something else (for ?,o
many things belong indeed, but not necessarily, others
neither necessarily nor indeed at all, but it is possible for
them to belong), it is clear that there will be different
syllogisms to prove each of these relations, and syllogisms
with differently related terms, one syllogism concluding from
what is necessary, another from what is, a third from what
is possible. 35

There is hardly any difference between syllogisms from

1 sc. in the first figure.

- viz. by reduction per impossibile to Celarent and Barbara.

2Q b ANALYTICA PRIORA

necessary premisses and syllogisms from premisses which
merely assert. When the terms are put in the same way,
then, whether something belongs or necessarily belongs (or
does not belong) to something else, a syllogism will or will
not result alike in both cases, the only difference being the
3<D a addition of the expression necessarily to the terms. For
the negative statement is convertible alike in both cases,
and we should give the same account of the expressions to
be contained in something as in a whole and to be predi
cated of all of something . With the exceptions to be
made below, the conclusion will be proved to be necessary
5 by means of conversion, in the same manner as in the case
of simple predication. But in the middle figure when the
universal statement is affirmative, and the particular nega
tive, and again in the third figure when the universal is
affirmative and the particular negative, the demonstration
will not take the same form, but it is necessary by the
exposition of a part of the subject of the particular negative
10 proposition, to which the predicate does not belong, to make
the syllogism in reference to this : with terms so chosen
the conclusion will necessarily follow. But if the relation
is necessary in respect of the part taken, it must hold of
some of that term in which this part is included : for the
part taken is just some of that. And each of the resulting
syllogisms is in the appropriate figure. 1

1 Baroco. All N is necessarily M.

Some O is necessarily not M.
. . Some O is necessarily not A r .
Bocardo. Some S is necessarily not P.

All S is necessarily R.
. . Some R is necessarily not P.

When the propositions are assertoric, the conclusions are proved by
reduction ad impossilrile. The contradictory of Some O is necessarily
not N is Every O is possibly N : but if this is combined with All
N is necessarily M , the combination of an apodictic with a problematic
premiss does not give an apodictic conclusion. Aristotle therefore falls
back on another method of proof. If some O is necessarily not M, take
some part of O viz. Q all of which is necessarily not M. Then
It is necessary that all A 7 be M.
It is necessary that no Q be M.
. . It is necessary that no Q be N.
. . It is necessary that some O be not N.

Baroco is proved by means of Camestres ; similarly Bocardo is
proved by means of Felapton each by a syllogism in the same figure

BOOK I. 9 30 a

9 It happens sometimes also that when one premiss is 15
necessary the conclusion is necessary, not however when
either premiss is necessary, but only when the major is,
e.g. if A is taken as necessarily belonging or not belonging
to B, but B is taken as simply belonging to C: for if the
premisses are taken in this way, A will necessarily belong 20
or not belong to C, For since A necessarily belongs, or
does not belong, to every B, and since C is one of the 5s,

it is clear that for C 1 also the positive or the negative rela
tion to A will hold necessarily. But if the major premiss
is not necessary, but the minor is necessary, the conclusion
will not be necessary. For if it were, it would result both 25
through the first figure and through the third that A belongs
necessarily to some B. But this is false ; for -B may be
such that it is possible that A should belong to none of it.
Further, an example also makes it clear that the conclusion
will not be necessary, e. g. if A were movement, B animal, 30
C man : man is an animal necessarily, but an animal does
not move necessarily, nor does man. Similarly also if the
major premiss is negative ; for the proof is the same.

In particular syllogisms, if the universal premiss is neces
sary, then the conclusion will be necessary ; but if the par- 35
ticular, the conclusion will not be necessary, whether the
universal premiss is negative or affirmative. First let the
universal be necessary, and let A belong to all B necessarily,
but let B simply belong to some C : it is necessary then that
A belongs to some C necessarily : for C falls under B, and 40
A was assumed to belong necessarily to all B. Similarly 3o b
also if the syllogism should be negative : for the proof will
be the same. But if the particular premiss is necessary, the
conclusion will not be necessary : for from the denial of such
a conclusion nothing impossible results, 2 just as it does not
in the universal syllogisms. The same is true of negative 5
syllogisms. Try the terms movement, animal, white.

10 In the second figure, if the negative premiss is necessary,
then the conclusion will be necessary, but if the affirmative,

as itself (1. 13). Camestres and Felapton can then byconversion be
proved by means of Celarent and Ferio (11. 3-5).

1 Read ro> r in 1. 22 with A, B, C, Phil., and Waitz.

" i. e. from the assumption all C is possibly not A . Cf. 36 a 22~5.

30 b ANALYTICA PRIORA

not necessary. First let the negative be necessary ; let A

10 be possible of no B, and simply belong to C. Since then
the negative statement is convertible,/? is possible of no A.
But A belongs to all C; consequently B is possible of no C.
For C falls under A. The same result would be obtained if
the minor premiss were 1 negative : for if A is possible of no

15 C, C is possible of no A : but A belongs to all B, conse
quently C is possible of none of the Bs : for again we have
obtained the first figure. Neither then is B possible of C:
for conversion is possible without modifying the relation.
But if the affirmative premiss is necessary, the conclusion

20 will not be necessary. Let A belong to all B necessarily,
but to no C simply. If then the negative premiss is con
verted, the first figure results. But it has been proved 2 in
the case of the first figure that if the negative major premiss
is not necessary the conclusion will not be necessary either.
Therefore the same result will obtain here. Further, if the

25 conclusion is necessary, it follows that C necessarily does not
belong to some A. For if B necessarily belongs to no C,
C will necessarily belong to no B. But B at any rate must
belong to some A, if it is true (as was assumed) that A
necessarily belongs to all B. Consequently it is necessary

30 that C does not belong to some A. But nothing prevents
such an A being taken that it is possible for C to belong
to all of it. Further one might show by an exposition of
terms that the conclusion is not necessary without qualifica
tion, though it is a necessary conclusion from the premisses.
For example let A be animal, B man, C white, and let the
premisses be assumed to correspond to what we had before : 3

35 it is possible that animal should belong to nothing white.
Man then will not belong to anything white, but not neces
sarily : for it is possible for man to be born white, not
however so long as animal belongs to nothing white. Con
sequently under these conditions the conclusion will be
necessary, but it is not necessary without qualification.
3l a Similar results will obtain also in particular syllogisms.
For whenever the negative premiss is both universal and

1 Read reflffy in 1. 14 with Al. 1 , Phil. 1 , and Them. 2 a 23-33.

3 1. 20.

BOOK I. 10 3 i a

necessary, then the conclusion will be necessary : but when
ever the affirmative premiss is universal, the negative par
ticular, the conclusion will not be necessary. First then let 5
the negative premiss be both universal and necessary : let it
be possible for no B that A should belong to it, and let A
simply belong to some C. Since the negative statement is
convertible, it will be possible for no A that B should belong
to it : but A belongs to some C; consequently B necessarily
does not belong to some of the Cs. Again let the affirmative 10
premiss be both universal and necessary, and let the major
premiss be affirmative. If then A necessarily belongs to all
B, but does not belong to some C y it is clear that B will not
belong to some C, but not necessarily. For the same terms
can be used to demonstrate the point, which were used in
the universal syllogisms. 1 Nor again, if the negative state- 15
ment is necessary but particular, will the conclusion be
necessary. The point can be demonstrated by means of
the same terms.

II In the last figure when the terms are related universally
to the middle, and both premisses are affirmative, if one of
the two is necessary, then the conclusion will be necessary. 20
But if one is negative, the other affirmative, whenever the
negative is necessary the conclusion also will be necessary,
but whenever the affirmative is necessary the conclusion will
not be necessary. First let both the premisses be affirmative,
and let A and B belong to all C, and let AC be necessary. 25
Since then B belongs to all C, C also will belong to some B,
because the universal is convertible into the particular:
consequently if A belongs necessarily to all C, and C belongs
to some B, it is necessary that A should belong to some B
also. For B is under C. The first figure then is formed. 3
A similar proof will be given also if BC is necessary. For
C is convertible with some A : consequently if B belongs
necessarily to all C, it will belong necessarily also to some A.
Again let AC be negative, BC affirmative, and let the
negative premiss be necessary. Since then C is convertible 3?
with some B, but A necessarily belongs to no C, A will

1 30^33-40.

3i a ANALYTICA PRIORA

necessarily not belong to some B either : for B is under C.
But if the affirmative is necessary, the conclusion will not
be necessary. For suppose BC is affirmative and necessary,
while AC is negative and not necessary. Since then the

4 o affirmative is convertible, C also will belong to some B
necessarily: consequently if A belongs to none of the Cs,
3I b while C belongs l to some of the Us, A will not belong to
some of the Bs but not of necessity ; for it has been proved,
in the case of the first figure, that if the negative premiss is
not necessary, neither will the conclusion be necessary.
Further, the point may be made clear by considering the
5 terms. Let the term A be good , let that which B signifies
be animal , let the term C be horse . It is possible then
that the term good should belong to no horse, and it is
necessary that the term animal should belong to every horse:
but it is not necessary that some animal should not be good,
since it is possible for every animal to be good. Or if that
is not possible, take as the term awake or asleep : for

10 every animal can accept these.

If, then, the premisses are universal, we have stated when
the conclusion will be necessary. But if one premiss is
universal, the other particular, and if both are affirmative,
whenever the universal is necessary the conclusion also must

15 be necessary. The demonstration is the same as before; 2
for the particular affirmative also is convertible. If then it
is necessary that B should belong to all C, and A falls under
C? it is necessary that B should belong to some A. But if B
must belong to some A, then A must belong to some B : for
conversion is possible. Similarly also if AC should be

20 necessary and universal : for B falls under C 4 But if the
particular premiss is necessary, the conclusion will not be
necessary. Let the premiss EC be both particular and
necessary, and let A belong to all C, not however necessarily.
If the proposition BC is converted the first figure is formed,

25 and the universal premiss is not necessary, but the particular
is necessary. But when the premisses were thus, the con
clusion (as we proved 5 ) was not necessary : consequently it

1 sc. necessarily. 2 a 24-33. 8 i- e - some C is A.

4 i.e. some C is B. c 30*35-7, b 1-5.

BOOK I. ii 31"

is not here either. Further, the point is clear if we look at
the terms. Let A be waking, B biped, and C animal. It is
necessary that B should belong to some C, but it is possible
for A to belong to C, and that A should belong to B is not 30
necessary. For there is no necessity that some biped should
be asleep or awake. Similarly and by means of the same
terms proof can be made, should the proposition AC be both
particular and necessary.

But if one premiss is affirmative, the other negative,
whenever the universal is both negative and necessary the
conclusion also will be necessary. For if it is not possible 35
that A should belong to any C, but B belongs to some C,
it is necessary that A should not belong to some B. But
whenever the affirmative proposition is necessary, whether
universal or particular, or the negative is particular, the
conclusion will not be necessary. The proof of this by
reduction will be the same as before; 1 but if terms are 40
wanted, when the universal affirmative is necessary, take
the terms waking animal man , man being middle,
and when the affirmative is particular and necessary, take 32*
the terms waking animal white : for it is necessary
that animal should belong to some white thing, but it is
possible that waking should belong to none, and it is not
necessary that waking should not belong to some animal.
But when the negative proposition being particular is
necessary, take the terms biped , moving , animal , 5
animal being middle.

12 It is clear then that a simple conclusion is not reached
unless both premisses are simple assertions, but a necessary
conclusion is possible although one only of the premisses is
necessary. But in both cases, whether the syllogisms are
affirmative or negative, it is necessary that one premiss 10
should be similar to the conclusion. I mean by similar ,
if the conclusion is a simple assertion, the premiss must be
simple ; if the conclusion is necessary, the premiss must be
necessary. Consequently this also is clear, that the con
clusion will be neither necessary nor simple unless a neces
sary or simple premiss is assumed.

1 Cf. a 37- b 4, 1( 20-7.

32 a ANALYTICA PRIORA

15 Perhaps enough has been said about the proof of 13
necessity, how it comes about and how it differs from the
proof of a simple statement. We proceed to discuss that
which is possible, when and how and by what means it can
be proved. I use the terms to be possible and the pos
sible of that which is not necessary but, being assumed,

20 results in nothing impossible. We say indeed ambiguously
of the necessary that it is possible. But that my definition
of the possible is correct is clear from the phrases by which
we deny or on the contrary affirm possibility. For the
expressions it is not possible to belong , it is impossible to
belong , and it is necessary not to belong are either iden
tical or follow from one another ; consequently their oppo-

25 sites also, it is possible to belong , it is not impossible to
belong , and it is not necessary not to belong , will either
be identical or follow from one another. For of everything
the affirmation or the denial holds good. That which is
possible then will be not necessary and that which is not
necessary will be possible. It results that all premisses in

30 the mode of possibility are convertible into one another.
I mean not that the affirmative are convertible into the
negative, but that those which are affirmative in form admit
of conversion by opposition, e.g. it is possible to belong
may be converted into it is possible not to belong , and
it is possible for A to belong to all B into it is possible
for A to belong to no B or not to all B , and it is possible

35 for A to belong to some B into it is possible for A not to
belong to some B . And similarly the other propositions
in this mode can be converted. For since that which is
possible is not necessary, and that which is not necessary
may possibly not belong, it is clear that if it is possible that
A should belong to />, it is possible also that it should not
belong to B : and if it is possible that it should belong to all,
it is also possible that it should not belong to all. The same

40 holds good in the case of particular affirmations : for the
32 b proof is identical. And such premisses are affirmative and
not negative ; for to be possible is in the same rank as
to be , as was said above. 1

1 2 b 21.

BOOK I. 13 3 2 b

Having made these distinctions we next point out that
the expression to be possible is used in two ways. In one 5
it means to happen generally and fall short of necessity,
e. g. man s turning grey or growing or decaying, or generally
what naturally belongs to a thing (for this has not its
necessity unbroken, since man s existence is not continuous
forever, although if a man does exist, it comes about either
necessarily or generally). In another sense the expression ro
means the indefinite, which can be both thus and not thus,
e. g. an animal s walking or an earthquake s taking place
while it is walking, or generally what happens by chance :
for none of these inclines by nature in the one way more
than in the opposite.

That which is possible in each of its two senses is con
vertible into its opposite, not however in the same way: 15
but what is natural is convertible because it does not neces
sarily belong (for in this sense it is possible that a man
should not grow grey x ) and what is indefinite is convertible
because it inclines this way no more than that. Science and
demonstrative syllogism are not concerned with things
which are indefinite, because the middle term is uncertain ;
but they are concerned with things that are natural, and 20
as a rule arguments and inquiries are made about things
which are possible in this sense. Syllogisms indeed can be
made about the former, but it is unusual at any rate to
inquire about them.

These matterswill be treated more definitely in the sequel ; 2
our business at present is to state the moods and nature of
the syllogism made from possible premisses. The expression
it is possible for this to belong to that may be understood 25
in two senses : that may mean either that to which that
belongs or that to which it may belong ; for the expression
A is possible of the subject of B means that it is possible
cither of that of which B is stated or of that of which B may
possibly be stated. It makes no difference whether we say,
A is possible of the subject of B, or all B admits of A. It is 3

1 i.e. it is because man does not necessarily grow grey that man
may grow grey is convertible into man may not grow grey .

2 Post. An. i. 8.

32 b ANALYTICA PRIORA

clear then that the expression A may possibly belong to
all B might be used in two senses. First then we must
state the nature and characteristics of the syllogism which
arises if B is possible of the subject of C, and A is possible
of the subject of B. For thus both premisses are assumed
35 in the mode of possibility ; but whenever A is possible of
that of which B is true, one premiss is a simple assertion,
the other a problematic. Consequently we must start from
premisses which are similar in form, 1 as in the other cases.

Whenever A may possibly belong to all B, and B to all C, 14
there will be a perfect syllogism to prove that A may possibly

40 belong to all C, This is clear from the definition : for it was
33 a in this way that we explained to be possible for one term
to belong to all of another . 2 Similarly if it is possible for A
to belong to no B, and for B to belong to all C, then it is
possible for A to belong to no C. For the statement that it
is possible for A not to belong to that of which B may be
true means (as we saw) that none of those things which can

5 possibly fall under the term B is left out of account. But
whenever A may belong to all B, and B may belong to
no C, then indeed no syllogism results from the premisses
assumed, but if the premiss EC is converted after the
manner of problematic propositions, the same syllogism
results as before. 3 For since it is possible that B should

10 belong to no C, it is possible also that it should belong to
all C. This has been stated above. 4 Consequently if B is
possible for all C, and A is possible for all B, the same
syllogism again results. Similarly if in both the premisses
the negative is joined with it is possible : e.g. if A may

15 belong to none of the />s, and B to none of the Cs. No
syllogism results from the assumed premisses, but if they
are converted we shall have the same syllogism as before/
It is clear then that if the minor premiss is negative, or if
both premisses are negative, either no syllogism results, or if

20 one does it is not perfect. For the necessity results from
the conversion.

1 Read n^oio(T\r]^mwv in 1. 37 with A.,, B, C, Al., Phil., and Waitz.

2 32 b 25-37. 3 In 32 38-40. 4 32*34.
5 Read oa-rrfp for u>s in 1. 17 with B.

BOOK I. 14 33*

But if one of the premisses is universal, the other particular,
when the major premiss is universal there will be a perfect
syllogism. For if A is possible for all B, and B for some C,
then A is possible for some C. This is clear from the
definition of being possible. 1 Again if A may belong to 25
no B, and B may belong to some of the Cs, it is necessary
that A may possibly not belong to some of the Cs. The
proof is the same as above. But if the particular premiss
is negative, and the universal is affirmative, the major still
being universal and the minor particular, e. g. A is possible
for all B, B may possibly not belong to some C, then a clear 3
syllogism does not result from the assumed premisses, but if
the particular premiss is converted and it is laid down that B
possibly may belong to some C, we shall have the same
conclusion as before, 2 as in the cases given at the beginning. 3

But if the major premiss is particular, the minor universal, 35
whether both are affirmative, or negative, or different in
quality, or if both are indefinite or particular, in no way
will a syllogism be possible. For nothing prevents B from
reaching beyond A, so that as predicates they cover unequal
areas. Let C be that by which B extends beyond A. To 6*4
it is not possible that A should belong either to all or to 33 b
none or to some or not to some, since premisses in the mode
of possibility are convertible and it is possible for B to
belong to more things than A can. Further, this is obvious
if we take terms ; for if the premisses are as assumed, the
major term is both possible for none of the minor and 5
must belong to all of it. Take as terms common to all the
cases under consideration animal white man , where
the major belongs necessarily to the minor ; animal
white garment , where it is not possible that the major
should belong to the minor. It is clear then that if the
terms are related in this manner, no syllogism results. For
every syllogism proves that something belongs either simply 10
or necessarily or possibly. It is clear that there is no proof
of the first or of the second. For the affirmative is destroyed
by the negative, and the negative by the affirmative. There
remains the proof of possibility. But this is impossible.
1 32^25-37. 2 1. 24. 3 11. 5-17.

645.24-S D

33 b ANALYTICA PRIORA

For it has been proved that if the terms are related in this
15 manner it is both necessary that the major should belong
to all the minor and not possible that it should belong to
any. Consequently there cannot be a syllogism to prove
the possibility ; for the necessary (as we stated) is not
possible. 1

It is clear that if the terms are universal in possible
premisses a syllogism always results in the first figure,
20 whether they are affirmative or negative, only a perfect
syllogism results in the first case, an imperfect in the
second. But possibility must be understood according to
the definition laid down, 2 not as covering necessity. This
is sometimes forgotten.

25 If one premiss is a simple proposition, the other a 15
problematic, whenever the major premiss indicates possi
bility all the syllogisms will be perfect and establish
possibility in the sense defined ; 3 but whenever the minor
premiss indicates possibility all the syllogisms will be
imperfect, and those which are negative will establish not

30 possibility according to the definition, but that the major
does not necessarily belong to any, or to all, of the minor.
For if this is so, we say it is possible that it should belong
to none or not to all. Let A be possible for all B> and let B
belong to all C. Since C falls under B, and A is possible for

35 all j5, clearly it is possible for all C also. So a perfect
syllogism results. Likewise if the premiss AB is negative,
and the premiss BC is affirmative, the former stating
possible, the latter simple attribution, a perfect syllogism

40 results proving that A possibly belongs to no C.

34 a It is clear that perfect syllogisms result if the minor

premiss states simple belonging : but that syllogisms will

result if the modality of the premisses is reversed, must be

proved per impossibile. At the same time it will be evident

that they are imperfect : for the proof proceeds not from

=, the premisses assumed. First we must state that if Z? s

being follows necessarily from A s being, It s possibility will

follow necessarily from A s possibility. Suppose, the terms

1 32*28. 2 32 a i8. 3 32*18.

BOOK I. 15 34 a

being so related, 1 that A is possible, and B is impossible.
If then that which is possible, when it is possible for it to
be, might happen, and if that which is impossible, when it
is impossible, could not happen, and if at the same time A J0
is possible and B impossible, it would be possible for A to
happen without B, and if to happen, then to be. For that
which has happened, when it has happened, is. But we
must take the impossible and the possible not only in the
sphere of becoming, but also in the spheres of truth and
predicability, and the various other spheres in which we
speak of the possible: for it will be alike in all. Further 15
we must understand the statement that B s being depends
on A s being, not as meaning that if some single thing A is,
B will be : for nothing follows of necessity from the being
of some one thing, but from two at least, i. c. when the
premisses are related in the manner stated to be that of the
syllogism. For if C is predicated of D, and D of F, then C 20
is necessarily predicated of F. And if each is possible, the
conclusion also is possible. If then, for example, one should
indicate the premisses by A, and the conclusion by B t it
would not only result that if A is necessary B is necessary,
but also that if A is possible, B is possible.

Since this is proved it is evident that if a false and not 25
impossible assumption is made, the consequence of the
assumption will also be false and not impossible : e. g. if A
is false, but not impossible, and if B is the consequence of A,
B also will be false but not impossible. For since it has
been proved that if B"s being is the consequence of A s
being, then Z>"s possibility will follow from A s possibility 30
(and A is assumed to be possible), consequently B will be
possible : for if it were impossible, the same thing would at
the same time be possible and impossible.

Since we have defined these points, let A belong to all B,
and B be possible for all C: it is necessary then that A 35
should be a possible attribute for all C. Suppose that it is
not possible, but assume that B belongs to all C: this is
false but not impossible. If then A is not possible for C
but B belongs to all C, then A is not possible for all B : for
1 That s being follows necessarily from A s being.
D 2

34 a ANALYTICA PRIORA

40 a. syllogism is formed in the third figure. But it was assumed

that A is a possible attribute for all B. It is necessary then

34 b that A is possible for all C. For though the assumption

we made l is false and not impossible, the conclusion is

impossible. 2 It is possible also in the first figure to bring

about the impossibility, by assuming that B belongs to C.

For if B belongs to all C, and A is possible for all B, then A

5 would be possible for all C. But the assumption was made

that A is not possible for all C.

We must understand that which belongs to all with no
limitation in respect of time, e. g. to the present or to a
particular period, but simply without qualification. For it
is by the help of such premisses that we make syllogisms,

10 since if the premiss is understood with reference to the
present moment, there cannot be a syllogism. For nothing
perhaps prevents man belonging at a particular time to
everything that is moving, i. e. if nothing else were moving :
but moving is possible for every horse ; yet man is
possible for no horse. Further let the major term be

15 animal , the middle moving , the minor man . The
premisses then will be as before, but the conclusion neces
sary, not possible. For man is necessarily animal. It is
clear then that the universal must be understood simply,
without limitation in respect of time.

Again let the premiss AB be universal and negative, and

20 assume that A belongs to no B y but B possibly belongs to
all C. These propositions being laid down, it is necessary
that A possibly belongs to no C. Suppose that it cannot
belong, and that B belongs to C, as above. 3 It is necessary
then that A belongs to some B : for we have a syllogism in

25 the third figure : but this is impossible. Thus it will be
possible for A to belong to no C; for if that is supposed
false, the consequence is an impossible one. This syllogism
then does not establish that which is possible according to
the definition, 4 but that which does not necessarily belong
to any part of the subject (for this is the contradictory of

1 That all C is B.

2 And therefore the other premiss, that A is not possible for all C,
must have been impossible.

8 a 36. 4 Cf. 32 a i8.

BOOK I. 15 84 1

the assumption which was made : for it was supposed that
A necessarily belongs to some C, but the syllogism per 3
impossibile establishes the contradictory which is opposed to
this). 1 Further, it is clear also from an example that the
conclusion will not establish possibility. Let A be raven ,
B intelligent , and C man . A then belongs to no B : for
no intelligent thing is a raven. But B is possible for all C\ 35
for every man may possibly be intelligent. But A neces
sarily belongs to no C\ so the conclusion does not establish
possibility. But neither is it always necessary. Let A be
moving , B science , C man . A then will belong to no B \
but B is ppssible for all C. And the conclusion will not be
necessary. For it is not necessary that no man should 4
move; rather it is not necessary that any man should move. 35
Clearly then the conclusion establishes that one term does
not necessarily belong to any instance of another term.
But we must take our terms better.

If the minor premiss is negative and indicates possibility,
from the actual premisses taken there can be no syllogism,
but if the problematic premiss is converted, a syllogism will =>
be possible, as before. 2 Let A belong to all B, and let B
possibly belong to no C. If the terms are arranged thus,
nothing necessarily follows : but if the proposition BC is
converted and it is assumed that B is possible for all C,
a syllogism results as before: 3 for the terms are in the 10
same relative positions. 4 Likewise if both the relations are
negative, if the major premiss states that A does not belong
to B, and the minor premiss indicates that B may possibly
belong to no C. Through the premisses actually taken
nothing necessary results in any way ; but if the problematic
premiss is converted, we shall have a syllogism. Suppose 15
that A belongs to no B. and B may possibly belong to no C.
Through these comes nothing necessary. But if B is
assumed to be possible for all C (and this is true) and if the
premiss AB remains as before, we shall again have the
same syllogism. But if it be assumed that B docs not *

1 Read a comma after \nrnp\f tv 1. 30 and remove the bracket to after
(iiTi^xicTfcos 1. 31.

2 33 a 7- 3 34 a 34 :

4 i.e. the major premiss is pure, the minor problematic.

35 a ANALYTICA PRIORA

belong to any C, instead of possibly not belonging, there
cannot be a syllogism anyhow, whether the premiss AB is
negative or affirmative. As common instances of a neces
sary and positive relation we may take the terms white
animal snow : of a necessary and negative relation, white-
animal pitch.

25 Clearly then if the terms are universal, and one of the
premisses is assertoric, the other problematic, whenever the
minor premiss is problematic a syllogism always results,
only sometimes it results from the premisses that are taken,
sometimes it requires the conversion of one premiss. We

30 have stated when each of these happens and the reason
why. But if one of the relations is universal, the other
particular, then whenever the major premiss is universal
and problematic, whether affirmative or negative, and the
particular is affirmative and assertoric, there will be a
perfect syllogism, just as when the terms are universal.

35 The demonstration is the same as before. 1 But whenever the
major premiss is universal, but assertoric, not problematic,
and the minor is particular and problematic, whether both
premisses are negative or affirmative, or one is negative, the
other affirmative, in all cases there will be an imperfect

40 syllogism. Only some of them will be proved per impossi-
35 b bile, others by the conversion of the problematic premiss,
as has been shown above. 2 And a syllogism will be possible
by means of conversion when the major premiss is universal
and assertoric, whether positive or negative, and the minor
5 particular, negative, and problematic, e. g. if A belongs to
all B or to no /?, and /> may possibly not belong to some C.
For if the premiss BC is converted in respect of possibility,
a syllogism results. But whenever the particular premiss is
assertoric and negative, there cannot be a syllogism. As
instances of the positive relation we may take the terms

10 white animal snow; of the negative, white animal-
pitch. For the demonstration must be made through the
indefinite nature of the particular premiss. 3 But if the
minor premiss is universal, and the major particular, whether
either premiss is negative or affirmative, problematic or
1 Cf. 33 b 33-40. 2 a i4. 3 Cf. 26 b i4, 2; b 2o.

BOOK I. 15 35

assertoric, nohow is a syllogism possible. Nor is a syllogism
possible when the premisses are particular or indefinite, 15
whether problematic or assertoric, or the one problematic,
the other assertoric. The demonstration is the same as
above. 1 As instances of the necessary and positive relation
we may take the terms animal white man ; of the neces
sary and negative relation, animal white garment. It is
evident then that if the major premiss is universal, a syllogism 20
always results, but if the minor is universal nothing at all can
ever be proved.

16 Whenever one premiss is necessary, the other problematic,
there will be a syllogism when the terms are related as
before ; ~ and a perfect syllogism when the minor premiss is 25
necessary. If the premisses arc affirmative the conclusion
will be problematic, not assertoric, whether the premisses
are universal or not : but if one is affirmative, the other
negative, when the affirmative is necessary the conclusion
will be problematic, not negative assertoric ; but when the 3
negative is necessary the conclusion will be problematic
negative, and assertoric negative, whether the premisses are
universal or not. Possibility in the conclusion must be
understood in the same manner as before. 3 There cannot
be an inference to the necessary negative proposition : for
not necessarily to belong is different from necessarily not 35
to belong .

If the premisses are affirmative, clearly the conclusionwhich
follows is not necessary. Suppose A necessarily belongs to all
B, and let B be possible for all C. We shall have an imper
fect syllogism to prove that A may belong to all C. That
it is imperfect is clear from the proof: for it will be proved 4
in the same manner as above. 4 Again, let A be possible 3&
for all Z>, and let B necessarily belong to all C. We shall
then have a syllogism to prove that A may belong to all C,
not that A does belong to all C\ and it is perfect, not 5
imperfect : for it is completed directly through the original
premisses.

But if the premisses are not similar in quality, suppose

1 33 a 34~ lj i7- 2 Cf. a 25- b 8. 3 33 h 29, 34 b 2?- " 34 a 34- lj 6.

b

36 a ANALYTICA PRIORA

first that the negative premiss is necessary, and let A
necessarily not be possible for any J3, but let B be possible

10 for all C. It is necessary then that A belongs to no C. For
suppose A to belong to all C or to some C. Now we
assumed that A is not possible for any B. Since then the
negative proposition is convertible, B is not possible for
any A. But A is supposed to belong to all C or to some C.
Consequently B will not be possible for any C or for all C.

15 But it was originally laid down that B is possible for all C.
And it is clear that the possibility of not belonging can be
inferred, since the fact of not belonging is inferred. Again, let
the affirmative premiss be necessary, and let A possibly not
belong to any B, and let B necessarily belong to all C.

20 The syllogism will be perfect, but it will establish a proble
matic negative, not an assertoric negative. For the major
premiss was problematic, and further it is not possible to
prove the assertoric conclusion per impossibile. For if it were
supposed that A belongs to some C, and it is laid down that A
possibly does not belong to any B, no impossible relation
between B and C follows from these premisses. But if the

25 minor premiss is* negative, when it is problematic a
syllogism is possible by conversion, as above ; * but when
it is necessary no syllogism can be formed. Nor again
when both premisses are negative, and the minor is neces
sary. The same terms as before 2 serve both for the positive

30 relation white animal snow, and for the negative rela
tion white animal pitch.

The same relation will obtain in particular syllogisms.
Whenever the negative proposition is necessary, the con
clusion will be negative assertoric : e. g. if it is not possible

35 that A should belong to any B, but B may belong to some
of the Cs, it is necessary that A should not belong to some
of the Cs. For if A belongs to all C, but cannot belong to
any B, neither can B belong to any A. So if A belongs to
all C, to none of the Cs can B belong. But it w r as laid down
that B may belong to some C. But when the particular

40 affirmative in the negative syllogism, e.g. BC the minor pre
miss, or the universal proposition in the affirmative syllogism,
1 35 b 7- Cf. 33*7. 2 35^10,

BOOK I. 16 36

e.g. AB the major premiss, is necessary, there will not be an 36
assertoric conclusion. The demonstration is the same*as
before. 1 But if the minor premiss is universal, and pro
blematic, whether affirmative or negative, and the major
premiss is particular and necessary, there cannot be a syllo- 5
gism. Premisses of this kind are possible both where the
relation is positive and necessary, e. g. animal white
man, and where it is necessary and negative, e. g. animal-
white garment. But when the universal is necessary, the
particular problematic, if the universal is negative we may
take the terms animal white raven to illustrate the posi
tive relation, or animal white pitch to illustrate the 10
negative ; and if the universal is affirmative we may take
the terms animal white swan to illustrate the positive rela
tion, and animal white snow to illustrate the negative and
necessary relation. Nor again is a syllogism possible when
the premisses are indefinite, or both particular. Terms
applicable in either case to illustrate the positive relation
are animal white man : to illustrate the negative, animal
white inanimate. For the relation of animal to some 15
white, and of white to some inanimate, is both necessary
and positive and necessary and negative. Similarly if the
relation is problematic : so the terms may be used for all
cases.

Clearly then from what has been said a syllogism results
or not from similar relations of the terms whether we are 20
dealing with simple existence or necessity, with this excep
tion, that if the negative premiss is assertoric the conclusion
is problematic, but if the negative premiss is necessary
the conclusion is both problematic and negative assertoric.
[It is clear also that all the syllogisms are imperfect and are
perfected by means of the figures above mentioned. 2 ] 2 5

17 In the second figure whenever both premisses are pro
blematic, no syllogism is possible, whether the premisses are
affirmative or negative, universal or particular. But when
one premiss is assertoric, the other problematic, if the

1 a i 9-25.

2 Maier, Syllogistik des Aristoieles, ii. I. 176, n. 2, shows that this
sentence has been wrongly introduced from 39* I.

36 b ANALYTICA PRIORA

30 affirmative is assertoric no syllogism is possible, but if the
universal negative is assertoric a conclusion can always be
drawn. Similarly when one premiss is necessary, the
other problematic. Here also we must understand the term
possible in the conclusions, in the same sense as before. 1

35 First we must point out that the negative problematic
proposition is not convertible, e.g. if A may belong to no /> ,
it does not follow that R may belong to no A. For suppose
it to follow and assume that B may belong to no A. Since
then problematic affirmations are convertible with negations,

40 whether they are contraries or contradictories, and since B
37 a may belong to no A, it is clear that B may belong to all A.
But this is false: for if all this can be that, it does not
follow that all that can be this : consequently the negative
proposition is not convertible. Further, these propositions
are not incompatible, A may belong to no B , B neces-
5 sarily does not belong to some of the As ; e.g. it is possible
that no man should be white (for it is also possible that
every man should be white), but it is not true to say that it
is possible that no white thing should be a man: for many
white things are necessarily not men, and the necessary (as
we saw 2 ) is other than the possible.

Moreover it is not possible to prove the convertibility of

10 these propositions by a reductio ad absurdnm, i. e. by claim
ing assent to the following argument : since it is false
that B may belong to no A, it is true that it cannot belong
to no A, for the one statement is the contradictory of the
other. But if this is so, it is true that B necessarily belongs
to some of the As : consequently A necessarily belongs to
some of the Us. But this is impossible. :! The argument
cannot be admitted, for it does not follow that some A is

15 necessarily B, if it is not possible that no A should be B.
For the latter expression is used in two senses, one if
some A is necessarily B, another if some A is necessarily
not B. For it is not true to say that that which necessarily
does not belong to some of the As may possibly not belong
to any A, just as it is not true to say that what necessarily

1 33 b 29, 34 b 2;. * 32 a 28.

5 Colon after B, full stop after u&vv.irov in 1. 14, with Maier.

BOOK I. 17 37*

belongs to some A may possibly belong to all A. If any 20
one then should claim that because it is not possible for C
to belong to all D, it necessarily does not belong to some D,
he would make a false assumption : for it does belong to
all D, but because in some cases it belongs necessarily,
therefore we say that it is not possible for it to belong to
all. Hence both the propositions A necessarily belongs to
some B and A necessarily does not belong to some B 25
are opposed to the proposition A may belong to all B .
Similarly also they arc opposed to the proposition A may
belong to no B . It is clear then that in relation to what
is possible and not possible, in the sense originally defined, 1
we must assume, not that A necessarily belongs to some B,
but that A necessarily does not belong to some B. But if
this is assumed, no absurdity results : consequently no 30
syllogism. It is clear from what has been said that the
negative proposition is not convertible. 2

This being proved, suppose it possible that A may belong
to no B and to all C, By means of conversion no syllogism
will result : for the major premiss, as has been said, is not
convertible. Nor can a proof be obtained by a rednctio ad 35

1 32 a i8.

2 The argument put into the mouth of Aristotle s opponent in
11. 10-14 is as follows :

If A may be true of no B, B may be true of no A.

(X) For if not, B cannot be true of no A.

( Y) . /. B must be true of some A.
. . A must be true of some B.

But this is impossible, since ex hypothesi A may be true of no B.
. . B may be true of no A.

Aristotle s criticism in 11. 14-31 is as follows :

The step from X to Y is unsound. B must be true of some A is
not the only alternative to B may be true of no A . There is also
the alternative B must be untrue of some A . Necessity, not only the
necessity that some B be A, but equally the necessity that some B be
not A, is incompatible with the possibility that no B be A.

The proper inference then in place of (Y) is Either B must be true
of some A, or B must be untrue of some A . And from the second
alternative no impossible conclusion follows, so that the proof per
impossibile that B may be true of no A fails.

Waltz s reading in 1. 28 ov m wtv (cod. B) TO e ai>uyKT]s . . . dXXa KU\
(BC) TO f dvdyicrjs is supported by Philop. and Them. But Al. has the
lectio difficilior without \i6vov and KIH, and the other is evidently only an
attempt to make things easier. Not either alternative, nor both, but
the disjunction of the two, is the proper inference from X. But in
answer to the opponent s assumption of Y we must make the counter-
assumption B must be untrue of some A .

37 a ANALYTICA PRIORA

absurdum : for if it is assumed that B can belong to all C, 1
no false consequence results : for A may belong both to all
C and to no C. In general, if there is a syllogism, it is clear
that its conclusion will be problematic because neither of

40 the premisses is assertoric ; and this must be either affirma
tive or negative. But neither is possible. Suppose the con-
37 b elusion is affirmative : it will be proved by an example
that the predicate cannot belong to the subject. Suppose
the conclusion* is negative : it will be proved that it is not
problematic but necessary. Let A be white, B man, C
5 horse. It is possible then for A to belong to all of the one
and to none of the other. But it is not possible for B to
belong nor not to belong to C. That it is not possible for
it to belong, is clear. For no horse is a man. Neither is
it possible for it not to belong. For it is necessary that no
horse should be a man, but the necessary we found to be

10 different from the possible. 2 No syllogism then results.
A similar proof can be given if the major premiss is nega
tive, the minor affirmative, or if both are affirmative or
negative. The demonstration can be made by means of
the same terms. And whenever one premiss is universal,
the other particular, or both are particular or indefinite, or

15 in whatever other way the premisses can be altered, the
proof will always proceed through the same terms. Clearly
then, if both the premisses are problematic, no syllogism
results.

But if one premiss is assertoric, the other problematic, 18
ao if the affirmative is assertoric and the negative problematic
no syllogism will be possible, whether the premisses are
universal or particular. The proof is the same as above,
and by means of the same terms. But when the affirma
tive premiss is problematic, and the negative assertoric,
25 we shall have a syllogism. Suppose A belongs to no B,
but can belong to all C. If the negative proposition is
converted, B will belong to no A. But A ex JiypotJiesi can

1 If Aristotle is to be saved from a fallacious inference we must, with
Maier, in 11. 35, 36 insert /xi} before navri and before \>napx (LV - But in
view of the consent of the MSS. and the ancient commentators the
mistake seems to go back to Aristotle.

32* 28.

BOOK I. 18 37 b

belong to all C: so a syllogism is made, proving by means
of the first figure that B may belong to no C. Similarly
also if the minor premiss is negative. But if both premisses
are negative, one being assertoric. the other problematic, 30
nothing follows necessarily from these premisses as they
stand, but if the problematic premiss is converted into its
complementary affirmative l a syllogism is formed to prove
that B may belong to no C, as before : for we shall again
have the first figure. But if both premisses are affirmative, 35
no syllogism will be possible. This arrangement of terms
is possible both when the relation is positive, e. g. health,
animal, man, and when it is negative, e.g. health, horse,
man.

The same will hold good if the syllogisms are particular. 40
Whenever the affirmative proposition is assertoric, whether
universal or particular, no syllogism is possible (this is 38 a
proved similarly and by the same examples as above), but
when the negative proposition is assertoric, a conclusion
can be drawn by means of conversion, as before. Again if
both the relations are negative, and the assertoric proposi- 5
tion js universal, although no conclusion follows from the
actual premisses, a syllogism can be obtained by converting
the problematic premiss into its complementary affirmative
as before. But if the negative proposition is assertoric, but
particular, no syllogism is possible, whether the other pre
miss is affirmative or negative. Nor can a conclusion be 10
drawn when both premisses are indefinite, whether affirma
tive or negative, or particular. The proof is the same and
by the same terms.

19 If one of the premisses is necessary, the other problematic,
then if the negative is necessary a syllogistic conclusion can
be drawn, not merely a negative problematic but also a 15
negative assertoric conclusion ; but if the affirmative premiss
is necessary, no conclusion is possible. Suppose that A
necessarily belongs to no />, but may belong to all C. If
the negative premiss is converted B will belong to no A :
but A ex hypothesi is capable of belonging to all C: so once

1 Cf. 32*29.

38 a ANALYTICA PRIORA

20 more a conclusion is drawn by the- first figure that B may
belong to no C. But at the same time it is clear that B will
not belong to any C. For assume that it does : then if A
cannot belong to any B, and B belongs to some of the Cs,
A cannot belong to some of the Cs : but ex hypothesi it

25 may belong to all. A similar proof can be given if the minor
premiss is negative. Again let the affirmative proposition
be necessary, and the other problematic; i.e. suppose that
A may belong to no B, but necessarily belongs to all C.
When the terms are arranged in this way, no syllogism is

30 possible. For (i) it sometimes turns out that B necessarily
does not belong to C. Let A be white, B man, C swan.
White then necessarily belongs to swan, but may belong to
no man ; and man necessarily belongs to no swan. Clearly
then we cannot draw a problematic conclusion ; for that

35 which is necessary is admittedly distinct from that which is
possible. (2) Nor again can we draw a necessary conclusion :
for that presupposes that both premisses are necessary, or at
any rate the negative premiss. 1 (3) Further it is possible
also, when the terms are so arranged, that B should belong
to C: for nothing prevents C falling under B,A being possible

40 for all B, and necessarily belonging to C; e.g. if C stands

for awake , B for animal , A for motion . For motion

38 b necessarily belongs to what is awake, and is possible for

every animal : and everything that is awake is animal.

Clearly then the conclusion cannot be the negative assertion,

if the relation must be positive when the terms are related

as above. Nor can the opposite affirmations 2 be established :

consequently no syllogism is possible, A similar proof is

5 possible if the major premiss is affirmative.

But if the premisses are similar in quality, when they are
negative a syllogism can always be formed by converting
the problematic premiss into its complementary affirmative
as before. 3 Suppose A necessarily does not belong to />,

1 Cf. 30^7, 31*21.

2 Read Kara</>uo-a>r in 1. 4 with cod. n, Al. [Amm.j, and Waitz. The
opposite affirmations are

Cmay be#
C must be B
C\s .

3 Cf. 32 a 29.

BOOK I. 19 38*

and possibly may not belong to C: if the premisses are 10
converted B belongs to no A, and A may possibly belong
to all C: thus we have the first figure. Similarly if the
minor premiss is negative. 1 But if the premisses are affirma
tive there cannot be a syllogism. Clearly the conclusion
cannot be a negative assertoric or a negative necessary 15
proposition because no negative premiss has been laid down
either in the assertoric or in the necessary mode. Nor can
the conclusion be a problematic negative proposition. For
if the terms are so related, there are cases in which B neces
sarily will not belong to C; e.g. suppose that A is white, 20
B swan, C man. Nor can the opposite affirmations 2 be
established, since we have shown a case in which B neces
sarily does not belong to C. A syllogism then is not
possible at all.

Similar relations will obtain in particular syllogisms. For
whenever the negative proposition is universal and necessary, 25
a syllogism will always be possible to prove both a pro
blematic and a negative assertoric proposition (the proof
proceeds by conversion) ; but when the affirmative proposi
tion is universal and necessary, no syllogistic conclusion can
be drawn. This can be proved in the same way as for
universal propositions, and by the same terms. 3 Nor is
a syllogistic conclusion possible when both premisses are 30
affirmative : this also may be proved as above. 4 But when
both premisses are negative, and the premiss that definitely
disconnects two terms is universal and necessary, 5 though
nothing follows necessarily from the premisses as they are
stated, a conclusion can be drawn as above c if the pro
blematic premiss is converted into its complementary affirma- 35
tive. But if both are indefinite or particular, no syllogism
can be formed. The same proof will serve, and the same
terms. 7

1 sc. and necessary.

" Read KririKpaa-fui in 1. 21 with Al. and Waitz.

3 Cf. a 26- 1J 5. 4 11. 12-23.

And necessary is pointless, as the whole chapter is concerned
only with combinations of a necessary with a problematic premiss.
Possibly we should read fj for KCU in 1. 32. The reading of Al. s lemma
(TTfprjTiKai Kal xadoXov <5e avaynaia suggests that Kai may have originated
by dittography. 6 11. 25-7. 7 Cf. 36 b 12-18.

38 b ANALYTICA PRIORA

It is clear then from what has been said that if the uni
versal and negative premiss is necessary, a syllogism is
40 always possible, proving not merely a negative problematic,
but also a negative assertoric proposition ; but if the affirma
tive premiss is necessary no conclusion can be drawn. It is
clear too that a syllogism is possible or not under the same
3g a conditions whether the mode of the premisses is assertoric or
necessary. And it is clear that all the syllogisms are im
perfect, and are completed by means of the figures mentioned.

In the last figure a syllogism is possible whether both or 2O
5 only one of the premisses is problematic. When the pre
misses are problematic the conclusion will be problematic ;
and also when one premiss is problematic, the other assertoric.
But when the other premiss is necessary, if it is affirmative
the conclusion will be neither necessary nor assertoric ; but

10 if it is negative the syllogism will result in a negative
assertoric proposition, as above. 1 In these also we must
understand the expression possible in the conclusion in
the same way as before.

First let the premisses be problematic and suppose that

15 both A and B may possibly belong to every C. Since then
the affirmative proposition is convertible into a particular,
and B may possibly belong to every C, it follows that C may
possibly belong to some B. So, if A is possible for every C,
and C is possible for some of the Bs, then A is possible for
some of the Bs. For we have got the first figure. And if

20 A may possibly belong to no C, but B may possibly belong
to all C, it follows that A may possibly not belong to some
B\ for we shall have the first figure again byconversion.
But if both premisses should be negative no necessary con
sequence will follow from them as they are stated, but if the

25 premisses are converted into their corresponding affirmatives
there will be a syllogism as before. For if A and B may
possibly not belong to C, if may possibly belong is sub
stituted we shall again have the first figure by means of
conversion. But if one of the premisses is universal, the other
particular, a syllogism will be possible, or not, under the

BOOK I. 20 39

same arrangement of the terms as in the case of assertonc 30
propositions. Suppose that A may possibly belong to all
C, and B to some C. We shall have the first figure again
if the particular premiss is converted. For if A is possible
for all C, and C for some of the ^s, then A is possible for
some of the Bs. Similarly if the proposition BC is universal. 35
Likewise also if the proposition AC is negative, and the
proposition B C affirmative : for we shall again have the first
figure by conversion. But if both premisses should be nega
tive the one universal and the other particular although
no syllogistic conclusion will follow from the premisses as 3g
they are put, it will follow if they are converted, as above.
But when both premisses are indefinite or particular, no
syllogism can be formed : for A must belong sometimes
to all B and sometimes to no B. To illustrate the affirmative
relation take the terms animal man white ; to illustrate 5
the negative, take the terms horse man white white
being the middle term.

21 If one premiss is pure, the other problematic, the con
clusion will be problematic, not pure ; and a syllogism will
be possible under the same arrangement of the terms as 10
before. 1 First let the premisses be affirmative : suppose
that A belongs to all C, and B may possibly belong to all C.
If the proposition BC is converted, we shall have the first
figure, and the conclusion that A may possibly belong to
some of the >s. For when one of the premisses in the first 15
figure is problematic, the conclusion also (as we saw 2 ) is
problematic. Similarly if the proposition BC is pure, A C
problematic ; or if AC is negative, BC affirmative, no matter
which of the two is pure ; in both cases the conclusion will
be problematic : for the first figure is obtained once more, 20
and it has been proved that if one premiss is problematic in
that figure the conclusion also will be problematic. But
if the minor premiss BC is negative," or if both premisses
are negative, no syllogistic conclusion can be drawn from

1 i.e. where the premisses were pure, or problematic.

2 33 b 25-40.

3 Omit tvdex6fj.vov in 1. 22 with cod. n, Al., Phil., Them., and Waitz.
eVSexo/^et/oi/ can easily be supplied in thought, since it is obvious that
a negative assertoric minor gives no conclusion in the third figure.

C45.24-S E

39 b ANALYTICA PRIORA

the premisses as they stand, but if they are converted a

25 syllogism is obtained as before.

If one of the premisses is universal, the other particular,
then when both are affirmative, or when the universal is
negative, the particular affirmative, we shall have the same
sort of syllogisms : for all are completed by means of the

30 first figure. So it is clear that we shall have not a pure but
a problematic syllogistic conclusion. But if the affirmative
premiss is universal, the negative particular, the proof will
proceed by a reductio ad impossibilc. Suppose that B belongs
to all C, and A may possibly not belong to some C: it

35 follows that A may possibly not belong to some B. For if
A necessarily belongs to all /?, and B (as has been assumed)
belongs to all C. A will necessarily belong to all C: for this
has been proved before. 1 But it was assumed at the outset
that A may possibly not belong to some C.
4O a Whenever both premisses are indefinite or particular, no
syllogism will be possible. The demonstration is the same
as was given in the case of universal premisses, 2 and proceeds
by means of the same terms.

If one of the premisses is necessary, the other problematic, 22
5 when the premisses are affirmative a problematic affirmative
conclusion can always be drawn ; when one proposition is
affirmative, the other negative, if the affirmative is necessary
a problematic negative can be inferred ; but if the negative
proposition is necessary both a problematic and a pure
negative conclusion are possible. But a necessary negative

10 conclusion will not be possible, any more than in the other
figures. Suppose first that the premisses are affirmative,
i. e. that A necessarily belongs to all C, and B may possibly
belong to all C. Since then A must belong to all C, and C
may belong to some B, it follows that A may (not does)

15 belong to some B: for so it resulted 3 in the first figure.
A similar proof may be given if the proposition BC is
necessary, and AC is problematic. Again suppose one

1 3o a is-23.

2 No such demonstration occurs in the discussion of the case of two
universal premisses. The reference is a careless one to the discussion
of the case of two problematic premisses, 39* 2-6.

3 35 a 26-8.

BOOK I. 22 40 a

proposition is affirmative, the other negative, the affirmative
being necessary : i. e. suppose A may possibly belong to
no C, but B necessarily belongs to all C. We shall have 20
the first figure once more : and since the negative premiss
is problematic it is clear that the conclusion will be pro
blematic: forwhen the premisses stand thus in the first figure,
the conclusion (as we found l ) is problematic. But if the
negative premiss is necessary, the conclusion will be not 25
only that A may possibly not belong to some B but also
that it does not belong to some B. For suppose that A
necessarily does not belong to C, but B may belong to all C.
If the affirmative proposition BC is converted, we shall have
the first figure, and the negative premiss is necessary. But
when the premisses stood thus, it resulted 2 that A might 3
possibly not belong to some C, and that it did not belong
to some C ; consequently here it follows that A does not
belong to some B. But when the minor premiss is negative,
if it is problematic we shall have a syllogism by altering
the premiss into its complementary affirmative, as before ; 35
but if it is necessary no syllogism can be formed. For A
sometimes necessarily belongs to all B, and sometimes cannot
possibly belong to any B. To illustrate the former take the
terms sleep sleeping horse man ; to illustrate the latter
take the terms sleep waking horse man.

Similar results will obtain if one of the terms is related
universally to the middle, the other in part. If both pre- 40
misses are affirmative, the conclusion will be problematic, not 4o b
pure ; and also when one premiss is negative, the other
affirmative, the latter being necessary. But when the nega
tive premiss is necessary, the conclusion also will be a pure
negative proposition ; for the same kind of proof can be 5
given whether the terms arc universal or not. For the
syllogisms must be made perfect by means of the first
figure, so that a result which follows in the first figure
follows also in the third. But when the minor premiss is
negative and universal, if it is problematic a syllogism can 10
be formed by means of conversion ; but if it is necessary
a syllogism is not possible. The proof will follow the same

E 2

40 b ANALYTICA PRIORA

course as where the premisses arc universal ; and the same
terms may be used.

It is clear then in this figure also when and how a syllo
gism can be formed, and when the conclusion is problematic,
and when it is pure. It is evident also that all syllogisms in
15 this figure are imperfect, and that they are made perfect by
means of the first figure.

It is clear from what has been said that the syllogisms in 23
these figures are made perfect by means of universal syllo
gisms in the first figure and are reduced to them. That

20 every syllogism without qualification can be so treated, will
be clear presently, when it has been proved that every
syllogism is formed through one or other of these figures.

It is necessary that every demonstration and every syllo
gism should prove either that something belongs or that it

25 does not, and this either universally or in part, and further
either ostensively or hypothetically. One sort of hypothetical
proof is the reductio ad impossibile. Let us speak first of
ostensive syllogisms : for after these have been pointed out
the truth of our contention will be clear with regard to those
which are proved per impossibile, and in general hypothe
tically.

30 If then one wants to prove syllogistically A of B, either
as an attribute of it or as not an attribute of it, one must
assert something of something else. If now A should be
asserted of fi, the proposition originally in question will have
been assumed. But if A should be asserted of C, but C
should not be asserted of anything, nor anything of it, nor
anything else of A, no syllogism will be possible. For

35 nothing necessarily follows from the assertion of some one
thing concerning some other single thing. Thus we must
take another premiss as well. If then A be asserted of
something else, or something else of A, or something
different of C, nothing prevents a syllogism being formed,
but it will not be in relation to B through the premisses

4 o taken. Nor when C belongs to something else, and that to

something else and so on, no connexion however being made

4i a with B, will a syllogism be possible concerning A in its

BOOK I. 23 41*

relation to /?. For in general \vc stated l that no syllogism
can establish the attribution of one thing to another, unless
some middle term is taken, which is somehow related to
each by way of predication. For the syllogism in general
is made out of premisses, and a syllogism referring to this 5
out of premisses with the same reference, and a syllogism
relating this to tJiat proceeds through premisses which relate
this to that. But it is impossible to take a premiss in
reference to B. if we neither affirm nor deny anything of it ;
or again to take a premiss relating A to B, if we take
nothing common, but affirm or deny peculiar attributes of 10
each. So we must take something midway between the
two, which will connect the predications, if we are to have
a syllogism relating this to that. If then we must take
something common in relation to both, and this is possible
in three ways (either by predicating A of C, and C of B, or C 15
of both, or both of C), and these are the figures of which we
have spoken, it is clear that every syllogism must be made
in one or other of these figures. The argument is the same
if several middle terms should be necessary to establish the
relation to B ; for the figure will be the same whether there
is one middle term or many. 20

It is clear then that the ostensive syllogisms are effected
by means of the aforesaid figures ; these considerations will
show that rcdnctiones ad impossibile also are effected in the
same way. For all who effect an argument per impossibile
infer syllogistically what is false, and prove the original con
clusion hypothetically when something impossible results 2 5
from the assumption of its contradictory ; e. g. that the
diagonal of the square is incommensurate with the side,
because odd numbers are equal to evens if it is supposed to
be commensurate. 2 One infers syllogistically that odd
numbers come out equal to evens, and one proves hypo
thetically the incommensurability of the diagonal, since
a falsehood results through contradicting this. For this 3
we found to be reasoning /w impossibile ^ viz. proving some-

1 Cf. 25" 32.

2 The proof is given in Euclid, Elements, Bk. x, App. 27 (ed.
Heiberg and Menge). Cf. B. Russell, Introduction to Mathematical
Philosophy, p. 67.

4i a ANALYTICA PRIORA

thing impossible by means of an hypothesis conceded at the
beginning. Consequently, since the falsehood is established
in reductions ad impossibile by an ostensive syllogism, and
the original conclusion is proved hypothetically, and we have
35 already stated that ostensive syllogisms are effected by
means of these figures, it is evident that syllogisms per
impossibile also will be made through these figures. Like
wise all the other hypothetical syllogisms : for in every case
the syllogism leads up to the proposition that is substituted
40 for the original thesis ; but the original thesis is reached by
means of a concession or some other hypothesis. 1 But if
4l b this is true, every demonstration and every syllogism must
be formed by means of the three figures mentioned above.
But when this has been shown it is clear that every syllogism
is perfected by means of the first figure and is reducible to
5 the universal syllogisms in this figure.

Further in every syllogism one of the premisses must be 24
affirmative, and universality must be present : unless one of
the premisses is universal either a syllogism will not be
possible, or it will not refer to the subject proposed, or the
original position will be begged. Suppose we have to prove

10 that pleasure in music is good. If one should claim as
a premiss that pleasure is good without adding all ,
no syllogism will be possible ; if one should claim that some
pleasure is good, then if it is different from pleasure in
music, it is not relevant to the subject proposed ; if it is
this very pleasure, one is assuming that which was proposed
at the outset to be proved. This is more obvious in geo
metrical proofs, e. g. that the angles at the base of an isosceles

15 triangle are equal. Suppose the lines A and B have been
drawn to the centre. If then one should assume that the
angle AC is equal to the angle BD, without claiming
generally that angles of semicircles are equal ; and again if
one should assume that the angle C is equal to the angle Z>,
without the additional assumption that every angle of

1 Aristotle is thinking of the method of establishing a proposition A
is B by inducing the opponent to agree that A is B if X is Y. All
that remains then is to establish syllogistically that X is Y, That A
is B thus follows from the agreement.

BOOK I. 24 41

a segment is equal to every other angle of the same segment ;
and further if one should assume that when equal angles are
taken from the whole angles, which are themselves equal,
the remainders E and F are equal, he will beg the thing to 20
be proved, unless he also states that when equals are taken
from equals the remainders are equal. 1

It is clear then that in every syllogism there must be
a universal premiss, and that a universal statement is
proved only when all the premisses are universal, while a
particular statement is proved both from two universal
premisses and from one only : consequently if the conclusion
is universal, the premisses also must be universal, but if the 25

1 The diagram Aristotle has in mind appears to be the following :

Here A and B are the equal sides, E and F the angles at the base
of the isosceles triangle. C and D are the angles formed by the base
with the circumference. The angles formed by the equal sides with
the base are loosely called A C, BD. That the angles of the semicircle
of the segment mean those formed by the diameter and the chord
respectively with the circumference (as supposed by Al., Phil., Pacius,
and Blancanus), not those in the semicircle and in the segment (as
supposed by Waitz) seems to be sufficiently indicated by the language
of Euclid, iii. 16, 31. Contrast /; eV ^iKvxXi w, Post, An, 94*28, Met.

4i b ANALYTICA PRIORA

premisses arc universal it is possible that the conclusion may
not be universal. And it is clear also that in every syllogism
either both or one of thepremisses must be like the conclusion.
I mean not only in being affirmative or negative, but also in

30 being necessary, pure, or problematic. We must consider
also the other forms of predication.

It is clear also when a syllogism in general can be made
and when it cannot ; and when a valid, 1 when a perfect
syllogism can be formed ; and that if a syllogism is formed
the terms must be arranged in one of the ways that have

35 been mentioned.

It is clear too that every demonstration will proceed 25
through three terms and no more, unless the same conclusion
is established by different pairs of propositions ; e. g. the
conclusion E may be established through the propositions
A and B, and through the propositions C and D, or through
the propositions A and B, or A and 7, or B and C. 2 For

40 nothing prevents there being several middles for the same
terms. But in that case there is not one but several
42 a syllogisms. Or again when each of the propositions A and
B is obtained by syllogistic inference, e. g. A by means of
D and E, and again B by means of F and G. Or one may
be obtained by syllogistic, the other by inductive inference.
But thus also the syllogisms are many ; for the conclusions
5 are many, e. g. A and B and C. But if this can be
called one syllogism, not many, the same conclusion may be
reached by more than three terms in this way, but it cannot
be reached as C is established by means of A and B:
Suppose that the proposition E is inferred from the premisses
A, B, C, and D. It is necessary then that of these one

10 should be related to another as whole to part : for it has
already been proved that if a syllogism is formed some of
its terms must be related in this way. 4 Suppose then that
A stands in this relation to B. Some conclusion then

1 sc.but imperfect.

2 Insert *m AF after AB in 1. 39 with A 2 , C, Al., Phil., and Waitz.

3 i.e. by way of a simple syllogism. This is incompatible with there
being more than three terms.

BOOK I. 25 42*

follows from them. It must cither be E or one or other of
C and D, or something other than these.

(1) If it is E the syllogism will have/4 and/) for its sole 15
premisses. But if C and D are so related that one is whole,
the other part, some conclusion will follow from them also ;
and it must be either E, or one or other of the propositions

A and /?, or something other than these. And if it is (i) E,
or (ii) A or B, either (i) the syllogisms will be more than one,
or (ii) the same thing happens to be inferred by means of
several terms only in the sense which we saw to be possible. 1
But if (iii) the conclusion is other than E or A or B, the 2 o
syllogisms will be many, and unconnected with one another.
But if C is not so related to D as to make a syllogism, the
propositions will have been assumed to no purpose, unless
for the sake of induction or of obscuring the argument or
something of the sort.

(2) But if from the propositions A and B there follows not
E but some other conclusion, and if from C and D either A or 25
B follows or something else, then there are several syllogisms,
and they do not establish the conclusion proposed : for we
assumed that the syllogism proved E. And if no conclusion
follows from C and D, it turns out that these propositions
have been assumed to no purpose, and the syllogism does
not prove the original proposition. 30

So it is clear that every demonstration and every syllogism
will proceed through three terms only.

This being evident, it is clear that a syllogistic conclusion
follows from two premisses and not from more than two.
For the three terms make two premisses, unless a new
premiss is assumed, as was said at the beginning, 2 to perfect
the syllogisms. It is clear therefore that in whatever 35
syllogistic argument the premisses through which the main
conclusion follows (for some of the preceding conclusions
must be premisses) are not even in number, this argument
either has not been drawn syllogistically or it has assumed
more than was necessary to establish its thesis. 4

1 1.6.

2 The reference is to the new premisses produced by conversion,
when a syllogism in the second or third figure is being reduced to one
in the first. Cf. 24^24.

4 2 b ANALYTICA PRIORA

42 b If then syllogisms are taken with respect to their main
premisses, every syllogism will consist of an even number of
premisses and an odd number of terms (for the terms exceed
the premisses by one), and the conclusions will be half the

5 number of the premisses. But whenever a conclusion is
reached by means of prosyllogisms or by means of several
continuous middle terms, 1 e. g. the proposition AH by means
of the middle terms C and D, the number of the terms will
similarly exceed that of the premisses by one (for the extra
term must either be added outside or inserted : but in either
case it follows that the relations of predication are one fewer

10 than the terms related), and the premisses will be equal in
number to the relations of predication. The premisses how
ever will not always be even, the terms odd ; but they will
alternate when the premisses are even, the terms must be
odd ; when the terms are even, the premisses must be odd :
for along with one term one premiss is added, if a term is
added from any quarter. Consequently since the premisses

15 were (as we saw) even, and the terms odd, we must make
them alternately even and odd at each addition. But the
conclusions will not follow the same arrangement either in
respect to the terms or to the premisses. For if one term is
added, conclusions will be added less by one than the
pre-existing terms : for the conclusion is drawn not in rela-

20 tion to the single term last added, but in relation to all the
rest, e.g. if to ABC the term D is added, two conclusions are
thereby added, one in relation to A, the other in relation to B.
Similarly with any further additions. And similarly too if
the term is inserted in the middle : for in relation to one
term only, a syllogism will not be constructed. Consequently

25 the conclusions will be much more numerous than the terms
or the premisses.

Since we understand the subjects with which syllogisms 26

are concerned, what sort of conclusion is established in each

figure, and in how many moods this is done, it is evident to us

both what sort of problem is difficult and what sort is easy

30 to prove. For that which is concluded in many figures and

1 Omit IJ.TI in 1. 6 with cod. n, Al., Them., and Waitz.

BOOK I. 26 42 b

through many moods is easier ; that which is concluded in
few figures and through few moods is more difficult to
attempt. The universal affirmative is proved by means of the
first figure only and by this in only one mood ; the universal
negative is proved both through the first figure and through
the second, through the first in one mood, through the 35
second in two. The particular affirmative is proved through
the first and through the last figure, in one mood through
the first, in three moods through the last. The particular
negative is proved in all the figures, but once in the first, in
two moods in the second, in three moods in the third. It is 40
clear then that the universal affirmative is most difficult to 43*
establish, most easy to overthrow. In general, universals
are easier game for the destroyer than particulars : for
whether the predicate belongs to none or not to some, they
are destroyed : and the particular negative is proved in all
the figures, the universal negative in two. Similarly with 5
universal negatives : the original statement is destroyed,
whether the predicate belongs to all or to some : and this
we found possible in two figures. But particular statements
can be refuted in one way only by proving that the
predicate belongs either to all or to none. But particular
statements are easier to establish : for proof is possible
in more figures and through more moods. And in general 10
we must not forget that it is possible to refute statements
by means of one another, I mean, universal statements by
means of particular, and particular statements by means of
universal : but it is not possible to establish universal
statements by means of particular, though it is possible
to establish particular statements by means of universal.
At the same time it is evident that it is easier to refute
than to establish. 15

The manner in which every syllogism is produced, the
number of the terms and premisses through which it proceeds,
the relation of the premisses to one another, the character of
the problem proved in each figure, and the number of the
figures appropriate to each problem, all these matters are
clear from what has been said.

We must now state how we may ourselves always have a 20

43 a ANALYTICA PRIORA

so supply of syllogisms in reference to the problem proposed 27
and by what road we may reach the principles relative to
the problem : for perhaps we ought not only to investigate
the construction of syllogisms, but also to have the power
of making them.

25 Of all the things which exist some are such that they
cannot be predicated of anything else truly and universally,
e. g. Cleon and Callias, i. e. the individual and sensible, but
other things may be predicated of them (for each of these
is both man and animal) ; and some things are themselves

30 predicated of others, but nothing prior is predicated of them ;
and some are predicated of others, and yet others of them,
e.g. man of Callias and animal of man. It is clear then
that some things are naturally not stated of anything : for
as a rule each sensible thing is such that it cannot be predi
cated of anything, save incidentally : for we sometimes say

35 that that white object is Socrates, or that that which
approaches is Callias. We shall explain in another place l
that there is an upward limit also to the process of predi
cating : for the present we must assume this. Of these
ultimate predicates it is not possible to demonstrate
another predicate, save as a matter of opinion, but these
may be predicated of other things. Neither can individuals

40 be predicated of other things, though other things can be
predicated of them. Whatever lies between these limits
can be spoken of in both ways : they may be stated of others,
and others stated of them. And as a rule arguments and
inquiries are concerned with these things.

43 We must select the premisses suitable to each problem in
this manner : first we must lay down the subject and the
definitions and the properties of the thing ; next we must
lay down those attributes which follow 2 the thing, and again
those which the thing follows, and those which cannot
5 belong to it. But those to which it cannot belong need not
be selected, because the negative statement implied above

1 Post. An. i. 19-22.

2 The term follow has been used to translate tnea-Qai with the
implication of logical sequence. Though the usage is hardly idiomatic
in regard to terms, one of which is consequent on or implied by the
other, it has become current with respect to propositions.

BOOK I. 27 43 b

is convertible. Of the attributes which follow we must
distinguish those which fall within the definition, those
which are predicated as properties, and those which are
predicated as accidents, and of the latter those which
apparently and those which really belong. The larger the
supply a man has of these, the more quickly will he reach 10
a conclusion ; and in proportion as he apprehends those
which are truer, the more cogently will he demonstrate. But
he must select not those which follow some particular but
those which follow the thing as a whole, e. g. not what follows
a particular man but what follows every man : for the
syllogism proceeds through universal premisses. If the
statement is indefinite, it is uncertain whether the premiss 15
is universal, but if the statement is definite, the matter is
clear. Similarly one must select those attributes which the
subject follows as wholes, for the reason given. But that
which follows one must not suppose to follow as a whole,
e.g. that every animal follows man or every science music,
but only that it follows, without qualification, as indeed we
state it in a proposition : for the other statement is useless 20
and impossible, e.g. that every man is every animal or
justice is all good. But that which something follows
receives the mark every . Whenever the subject, for
which we must obtain the attributes that follow, is contained
by something else, what follows or does not follow the
highest term universally must not be selected in dealing with
the subordinate term (for these attributes have been taken 25
in dealing with the superior term ; for what follows animal
also follows man, and what does not belong to animal does
not belong to man) ; but we must choose those attributes
which are peculiar to each subject. For some things
are peculiar to the species as distinct from the genus ; for
species being distinct there must be attributes peculiar
to each. Nor must we take as things which the superior
term follows, those things which the inferior term follows,
e. g. take as subjects of the predicate animal what are really 3
subjects of the predicate man . It is necessary indeed,
if animal follows man, that it should follow all these also.
But these belong more properly to the choice of what

43 b ANALYTICA PRIORA

concerns man. One must apprehend also normal conse
quents and normal antecedents ; for propositions which
obtain normally are established syllogistically from premisses
35 which obtain normally, some if not all of them having this
character of normality. For the conclusion of each syl
logism resembles its principles. We must not however
choose attributes which are consequent upon all the terms : 1
for no syllogism can be made out of such premisses. The
reason why this is so will be clear in the sequel. 2

If men wish to establish something about some whole, 28
4 o they must look to the subjects of that which is being
established (the subjects of which it happens to be asserted),
and the attributes which follow that of which it is to be
predicated. For if any of these subjects is the same as any
of these attributes, the attribute originally in question must
belong to the subject originally in question. 3 But if the
purpose is to establish not a universal but a particular
proposition, they must look for the terms of which the
44 a terms in question are predicable : for if any of these are
identical, the attribute in question must belong to some of
the subject in question. 4 Whenever the one term has to
belong to none of the other, one must look to the conse
quents of the subject, and to those attributes which cannot
possibly be present in the predicate in question : 5 or con
versely to the attributes which cannot possibly be present
r in the subject, and to the consequents of the predicate.
If any members of these groups are identical, one of the
terms in question cannot possibly belong to any of the
other. For sometimes a syllogism in the first figure
results. 7 sometimes a syllogism in the second. But if the
object is to establish a particular negative proposition, we
must find antecedents of the subject in question and attri-
io butes which cannot possibly belong to the predicate in
question. 8 If any members of these two groups are identical,

1 i.e. on the major and minor terms. Two affirmative premisses in
the second figure give no conclusion. - 44 20.

s We thus get a syllogism in Barbara.

4 Darapti. 5 Cesare. n Camestres.

7 By converting the major premiss of the Cesare syllogism or the
minor premiss of the Camestres syllogism. 8 Felapton, byconversion.

BOOK I. 28 44 a

it follows that one of the terms in question does not belong
to some of the other. Perhaps each of these statements
will become clearer in the following way. Suppose the
consequents of A are designated by B, the antecedents
of A by C, attributes which cannot possibly belong to A
by D. Suppose again that the attributes of E are designated 1 5
by F y the antecedents of E by G, and attributes which
cannot belong to E by //. If then one of the Cs should be
identical with one of the Fs, A must belong to all E : for F
belongs to all E, and A l to all C, consequently A belongs
to all E. If C and G are identical, A must belong to some 20
of the Es : for A follows C, and E follows all G. If F
and D are identical, A will belong to none of the Es by
a prosyllogism : for since the negative proposition is con
vertible, and F is identical with D. A will belong to none of
the Fs, but /" belongs to all E. Again, if B and H are
identical, A will belong to none of the Es : for B will belong 25
to all A, but to no E : 2 for it was assumed to be identical
with //, and H belonged to none of the Es. If D and G
are identical, A will not belong to some of the Es: for it
will not belong to G. because it does not belong to D : but
G falls under E : consequently A will not belong to some 30
of the Es. If B is identical with G, there will be a con
verted syllogism: for E* will belong to all A, since B
belongs to A and E to B (for B was found to be identical
with G) : but that A should belong to all E is not necessary,
but it must belong to some E because it is possible to convert
the universal statement into a particular. 35

It is clear then that in every proposition which requires
proof we must look to the aforesaid relations of the subject
and predicate in question : for all syllogisms proceed through
these. But if we are seeking consequents and antecedents
we must look for those which are primary and most universal,
e. g. in reference to E we must look to KF rather than to F 4 o
alone, and in reference to A we must look to KC rather than

1 r<a A in Bekker, 1. 19, is a misprint for TO A.
- Read rw & for TO 8 in 1. 26 with A 2 , C, and Waitz.
3 Read E in 1. 31 with A, B 2 > C, and treat ro yap . . . H 11. 32-3 as
parenthetical (Waitz).

44 b

44 b to C alone. 1 For if A belongs to KF, it belongs both to F
and to E : but if it does not follow KF, it may yet follow F.
Similarly we must consider the antecedents of A itself: for
if a term follows the primary antecedents, it will follow those
also which are subordinate, but if it does not follow the
5 former, it may yet follow the latter.

It is clear too that the inquiry proceeds through the three
terms and the two premisses, and that all the syllogisms
proceed through the aforesaid figures. For it is proved
that A belongs to all , whenever an identical term is found
among the Cs and Fs. This will be the middle term ; A and

10 E will be the extremes. So the first figure is formed. And
A will belong to some E, whenever C and G are apprehended
to be the same. This is the last figure : for G becomes the
middle term. And A will belong to no E, when D and F
are identical. Thus we have both the first figure and the
middle figure ; the first, because A belongs to no F, since

15 the negative statement is convertible, and F belongs to
all E\ the middle figure because D belongs to no A, and
to all E. And A will not belong to some E, whenever D
and G are identical. This is the last figure : for A will
belong to no G, and E will belong to all G. Clearly then

20 all syllogisms proceed through the aforesaid figures, and we
must not select consequents of all the terms, 2 because no
syllogism is produced from them. For (as we saw) 3 it is
not possible at all to establish a proposition from conse
quents, and it is not possible to refute by means of a
consequent of both the terms in question : for the middle
term must belong to the one, and not belong to the
other.

1 Aristotle has in mind the proof in a 12-19, where

All E is F.

F = C.

All CisA.

. . All E is A.

He now points out that it is preferable to take both the antecedents
and the consequents of A and of E in their most general form, e.g. to
take KF, a Ka6u\ov which includes /", and KC, a na66\ov which includes
C. If all KF is A y then all F and . . all E is A, and by taking account
of KF as well as of F we shall have put the proof in a ( more satisfactory
because more universal way.

2 i.e. the consequents of A and E. 3 27* 18-20, b 23~8.

BOOK I. 28 44 b

It is clear too that other methods of inquiry by selection 25
of middle terms arc useless to produce a syllogism, e. g. if
the consequents of the terms in question are identical, or
if the antecedents of A are identical with those attributes
which cannot possibly belong to E, or if those attributes
are identical which cannot belong to either term : for no
syllogism is produced by means of these. For if the
consequents are identical, e. g. B and /<", we have the 30
middle figure with both premisses affirmative : if the ante
cedents of A are identical with attributes which cannot
belong to E, e. g. C with H, we have the first figure with its
minor premiss negative. If attributes which cannot belong
to either term are identical, e. g. 7 and H, both premisses are 35
negative, either in the first or in the middle figure. But no
syllogism is possible in this way.

It is evident too that we must find out which terms in
this inquiry are identical, not which are different or contrary,
first because the object of our investigation is the middle 40
term, and the middle term must be not diverse but identical.
Secondly, wherever it happens that a syllogism results from 45**
taking contraries or terms which cannot belong to the same
thing, all arguments can be reduced to the aforesaid moods,
e. g. if B and F are contraries or cannot belong to the same
thing. For if these are taken, a syllogism will be formed 5
to prove that A belongs to none of the s, not however
from the premisses taken but in the aforesaid mood. For B
will belong to all A and to no E. Consequently B must
be identical with one of the Hs. Again, if B and G cannot
belong to the same thing, it follows that A will not belong 10
to some of the Es : for then too we shall have the middle
figure : for B will belong to all A and to no G. 1 Conse
quently B must be identical with some of the Hs? For
the fact that B and G cannot belong to the same thing
differs in no way from the fact that B is identical with
some of the Hs : for that includes everything which cannot 15
belong to E.

It is clear then that from the inquiries taken by them-

1 And . . not to some E,

- This does not actually follow.

45 a ANALYTICA PRIORA

selves no syllogism results ; but if B and F are contraries
B must be l identical with one of the ffs, and the syllogism
20 results through these terms. It turns out then that those
who inquire in this manner are looking gratuitously for
some other way than the necessary way because they have
failed to observe the identity of the .Z?s with the Pis,.

Syllogisms which lead to impossible conclusions are similar
to ostensive syllogisms ; they also are formed by means of

25 the consequents and antecedents of the terms in question.
In both cases the same inquiry is involved. For what is
proved ostensively may also be concluded syllogistically
per impossibile by means of the same terms ; and what is
proved per impossibile may also be proved ostensively,
e. g. that A belongs to none of the Es. For suppose A
to belong to some E : then since B belongs to all A and A

30 to some of the Es, B will belong to some of the Es : but it
was assumed that it belongs to none. Again we may prove
that A belongs to some E : for if A belonged to none of
the Es, and E belongs to all G, A will belong to none of
the Gs : but it was assumed to belong to all. Similarly
with the other propositions requiring proof. The proof

35 per impossibile will always and in all cases be from the
consequents and antecedents of the terms in question.
Whatever the problem the same inquiry is necessary
whether one wishes to use an ostensive syllogism or a
reduction to impossibility. For both the demonstrations
start from the same terms, e. g. suppose it has been proved
that A belongs to no E, because it turns out that otherwise

4 o B belongs to some of the Es and this is impossible if now
it is assumed that B belongs to no E and to all A, it is clear
45 b that A will belong to no E. Again if it has been proved
by an ostensive syllogism that A belongs to no E, assume
that A belongs to some E and it will be proved per impossi
bile to belong to no E. Similarly with the rest. In all
cases it is necessary to find some common term other than
5 the subjects of inquiry, to which the syllogism establishing
the false conclusion may relate, so that if this premiss is

1 Read nvuKi S" for tav 6e in 1, 18 with Bnu and Waitz.

b

BOOK I. 29 45

converted, 1 and the other remains as it is, the syllogism
will be ostensive by means of the same terms. For the
ostensive syllogism differs from the reductio ad impossibile
in this : in the ostensive syllogism both premisses are laid
down in accordance with the truth, in the reductio ad 10
impossibile one of the premisses is assumed falsely.

These points will be made clearer by the sequel, 2 when
we discuss the reduction to impossibility : at present this
much must be clear, that we must look to terms of the kinds
mentioned whether we wish to use an ostensive syllogism
or a reduction to impossibility. In the other hypothetical 15
syllogisms, I mean those which proceed by substitution, 3 or
by positing a certain quality, 4 the inquiry will be directed
to the terms of the problem to be proved not the terms of
the original problem, but the new terms introduced ; and
the method of the inquiry will be the same as before. But
we must consider and determine in how many ways hypo- 20
thetical syllogisms are possible.

Each of the problems then can be proved in the manner
described ; but it is possible to establish some of them
syllogistically in another way, e. g. universal problems by
the inquiry which leads up to a particular conclusion, with
the addition of an hypothesis. 5 For if the Cs and the (7s
should be identical, but E should be assumed to belong to
the Gs only, then A would belong to every E : and again 25
if the Ds and the Gs should be identical, but E should be
predicated, of the Gs only, it follows that A will belong to
none of the Es. Clearly then we must consider the matter
in this way also. The method is the same whether the
relation is necessary or possible. For the inquiry will be
the same, and the syllogism will proceed through terms

1 i.e. if this false conclusion is replaced by its contradictory and
this is treated as a premiss.

- ii. 14. 3 Cf. 41*39.

4 Al. and Phil, interpret this as referring to arguments d;ro TOU
poXXop Km rjTTov KOI ofjioiov, from the possession of a quality in unequal
or equal degree by two terms, i.e. arguments a fortiori and by analogy.

6 i.e. the assumption that C = G, which in 44*19-21 proved that
some E is A, will, if we add the hypothesis that only G is E, prove
that all E is A ; and the assumption that D = G, which in 44* 28-30
proved that some E is not A, will, if we suppose that only G is E,
prove that no E is A.

2

45 b ANALYTICA PRIORA

30 arranged in the same order whether a possible or a pure
proposition is proved. We must find in the case of possible
relations, as well as terms that belong, terms which can
belong though they actually do not : for we have proved
that the syllogism which establishes a possible relation

35 proceeds through these terms as well. Similarly also with
the other modes of predication. 1

It is clear then from what has been said not only that all
syllogisms can be formed in this way, but also that they
cannot be formed in any other. For every syllogism has
been proved to be formed through one of the aforementioned

40 figures, and these cannot be composed through other terms

than the consequents and antecedents of the terms in ques-

46 a tion : for from these we obtain the premisses and find the

middle term. Consequently a syllogism cannot be formed

by means of other terms.

The method is the same in all cases, in philosophy, in 30
any art or study. We must look for the attributes and the
5 subjects of both our terms, 2 and we must supply ourselves
with as many of these as possible, and consider them by
means of the three terms, refuting statements in one way,
confirming them in another, in the pursuit of truth starting
from premisses in which the arrangement of the terms is in
accordance with truth, while if we look for dialectical syllo-

10 gisms we must start from probable premisses. The principles
of syllogisms have been stated in general terms, both how
they are characterized and how we must hunt for them,
so as not to look to everything that is said about the
terms of the problem or to the same points whether we
are confirming or refuting, or again whether we are con-

15 firming of all or of some, and whether we are refuting of
all or some ; we must look to fewer points and they must
be definite. We have also stated how we must select with
reference to everything that is, e. g. about good or know
ledge. But in each science the principles which are peculiar 3
are the most numerous. Consequently it is the business

e.g. propositions asserting non-necessity, impossibility, &c.

2 Read e f *arepoj> in 1. 5 with A, B, C, Al., and Waitz.

3 Read I8iai in 1. 17 with Al. and Waitz.

BOOK I. 30 46

of experience to give the principles which belong to each
subject. I mean for example that astronomical experience
supplies the principles of astronomical science : for once the 20
phenomena were adequately apprehended, the demonstra
tions of astronomy were discovered. Similarly with any
other art or science. Consequently, if the attributes of the
thing are apprehended, our business will then be to exhibit
readily the demonstrations. For if none of the true attri
butes of things had been omitted in the historical survey, 25
we should be able to discover the proof and demonstrate
everything which admitted of proof, and to make that clear,
whose nature does not admit of proof.

In general then we have explained fairly well how we
must select premisses : we have discussed the matter
accurately in the treatise concerning dialectic. 1 ?>

31 It is easy to see that division into classes 2 is a small part
of the method we have described : for division is, so to
speak, a weak syllogism ; for what it ought to prove, it
begs, and it always establishes something more general
than the attribute in question. First, this very point had
escaped all those who used the method of division ; and 35
they attempted to persuade men that it was possible to
make a demonstration of substance and essence. Conse
quently they did not understand what it is possible to prove
syllogistically by division, 3 nor did they understand that it
was possible to prove syllogistically in the manner we have
described. 4 In demonstrations, when there is a need to
prove a positive statement, the middle term through which 40
the syllogism is formed must always be inferior to and not 46
comprehend the first of the extremes. But division has
a contrary intention : for it takes the universal as middle.
Let animal be the term signified by A, mortal by B t and
immortal by C, and let man, whose definition is to be got,

1 Topics, especially i. 14.

2 Aristotle is thinking of Plato s establishment of definitions by
means of division by dichotomy.

3 Read 8uupovfj.tvovs in 1. 38 with codd. mn, Al., Phil., Them., and
Waitz.

4 In cc. 1-30.

46 h ANALYTICA PRIORA

5 be signified by D. The man who divides assumes that
every animal is either mortal or immortal : i. e. whatever
is A is all either B or C. Again, always dividing, he lays
it down that man is an animal, so he assumes A of D as
belonging to it. Now the true conclusion is that every D

10 is either B or C, consequently man must be either mortal or
immortal, but it is not necessary that man should be a mortal
animal this is begged : and this is what ought to have been
proved syllogistically. And again, taking A as mortal animal,
B as footed, C as footless, and D as man, he assumes in the

i? same way that A inheres either in B or in C (for every mortal
animal is either footed or footless), and he assumes A of D
(for he assumed man, as we saw, to be a mortal animal) ;
consequently it is necessary that man should be either a
footed or a footless animal ; but it is not necessary that man
should be footed : this he assumes : and it is just this again
which he ought to have demonstrated. Always dividing

20 then in this way it turns out that these logicians assume as
middle the universal term, and as extremes that which
ought to have been the subject of demonstration and the
differentiae. In conclusion, they do not make it clear, and
show it to be necessary, that this is man or whatever the
subject of inquiry may be : for they pursue the other method

25 altogether, never even suspecting the presence of the rich
supply of evidence which might be used. It is clear that it
is neither possible to refute a statement by this method of
division, nor to draw a conclusion about an accident or
property of a thing, nor about its genus, nor in cases in
which it is unknown whether it is thus or thus, e. g. whether
the diagonal is incommensurate. For if he assumes that

30 every length is either commensurate or incommensurate,
and the diagonal is a length, he has proved that the diagonal
is either incommensurate or commensurate. But if he should
assume that it is incommensurate, he will have assumed what
he ought to have proved. He cannot then prove it : for this
is his method, but proof is not possible by this method.
Let A stand for incommensurate or commensurate , B for

35 length , C for diagonal . It is clear then that this method
of investigation is not suitable for every inquiry, nor is it

BOOK I. 31 46*

useful in those cases in which it is thought to be most
suitable.

From what has been said it is clear from what elements
demonstrations are formed and in what manner, and to
what points we must look in each problem.

32 Our next business is to state how we can reduce syllogisms
to the aforementioned figures : for this part of the inquiry 47
still remains. If we should investigate the production of
the syllogisms and had the power of discovering them, and
further if we could resolve the syllogisms produced into
the aforementioned figures, our original problem would be 5
brought to a conclusion. It will happen at the same time
that what has been already said will be confirmed and its
truth made clearer by what we are about to say. For
everything that is true must in every respect agree with
itself.

First then we must attempt to select the two premisses 10
of the syllogism (for it is easier to divide into large parts
than into small, 1 and the composite parts are larger than
the elements out of which they are made) ; next we must
inquire which are universal and which particular, and if
both premisses have not been stated, we must ourselves
assume the one which is missing. For sometimes men put
forward the universal premiss, but do not posit the premiss 15
which is contained in it, either in writing or in discussion :
or men put forward the premisses of the principal syllo
gism, but omit those through which they are inferred,
and invite the concession of others to no purpose. 2 We
must inquire then whether anything unnecessary has been
assumed, or anything necessary has been omitted, and we
must posit the one and take away the other, until we have 20
reached the two premisses : for unless we have these, we
cannot reduce 3 arguments put forward in the way described.
In some arguments it is easy to see what is wanting, but
some escape us, and appear to be syllogisms, because
something necessary results from what has been laid

1 i. e. the terms. 2 Top. viii. i.

3 Read dvayayt iv in 1. 21 with B, C. 2 , Al., and Waitz.

4 7 a ANALYTICA PRIORA

down, e. g. if the assumptions were made that substance is

25 not annihilated by the annihilation of what is not substance,
and that if the elements out of which a thing is made
are annihilated, then that which is made out of them is
destroyed : these propositions being laid down, it is neces
sary that any part of substance is substance ; this has not
however been drawn by syllogism from the propositions
assumed, but premisses are wanting. Again if it is necessary
that animal should exist, if man does, and that substance
should exist, if animal does, it is necessary that substance

30 should exist if man does : but as yet the conclusion has not
been drawn syllogistically : for the premisses are not in the
shape we required. We are deceived in such cases because
something necessary results from what is assumed, since
the syllogism also is necessary. But that which is necessary
is wider than the syllogism : for every syllogism is necessary,

35 but not everything which is necessary is a syllogism. Con
sequently, though something results when certain proposi
tions are assumed, we must not try to reduce it directly,
but must first state the two premisses, then divide them into
their terms. We must take that term as middle which
is stated in both the premisses : for it is necessary that the

40 middle should be found in both premisses in all the figures.
47 b If then the middle term is a predicate and a subject of
predication, or if it is a predicate, and something else is
denied of it, we shall have the first figure : if it both is a
predicate and is denied of something, the middle figure :
if other things are predicated of it, or one is denied, the other
5 predicated, the last figure. For it was thus that we found
the middle term placed in each figure. It is placed similarly
too if the premisses are not universal : for the middle term
is determined in the same way. Clearly then, if the same
term is not stated more than once in the course of an
argument, a syllogism cannot be made : for a middle term
has not been taken. Since we know what sort of thesis is

10 established in each figure, and in which the universal, in
what sort the particular is established, clearly we must not
look for all the figures, but for that which is appropriate to
the thesis in hand. If the thesis is established in more

BOOK I. 32 47 l

figures than one, we shall recognize the figure by the
position of the middle term.

33 Men are frequently deceived about syllogisms because 15
the inference is necessary, as has been said above; 1 some
times they are deceived by the similarity in the positing of
the terms ; and this ought not to escape our notice. E. g.
if A is stated of B, and B of C: it would seem that a
syllogism is possible since the terms stand thus : but nothing
necessary results, nor does a syllogism. Let A represent 20
the term being eternal , B Aristomenes as an object of
thought . C Aristomenes . It is true then that A belongs
to B. For Aristomenes as an object of thought is eternal.
But B also belongs to C: for Aristomenes is Aristomenes
as an object of thought. But A does not belong to C: for 25
Aristomenes is perishable. For no 2 syllogism was made
although the terms stood thus : that required that the
premiss AB should be stated universally. But this is false,
that every Aristomenes who is an object of thought is
eternal, since Aristomenes is perishable. Again let C stand
for Miccalus , B for musical Miccalus , A for perishing 30
to-morrow . It is true to predicate B of C: for Miccalus is
musical Miccalus. Also A can be predicated of B : for
musical Miccalus might perish to-morrow. 3 But to state A
of C is false at any rate. This argument then is identical
with the former ; for it is not true universally that musical 35
Miccalus perishes to-morrow : but unless this is assumed,
no syllogism (as we have shown) is possible.

This deception then arises through ignoring a small
distinction. For we accept the conclusion as though it
made no difference whether we said This belongs to that
or This belongs to all of that .

54 Men will frequently fall into fallacies through not setting 48*
out the terms of the premiss well, e. g. suppose A to be
health, B disease, C man. It is true to say that A cannot
belong to any B (for health belongs to no disease) and
again that B belongs to every C (for every man is capable 5

1 ;l 31. Read ov yap in 1. 26 with A, B, C, and Waitz.

3 i.e. Miccalus might to-morrow cease to be musical.

48 a ANALYTICA PRIORA

of disease). It would seem to follow that health cannot
belong to any man. The reason for this is that the terms
are not set out well in the statement, since if the things
which are in the conditions are substituted, no syllogism

10 can be made, e.g. if healthy is substituted for health
and diseased for disease . For it is not true to say that
being healthy cannot belong to one who is diseased. But
unless this is assumed no conclusion results, save in respect
of possibility : but such a conclusion is not impossible : for

15 it is possible that health should belong to no man. Again
the fallacy may occur in a similar way in the middle
figure : it is not possible that health should belong to any
disease, but it is possible that health should belong to every
man, consequently it is not possible that disease should
belong to any man . In the third figure the fallacy results
in reference to possibility. For health and disease, and

20 knowledge and ignorance, and in general contraries, may
possibly belong to the same thing, but cannot belong to
one another. This is not in agreement with what was said
before : for we stated l that when several things could
belong to the same thing, they could belong to one another.
It is evident then that in all these cases the fallacy arises

2 ? from the setting out of the terms : for if the things that are
in the conditions are substituted, no fallacy arises. It is
clear then that in such premisses what possesses the condi
tion ought always to be substituted for the condition and
taken as the term.

We must not always seek to set out the terms in a single 35

30 word : for we shall often have complexes of words to which

a single name is not given. Hence it is difficult to reduce

syllogisms with such terms. Sometimes too fallacies will

result from such a search, e.g. the belief that syllogism can

establish that which has no mean. Let A stand for two

right angles, B for triangle. C for isosceles triangle. A then

35 belongs to C because of B : but A belongs to B without

the mediation of another term : for the triangle in virtue of

its own nature contains two right angles, consequently

1 39

BOOK I. 35 4 8

there will be no middle term for the proposition AB,
although it is demonstrable. For it is clear that the middle
must not always be assumed to be an individual thing,
but sometimes a complex of words, as happens in the case
mentioned.

36 That the first term belongs to the middle, and the middle 4
to the extreme, 1 must not be understood in the sense that
they can always be predicated of one another or that the
first term will be predicated of the middle in the same way 48
as the middle is predicated of the last term. The same
holds if the premisses are negative. But we must suppose
the verb to belong to have as many meanings as the
senses in which the verb to be is used, and in which the
assertion that a thing is may be said to be true. Take
for example the statement that there is a single science 5
of contraries. Let A stand for there being a single science ,
and B for things which are contrary to one another. Then
A belongs to B, not in the sense that contraries are 2 the
fact of there being a single science of them, but in the sense
that it is true to say of the contraries that there is a single
science of them.

It happens sometimes that the first term is stated of the 10
middle, but the middle is not stated of the third term,
e.g. if wisdom is knowledge, and wisdom is of the good, the
conclusion is that there is knowledge of the good. The
good then is not knowledge, though wisdom is knowledge.
Sometimes the middle term is stated of the third, but the 15
first is not stated of the middle, e.g. if there is a science of
everything that has a quality, or is a contrary, and the
good both is a contrary and has a quality, the conclusion
is that there is a science of the good, but the good is
not science, nor is that which has a quality or is a
contrary, though the good is both of these. Sometimes
neither the first term is stated of the middle, nor the 20
middle of the third, while the first is sometimes stated
of the third, and sometimes not : e. g. if there is a genus of
that of which there is a science, and if there is a science

1 i.e. the minor.

2 Omit the comma after tvavria in 1. 7 with Al. and Waitz.

4 8 b ANALYTICA PRIORA

of the good, we conclude that there is a genus of the
good. But nothing is predicated of anything. And if that

25 of which there is a science is a genus, and if there is a
science of the good, we conclude that the good is a genus.
The first term then is predicated of the extreme, but in the
premisses one thing is not stated of another.

The same holds good where the relation is negative.
For that does not belong to this does not always mean

30 that e this is not that , but sometimes that this is not of
that or for that , e.g. there is not a motion of a motion
or a becoming of a becoming, but there is a becoming of
pleasure : so pleasure is not a becoming. Or again it may
be said that there is a sign of laughter, but there is not
a sign of a sign, consequently laughter is not a sign. This
holds in the other cases too, in which the thesis is refuted

35 because the genus is asserted in a particular way, in relation
to the terms of the thesis. 1 Again take the inference
opportunity is not the right time : for opportunity belongs
to God, but the right time does not, since nothing is useful
to God . We must take as terms opportunity right time
God : but the premiss must be understood according to
the case of the noun. For we state this universally without

40 qualification, that the terms ought always to be stated in
the nominative, e.g. man, good, contraries, not in oblique
49 a cases, e.g. of man, of good, of contraries, but the premisses
ought to be understood with reference to the cases of each
term either the dative, e.g. equal to this , or the genitive,
e.g. double of this , or the accusative, e.g. that which
strikes or sees this , or the nominative, e. g. man is an

5 animal , or in whatever other way the word falls in the
premiss.

The expressions this belongs to that and this holds 37
true of that must be understood in as many ways as there
are different categories, and these categories must be taken
either with or without qualification, and further as simple
or compound : the same holds good of the corresponding

1 .e. negative syllogisms in the second figure in which the middle
term is not strictly predicated of the extremes but is said to stand in
some relation to them such as is indicated by the use of an oblique case.

BOOK I. 37 49 g

negative expressions. We must consider these points and 10
define them better.

38 A term which is repeated in the premisses ought to be
joined to the first extreme, not to the middle. I mean for
example that if a syllogism should be made proving that
there is knowledge of justice, that it is good, the expression
that it is good (or qua good ) should be joined to the
first term. Let A stand for knowledge that it is good , 15
B for good, C for justice. It is true to predicate A of
B. For of the good there is knowledge that it is good.
Also it is true to predicate B of C. For justice is identical
with a good. In this way an analysis of the argument
can be made. But if the expression that it is good were
added to B, the conclusion will not follow : for A will be 20
true of B, but B will not be true of C. For to predicate of
justice the term good that it is good is false and not
intelligible. Similarly if it should be proved that the
healthy is an object of knowledge qua good, or goat-stag
an object of knowledge qua not existing, 1 or man perishable
qu& an object of sense : in every case in which an addition
is made to the predicate, the addition must be joined to the 25
extreme. 2

The position of the terms is not the same when some
thing is established without qualification and when it is
qualified by some attribute or condition, e.g. when the
good is proved to be an object of knowledge and when it is
proved to be an object of knowledge that it is good. 3 If it
has been proved to be an object of knowledge without 30
qualification, we must put as middle term that which is ,
but if we add the qualification that it is good , the middle
term must be that which is something . Let A stand for
knowledge that it is something , B stand for something ,
and C stand for good , It is true to predicate A of B : for
ex hypotliesi there is a science of that which is something,
that it is something. B too is true of C: for that which C

1 i.e. in the sense that it can be known not to exist. Omit Sngao-rbv
in 1. 24 with A, B, C, Al., Phil., and Waitz.

2 i.e. the major term.

3 Omit ri in 1. 29 with Al., Phil., Them., and Waitz.

49 a ANALYTICA PRIORA

35 represents is something. Consequently A is true of C :
there will then be knowledge of the good, that it is good :
for ex hypothesi the term something indicates the thing s
special nature. But if being were taken as middle and
being simply were joined to the extreme, not being some
thing , we should not have had a syllogism proving that
there is knowledge of the good, that it is good, but that
49 b it is ; e. g. let A stand for knowledge that it is, B for being,
C for good. Clearly then in syllogisms which are thus
limited we must take the terms in the way stated.

We ought also to exchange terms which have the same 39
value, word for word, and phrase for phrase, and word and
5 phrase, and always take a word in preference to a phrase :
for thus the setting out of the terms will be easier. For
example if it makes no difference whether we say that the
supposable is not the genus of the opinable or that the
opinable is not identical with a particular kind of supposable
(for what is meant is the same in both statements), it is
better to take as the terms the supposable and the opinable
in preference to the phrase suggested.

10 Since the expressions pleasure is good and, pleasure is 40
the good are not identical, we must not set out the terms
in the same way ; but if the syllogism is to prove that
pleasure is the good, the term must be the good , but
if the object is to prove that pleasure is good, the term
will be good . Similarly in all other cases.

15 It is not the same, either in fact or in speech, that A 41
belongs to all of that to which B belongs, and that A belongs
to all of that to all of which B belongs : for nothing
prevents B from belonging to C, though not to all C: e.g.
let B stand for beautiful, and C for white. If beauty belongs
to something white, it is true to say that beauty belongs to
that which is white ; but not perhaps to everything that is

20 white. If then A belongs to B, but not to everything of
which B is predicated, then whether B belongs to all C or
merely belongs to C, it is not necessary that A should
belong, I do not say to all C, but even to C at all. But if
A belongs to everything of which B is truly stated, it will

b

BOOK I. 41 49

follow that A can be said of all of that of all of which B is
said. If however A is said of that of all of which T B may 25
be said, nothing prevents B belonging to C, and yet A not
belonging to all C or to any C at all. If then we take three
terms it is clear that the expression A is said of all of which
B is said 2 means this, A is said of all the things of which
B is said . And if B is said of all of a third term, so also is 30
A : but if B is not said of all of the third term, there is no
necessity that A should be said of all of it.

We must not suppose that something absurd results
through setting out the terms : for we do not use
the existence of this particular thing, but imitate the
geometrician who says that this line a foot long or this 35
straight line or this line without breadth exists although
it does not, but does not use the diagrams in the sense that
he reasons from them. For in general, if two things are not
related as whole to part and part to whole, the prover
does not prove from them, and so no syllogism is formed.
We (I mean the learner) use the process of setting out terms 50*
like perception by sense, not as though it were impossible to
demonstrate without these illustrative terms, as it is to
demonstrate without the premisses of the syllogism.

42 We should not forget that in the same syllogism not all 5
conclusions are reached through one figure, but one through
one figure, another through another. Clearly then we must
analyse arguments in accordance with this. Since not every
problem is proved in every "figure, but certain problems
in each figure, it is clear from the conclusion in what figure 10
the premisses should be sought.

43 In reference to those arguments aiming at a definition
which have been directed to prove some part of the definition,
we must take as a term the point to which the argument has
been directed, not the whole definition : for so we shall
be less likely to be disturbed by the length of the term : e.g.
if a man proves that water is a drinkable liquid, we must
take as terms drinkable and water. 15

1 Omit the comma after Xe yqrai in 1. 26 with Waitz.
" Omit the comma after B in 1. 28 with Waitz. The Greek phrase
is there ambiguous, and Aristotle s object is to remove this ambiguity.

5o a ANALYTICA PRIORA

Further we must not try to reduce hypothetical syllogisms ; 44
for with the given premisses it is not possible to reduce them.
For they have not been proved by syllogism, but assented
to by agreement. For instance if a man should suppose

20 that unless there is one faculty of contraries, there cannot be
one science, and should then argue that not every T faculty
is of contraries, e. g. of what is healthy and what is sickly :
for the same thing will then be at the same time healthy
and sickly. He has shown 2 that there is not one faculty of
all contraries, but he has not proved that there is not

25 a science. And yet one must agree. But the agreement
does not come from a syllogism, but from an hypothesis.
This argument cannot be reduced : but the proof that there
is not a single faculty can. The latter argument perhaps
was a syllogism : but the former was an hypothesis.

The same holds good of arguments which are brought

30 to a conclusion per impossibile. These cannot be analysed
either ; but the reduction to what is impossible can be
analysed since it is proved by syllogism, though the rest of
the argument cannot, because the conclusion is reached from
an hypothesis. But these differ from the previous arguments :
for in the former a preliminary agreement must be reached
if one is to accept the conclusion ; e. g. an agreement that if
there is proved to be one faculty of contraries, then contraries

35 fall under the same science ; whereas in the latter, even if no
preliminary agreement has been made, men still accept the
reasoning, because the falsity is patent, e. g. the falsity of
what follows from the assumption that the diagonal is com
mensurate, viz. that then odd numbers are equal to evens. 3
Many other arguments are brought to a conclusion by the

40 help of an hypothesis ; these we ought to consider and mark
out clearly. We shall describe in the sequel 4 their differences,
5O b and the various ways in which hypothetical arguments are
formed : but at present this much must be clear, that it is
not possible to resolve such arguments into the figures. And
we have explained the reason.

1 Read naan for p.ia in 1. 21 with B, Al., and Waitz.

2 Read fViSeSeiKroi for aTroSe SeiKrni in 1. 24 with A, B, C, and Waitz.

3 Cf. 41*26.

4 This promise is not fulfilled in Aristotle s extant works.

BOOK I. 45 5 o b

45 Whatever problems are proved in more than one figure, it 5
they have been established in one figure by syllogism, can
be reduced to another figure, e. g. a negative syllogism in
the first figure can be reduced to the second, and a syllogism
in the middle figure to the first, not all however but some
only. The point will be clear in the sequel. If A belongs
to no B, and B to all C, then A belongs to no C. Thus the 10
first figure ; but if the negative statement is converted, we
shall have the middle figure. For B belongs to no A, and
to all C. Similarly if the syllogism is not universal but
particular, e. g. if A belongs to no B, and B to some C.
Convert the negative statement and you will have the 15
middle figure.

The universal syllogisms in the second figure can be
reduced to the first, but only one of the two particular
syllogisms. Let A belong to no B and to all C. Convert
the negative statement, and you will have the first figure. 30
For B will belong to no A, and A to all C. But if the
affirmative statement concerns B, and the negative C, C must
be made first term. For C belongs to no A, and A to all B :
therefore C belongs to no B. B then belongs to no C : for
the negative statement is convertible. 2 c

But if the syllogism is particular, whenever the negative
statement concerns the major extreme, reduction to the
first figure will be possible, e.g. if A belongs to no B and to
some C: convert the negative statement and you will have
the first figure. For B will belong to no A, and A to some
C. But when the affirmative statement concerns the major 30
extreme, no resolution will be possible, e. g. if A belongs to
all B, but not to all C: for the statement AB does not
admit of conversion, 1 nor would there be a syllogism if it
did.

Again syllogisms in the third figure cannot all be resolved 35
into the first, though all syllogisms in the first figure can be
resolved into the third. Let A belong to all B and B to
some C. Since the particular affirmative is convertible, C
will belong to some B : but A belonged to all B : so that
the third figure is formed. Similarly if the syllogism is
1 i.e. simple conversion.

50 b ANALYTICA PRIORA

negative : for the particular affirmative is convertible : there-

4 fore A will belong to no B, and to some C.

5l a Of the syllogisms in the last figure one only cannot

be resolved into the first, viz. when the negative statement is

not universal : all the rest can be resolved. Let A and B be

affirmed of all C: then C can be converted partially with

5 either A or B : C then belongs to some B. Consequently

we shall get the first figure, if A belongs to all C, and C to

some of the Bs. If A belongs to all C and B to some C,

the argument is the same : for B is convertible in reference

to C. But if B belongs to all C and A to some 6", the first

10 term must be B : for B belongs to all C, and C to some A,
therefore B belongs to some A. But since the particular
statement is convertible, A will belong to some B. If the
syllogism is negative, when the terms arc universal we must
take them in a similar way. Let B belong to all C, and A

15 to no C: then C will belong to some B, and A to no C; and
so C will be middle term. Similarly if the negative state
ment is universal, the affirmative particular : for A will
belong to no C, and C to some of the Bs. But if the
negative statement is particular, no resolution will be
possible, e. g. if B belongs to all C, and A does not belong

20 to some C: convert the statement BC and both premisses
will be particular.

It is clear that in order to resolve the figures l into one
another the premiss which concerns the minor extreme must
be converted in both the figures : for when this premiss is

25 altered, the transition to the other figure is made.

One of the syllogisms in the middle figure can, the other
cannot, be resolved into the third figure. Whenever the
universal statement is negative, resolution is possible. For
if A belongs to no B and to some C, both B and C alike are
convertible in relation to A, so that B belongs to no A, and

3 o C to some A. A therefore is middle term. But when A
belongs to all B, and not to some C, resolution will not be
possible : for neither of the premisses is universal after
conversion.

Syllogisms in the third figure can be resolved into the
1 i.e. the first and third figures.

BOOK I. 45 5i a

middle figure, whenever the negative statement is universal, 35
e. g. if A belongs to no C, and B to sonic or all C. For C
then will belong to no A and to some />. But if the negative
statement is particular, no resolution will be possible : for
the particular negative does not admit of conversion.

It is clear then that the same syllogisms cannot be 4 o
resolved in these figures which could not be resolved into the
first figure, and that when syllogisms are reduced to the 5i b
first figure these alone are confirmed by reduction to what is
impossible.

It is clear from what we have said how we ought to
reduce syllogisms, and that the figures may be resolved into
one another.

46 In establishing or refuting, it makes some difference 5
whether we suppose the expressions ; not to be this and
to be not-this are identical or different in meaning, e. g.
not to be white and to be not-white . For they do not
mean the same thing, nor is to be not-white the negation
of to be white , but not to be white . The reason for this 10
is as follows. The relation of he can walk to he can not-
walk is similar to the relation of it is white to it is not-
white ; so is that of he knows what is good to : he knows
what is not-good . For there is no difference between the ex
pressions he knows what is good and he is knowing what
is good , or he can walk and he is able to walk : there- 15
fore there is no difference between their contraries he cannot
walk he is not able to walk . If then he is not able to
walk means the same as he is able not to walk , capacity
to walk and incapacity to walk will belong at the same time
to the same person (for the same man can both walk and not-
walk, and is possessed of knowledge of what is good and of 20
what is not-good), but an affirmation and a denial which are
opposed to one another do not belong at the same time to
the same thing. As then not to know what is good is not
the same as to know what is not good , so to be not-good
is not the same as not to be good . For when two pairs
correspond, if the one pair are different from one another, the
other pair also must be different. Nor is to be not-equal the 25

G 2

5i b ANALYTICA PRIORA

same as not to be equal : for there is something underlying
the one, viz. that which is not-equal, and this is the unequal,
but there is nothing underlying the other. Wherefore not
everything is either equal or unequal, but everything is equal
or is not equal. Further the expressions it is a not-white
log and it is not a white log do not imply one another s

30 truth. For if it is a not-white log , it must be a log:
but that which is not a white log need not be a log at
all. Therefore it is clear that it is not-good is not the
denial of it is good . If then every single statement
may truly be said to be either an affirmation or a negation,
if it is not a negation clearly it must in a sense be an
affirmation. But every affirmation has a corresponding

35 negation. The negation then of it is not-good is it is
not not-good . The relation of these statements to one
another is as follows. Let A stand for to be good , B
for not to be good , let C stand for to be not-good and
be placed under B^ and let D stand for not to be not-good
and be placed under A. Then either A or B will belong to
everything, but they will never belong to the same thing ;

40 and either C or D will belong to everything, but they will
never belong to the same thing. And B must belong
to everything to which C belongs. For if it is true to say
52 a it is not-white , it is true also to say it is not white : for
it is impossible that a thing should simultaneously be white
and be not-white, or be a not-white log and be a white log ;
consequently if the affirmation does not belong, the denial
must belong. But C does not always belong to B : for what
5 is not a log at all, cannot be a not-white log either. On the
other hand D belongs to everything to which A belongs.
For either C or D belongs to everything to which A belongs.
But since a thing cannot be simultaneously not-white

1 The text implies the following diagram :

A (It is good.) B (It is not good.)

D (It is not not-good.) C (It is not-good.)

Aristotle points out that A and B are contradictory.

CandD

A and C ,, contrary.

B and D ,, compatible.

D is inferable from A .

BOOK I. 46 52 s

and white, D must belong to everything to which A belongs.
For of that v/hich is white it is true to say that it is not not-
white. But A is not true of all D. For of that which
is not a log at all it is not true to say A, viz. that it is a 10
white 1 log. Consequently D is true, but A is not true, i. e.
that it is a white log. It is clear also that A and C cannot
together belong to the same thing, and that B and D may
possibly belong to the same thing.

Privative terms are similarly related to positive terms in 15
respect of this arrangement. Let A stand for equal , B
for not equal , C for unequal , D for not unequal .

In many things also, to some of which something belongs
which does not belong to others, the negation may be true
in a similar way, 2 viz. that all are not white or that each is 20
not white, while that each is not-white or all are not-white
is false. Similarly also every animal is not-white is not
the negation of every animal is white (for both are false) :
the proper negation is every animal is not white . Since it
is clear that it is not -white and it is not white mean 25
different things, and one is an affirmation, the other a denial,
it is evident that the method of proving each cannot be the
same, e. g. that whatever is an animal is not white or may
not be white, and that it is true to call it not-white ; for this
means that it is not-white. But we may prove that it is true
to call it white or not-white in the same way for both are 30
proved constructively by means of the first figure. For the
expression it is true stands on a similar footing to it is .
For the negation of it is true to call it white is not it is
true to call it not- white but it is not true to call it white .
If then it is to be 3 true to say that whatever is a man is
musical or is not-musical, we must assume that whatever 35
is an animal either is musical or is not-musical; and the
proof has been made. That whatever is a man is not musical
is proved destructively in the three ways mentioned. 4

In general whenever A and B are such that they cannot
belong at the same time to the same thing, and one of the 40
two necessarily belongs to everything, and again C and D

1 Omit ov in 1. 1 1 with B, C 2 , AL, and VVaitz. 2 Cf. 11. 4, 5.

3 Read ecmu in 1. 34. * Celarent, Cesare, Camestres.

52 b ANALYTICA PRIORA

52 b are related in the same way, and A follows C but the relation
cannot be reversed, then D must follow B and the relation
cannot be reversed. And A and D may belong to the same
thing, but B and C cannot. First it is clear from the
5 following consideration that D follows B. For since either
C or D necessarily belongs to everything ; and since C can
not belong to that to which B belongs, because it carries A
along with it and A and B cannot belong to the same thing ;
it is clear that D must follow B. Again since C does not
reciprocate with A, but C or D belongs to everything, it is

10 possible that A and D should belong to the same thing.
But B and C cannot belong to the same thing, because
A follows C , and so something impossible results. It is
clear then that B does not reciprocate with D either, since
it is possible that D and A should belong at the same time
to the same thing.

It results sometimes even in such an arrangement of terms

15 that one is deceived through not apprehending the opposites
rightly, one of which must belong to everything, e.g. we may
reason that if A and B cannot belong at the same time to
the same thing, but it is necessary that one of them should
belong to whatever the other does not belong to : and again
C and D are related in the same way, and A follows every
thing which C follows : it will result l that B belongs
necessarily to everything to which D belongs : but this

20 is false. Assume that F stands for the negation of A and B,
and again that H stands for the negation of C and D. It is
necessary then that either A or F should belong to every
thing : for either the affirmation or the denial must belong.
And again either C or // must belong to everything : for
they are related as affirmation and denial. And ex Jiypothesi
A belongs to everything to which C belongs. Therefore H

25 belongs to everything to which F belongs. Again since
either F or B belongs to everything, and similarly either H
or D, and since H follows F, B must follow D : for we know
this. 2 If then A follows C, B must follow D\ But this is
false : for as we proved 3 the sequence is reversed in terms

1 Omit y<\p in 1. 19 with A and B. 2 From a 39~ b 13.

BOOK I. 46 5 2 b

so constituted. The fallacy arises because perhaps it is not
necessary that A or F should belong to everything, or that 3
F or B should belong to everything : for F is not the denial
of A. For not-good is the negation of good : and not-good
is not identical with neither good nor not-good . Similarly
also with C and D. For two negations have been assumed
in respect to one term. 1

1 In 11. 18, 21.

BOOK II

52 b WE have already explained the number of the figures, the I
character and number of the premisses, when and how

4 a syllogism is formed ; l further what we must look for when
53 a refuting and establishing propositions, and how we should
investigate a given problem in any branch of inquiry, also
by what means we shall obtain principles appropriate to
each subject. 2 Since some syllogisms are universal, others
5 particular, all the universal syllogisms give more than one
result, and of particular syllogisms the affirmative yield more
than one, the negative yield only the stated conclusion. For
all propositions are convertible save only the particular
negative : and the conclusion states one definite thing about
another definite thing. Consequently all syllogisms save the
particular negative yield more than one conclusion, e. g. if

10 A has been proved to belong to all or to some , then B
must belong to some A : and if A has been proved to belong
to no B t then B belongs to no A. This is a different
conclusion from the former. But if A does not belong-
to some B t it is not necessary that B should not belong to
some A : for it may possibly belong to all A.

15 This then is the reason common to all syllogisms whether
universal or particular. But it is possible to give another
reason concerning those which are universal. For all the
things that are subordinate to the middle term or to the
conclusion may be proved by the same syllogism, if the
former are placed in the middle, the latter in the conclusion ;

20 e. g. if the conclusion AB is proved through C, whatever is
subordinate to B or C must accept the predicate A : for if D
is included in B as in a whole, and B is included in A, then
D will be included in A. Again if E is included in C as in
a whole, and Cis included in A, then E will be included in
A. Similarly if the syllogism is negative. In the second

1 i. 1-26. 2 . 27-31.

BOOK II. i 53*

figure it will be possible to infer only that which is subordi- 25
nate to the conclusion, e. g. if A belongs to no B and to all
C\ we conclude that B belongs to no C. If then D
is subordinate to C, clearly B does not belong to it. But
that B does not belong to what is subordinate to A, is not
clear by means of the syllogism. And yet B does not 3
belong to E, if E is subordinate to A. But while it has
been proved through the syllogism that B belongs to no C,
it has been assumed without proof that B does not belong to
A, consequently it does not result through the syllogism that
B does not belong to E.

But in particular syllogisms there will be no necessity of
inferring what is subordinate to the conclusion (for a syllogism 35
does not result when this premiss l is particular), but what
ever is subordinate to the middle term may be inferred,
not however through the syllogism, e. g. if A belongs to all
B and B to some C. Nothing can be inferred about that
which is subordinate to C ; something can be inferred
about that which is subordinate to B, but not through the
preceding syllogism. Similarly in the other figures. That 40
which is subordinate to the conclusion cannot be proved ;
the other subordinate can be proved, only not through the 53 b
syllogism, just as in the universal syllogisms what is
subordinate to the middle term is proved (as we saw) from
a premiss which is not demonstrated : consequently either a
conclusion is not possible in the case of universal syllogisms
or else it is possible also in the case of particular syllogisms

2 It is possible for the premisses of the syllogism to be
true, or to be false, or to be the one true, the other false. 5
The conclusion is either true or false necessarily. From
true premisses it is not possible to draw a false conclusion,
but a true conclusion may be drawn from false premisses,
true however only in respect to the fact, not to the reason.
The reason cannot be established from false premisses : why
this is so will be explained in the sequel. 2 10

1 i.e. the conclusion of the original syllogism, which would have to
become the major premiss of the further syllogism required. A parti
cular major premiss yields no conclusion (in the first figure).

2 57 a 40-^17.

53 b ANALYTICA PRIORA

First then that it is not possible to draw a false conclusion
from true premisses, is made clear by this consideration.
If it is necessary that B should be when A is, it is necessary
that A should not be when B is not. If then A is true,
B must be true : otherwise it will turn out that the same

15 thing both is and is not at the same time. But this is
impossible. Let it not, because A is laid down as a single
term, be supposed that it is possible, when a single fact is
given, that something should necessarily result. For that
is not possible. For what results necessarily is the con
clusion, and the means by which this comes about are at
the least three terms, and two relations of subject and

20 predicate or premisses. If then it is true that A belongs
to all that to which B belongs, and that B belongs to all
that to which C belongs, it is necessary that A should
belong to all that to which C belongs, and this cannot be
false : for then the same thing will belong and not belong
at the same time. So A is posited as one thing, being two
premisses taken together. The same holds good of negative

25 syllogisms : it is not possible to prove a false conclusion
from true premisses.

But from what is false a true conclusion may be drawn,
whether both the premisses are false or only one, provided
that this is not either of the premisses indifferently, 1 if it is
taken as wholly false : but if the premiss is not taken as
wholly false, it does not matter which of the two is false. 2

30 (i) Let A belong to the whole of C, but to none of the Bs,

1 Omit uXXn TTJS dfvrtpas in 1. 28 with codd. Bu.

2 The following cases are discussed in the sequel :

Universal premisses.

53 b 3~S4 a I Both premisses wholly false, conclusion true.

54 a I, 2 Both premisses partly false, conclusion true.

54 a 2-i8 Major wholly false, minor true, conclusion false.

54 a 18-28 Major partly false, minor true, conclusion true.

54 a 28- b 2 Major true, minor wholly false, conclusion true.

54 b 2-l6 Major true, minor partly false, conclusion true.

One premiss part^c^tlar.

54 b 21-35 Major wholly false, minor true, conclusion true.
54 b 35-55*4 Major partly false, minor true, conclusion true.
55 a 4~l9 Major true, minor wholly false, conclusion true.
55 a 19-28 Major partly false, minor wholly false, conclusion true.
55 a 28- b 2 Both premisses wholly false, conclusion true.

BOOK II. 2 53 b

neither let B belong to C. This is possible, e.g. animal
belongs to no stone, nor stone to any man. If then A is
taken to belong to all B and B to all C, A will belong to
all C\ consequently though both the premisses are false the
conclusion is true : for every man is an animal. Similarly 35
with the negative. For it is possible that neither A nor B
should belong to any C, although A belongs to all B, e. g. if
the same terms are taken and man is put as middle : for
neither animal nor man belongs to any stone, but animal
belongs to every man. 1 Consequently if one term is taken
to belong to none of that to which it does belong, and the 40
other term is taken to belong to all of that to which it does
not belong, though both the premisses are false the con
clusion will be true. (2) A similar proof may be given if 54 a
each premiss is partially false.

(3) But if one only of the premisses is false, when the first
premiss is wholly false, e. g. AB t the conclusion will not be
true, but if the premiss BC is wholly false, a true conclusion
will be possible. I mean by wholly false the contrary of
the truth, e. g. if what belongs to none is assumed to belong 5
to all, or if what belongs to all is assumed to belong to none.
Let A belong to no B, and B to all C. If then the premiss
BC which I take is true, and the premiss AB is wholly false,
viz. that A belongs to all B, it is impossible that the con
clusion should be true : for A belonged to none of the 6s,
since A belonged to nothing to which B belonged, and B 10
belonged to all C. Similarly there cannot be a true con
clusion if A belongs to all B, and B to all C, but while the
true premiss BC is assumed, the wholly false premiss AB is
also assumed, viz. that A belongs to nothing to which B
belongs : here the conclusion must be false. For A will
belong to all C, since A belongs to everything to which B 1 5
belongs, and B to all C. It is clear then that when the first
premiss is wholly false, whether affirmative or negative, and
the other premiss is true, the conclusion cannot be true.

(4) But if the premiss is not wholly false, a true conclusion

1 No B (men) are A (animals).

All C (stones) are B (men).
. . No C (stones) are A (animals).

54 a ANALYTICA PRIORA

is possible. For if A belongs to all C and to some B, and if B
20 belongs to all C, e. g. animal to every swan and to some
white thing, and white to every swan, then if we take as
premisses that A belongs to all B, and B to all C, A will
belong to all C truly : for every swan is an animal. Similarly
if the statement AB is negative. For it is possible that A
25 should belong to some B and to no C, and that B should
belong to all C, e. g. animal to some white thing, but to no
snow, and white to all snow. If then one should assume
that A belongs to no B, and B to all C, then A will belong
to no C.

(5) But if the premiss AB, which is assumed, is wholly true,

and the premiss BC is wholly false, a true syllogism will be

30 possible : for nothing prevents A belonging to all B and to

all C y though B belongs to no C, e. g. these being species of

the same genus which are not subordinate one to the other :

for animal belongs both to horse and to man, but horse to

no man. If then it is assumed that A belongs to all B and

B to all C, the conclusion will be true, although the premiss

f>5 BC is wholly false. Similarly if the premiss AB is negative.

For it is possible that A should belong neither to any B nor

to any C, and that B should not belong to any C, e. g. a genus

to species of another genus : for animal belongs neither to

music nor to the art of healing, nor does music belong to

54 b the art of healing. If then it is assumed that A belongs to

no B } and B to all C, the conclusion will be true.

(6) And if the premiss BC is not wholly false but in part
only, even so the conclusion may be true. For nothing
5 prevents A belonging to the whole of B and of C, while B
belongs to some C, e. g. a genus to its species and difference :
for animal belongs to every man and to every footed thing,
and man to some footed things though not to all. If then
it is assumed that A belongs to all B, and B to all C, A will
belong to all C: and this ex hypothesi is true. Similarly
10 if the premiss AB is negative. For it is possible that A
should neither belong to any B nor to any C, though B
belongs to some C, e. g. a genus to the species of another
genus and its difference : for animal neither belongs to any
wisdom nor to any instance of speculative , but wisdom

BOOK II. 2 54 b

belongs to some instance of speculative . If then it should
be assumed that A belongs to no B, and B to all C, A will 15
belong to no C: and this ex hypothesi is true.

In particular syllogisms it is possible when the first
premiss is wholly false, and the other true, that the con
clusion should be true ; also when the first premiss is false
in part, and the other true ; l and when the first is true, and 20
the particular is false ; and when both arc false. (7) For
nothing prevents A belonging to no B, but to some C, and
B to some C, e. g. animal belongs to no snow, but to some
white thing, and snow to some white thing. If then 2 snow
is taken as middle, and animal as first term, and it is assumed 25
that A belongs to the whole of B, and B to some C, then
the premiss AB is wholly false, the premiss BC true, and
the conclusion true. Similarly if the premiss AB is nega
tive : for it is possible that A should belong to the whole
of B, but not to some C, although B belongs to some C, 30
e.g. animal belongs to every man, but does not follow 3
some white, but man belongs to some white ; consequently
if man be taken as middle term and it is assumed that A
belongs to no B but B belongs to some C, the conclusion
will be true although the premiss AB is wholly false.

(8) If the premiss AB is false in part, the conclusion may 35
be true. For nothing prevents A belonging both to B and to
some C, and B belonging to some C, e. g. animal to some
thing beautiful and to something great, and beautiful
belonging to something great. If then A is assumed to
belong to all B, and B to some C, the premiss AB will be
partially false, the premiss BC will be true, and the con- 55
elusion true. Similarly if the premiss AB is negative. For
the same terms will serve, and in the same positions, to
prove the point. 4

(9) Again if the premiss AB is true, and the premiss BC is
false, the conclusion may be true. For nothing prevents A ;
belonging to the whole of B and to some C, while B belongs

1 Omit 0X77? in 1. 20 with A, B, C, and Waitz.

2 ov in 1. 24 (Bekker) is a misprint for o5t>.
J See note 43 3.

4 viz. that a true conclusion may follow if one premiss is partially
false, the other true.

55 a ANALYTICA PRIORA

to no C, e. g. animal to every swan and to some black things,
though swan belongs to no black thing. Consequently if it
should be assumed that A belongs to all B, and B to some C,
10 the conclusion will be true, although the statement BC is
false. Similarly if the premiss AB is negative. For it is
possible that A should belong to no B, and not to some C,
while B belongs to no C, e. g. a genus to the species of
another genus and to the accident of its own species : for
15 animal belongs to no number and not to some white things, 1
and number belongs to nothing white. If then number is
taken as middle, and it is assumed that A belongs to no >,
and B to some C, then A will not belong to some C, which
ex hypothesi is true. And the premiss AB is true, the
premiss BC false.

(10) Also if the premiss AB is partially false, and the pre-
20 miss BC is false too, the conclusion may be true. For nothing
prevents A belonging to some B and to some C, though B
belongs to no C, c. g. if B is the contrary of C, and both are
accidents of the same genus : for animal belongs to some
white things and to some black things, but white belongs to
25 no black thing. If then it is assumed that A belongs to all
B, and B to some C, the conclusion will be true. Similarly
if the premiss AB is negative : for the same terms arranged
in the same way will serve for the proof.

(u) Also though both premisses are false the conclusion
may be true. For it is possible that A may belong to no B
30 and to some C, while B belongs to no C, e. g. a genus in rela
tion to the species of another genus, and to the accident of its
own species : for animal belongs to no number, but to some
white things, and number to nothing white. If then it is
assumed that A belongs to all B and B to some C, the
35 conclusion will be true, though both premisses are false.
Similarly also if the premiss AB is negative. For nothing
prevents A belonging to the whole of B, and not to some C,
while B belongs to no C, e.g. animal belongs to every swan,

1 Read in 1. 15 TIV\ ou, which seems to have been read by Phil.

No B (number) is A (animal). (True.)

Some C (white) is B (number). (False.)

. . Some C (white) is not A (animal). (True.)

BOOK IT. 2 55 a

and not to some black things, and swan belongs to nothing
black. Consequently if it is assumed that A belongs to 4 o
no B, and B to some 6", then A does not belong to some C, 55 b
The conclusion then is true, but the premisses are false.

3 In the middle figure it is possible in every way to reach
a true conclusion through false premisses, whether the syllo
gisms are universal or particular, viz. when both premisses
are wholly false ; when each is partially false ; when one 5
is true, the other wholly false (it does not matter which of
the two premisses is false) ; if both premisses are partially
false ; if one is quite true, the other partially false ; if one is
wholly false, the other partially true. 1 For (i) if A belongs 10
to no B and to all C, e. g. animal to no stone and to every
horse, then if the premisses are stated contrariwise and it is
assumed that A belongs to all B and to no C, though the
premisses are wholly false they will yield a true conclusion.

1 The possible combinations of premisses in which there is some
element of falsity are :

(1) Wholly false with wholly false.

(2) True with wholly false.

(3) Partly false with partly false.

(4) True with partly false.

(5) Wholly false with partly false.

eni TI fKarepaf seems, in the light of 56 " 20-33, to mean the third (and
not the fifth) of these cases, which is also expressed by KU\ el dp.(f>6repai
eni TI \ls(v8( is. Waitz would excise the latter clause for this reason,
and Ktii el 77 jj.fi> oXrj i^euS /f f) 8 eni TI aXrjOj js because (ai eni TI dXrjdr/s
does not occur elsewhere in Aristotle, (b) it must mean either (i) the
same as partly false , so that case (5) is meant, a case entirely
ignored by Aristotle throughout cc. 2-4, and therefore not to be expected
here, or (ii) something else, in which case Aristotle illogically omits all
the other combinations which include one partly true premiss.

To (a) it may be replied that eni TI dXrjdfjs is justified by the use of
its opposite dTrXw? dXrjdrjs 1. 7, which Waitz does not reject (cf. oXr;
dXrjdrjs 1. 17, c.). To (b) it may be replied that the clause plainly
does indicate case (5) and that this case is expressly dealt with in the
discussion of the first figure, 55 a 19-28. It is true that this case is
omitted in the detailed discussion of the second figure, where with
reference to universal syllogisms (i) is discussed in 55 b io-i6, (2) in
55 b 16-23, (4) in 55 b 23-38, (3) in 55 38-56* 4, and with reference to
particular syllogisms (2) fs discussed in 56 a 5-32, (i) in 56 a 32- b 3- But
similarly (3) is omitted in the discussion of particular syllogisms in the
first figure. Aristotle does not attempt to work out all the possibilities.

There remains the repetition involved in eni e /care pa? and el
up.(f)6rtpui eni TI \lsev8eis. It is quite possible that through confusion
Aristotle wrote the passage as it stands; if anything is to go it seems
better to excise eni TI enure pus as introduced by imitation of c. 4, 56 5.

55 b ANALYTICA PRIORA

15 Similarly if A belongs to all B and to no C: for we shall
have the same syllogism.

(2) Again if one premiss is wholly false, the other wholly
true : for nothing prevents A belonging to all B and to all C,
though B belongs to no C, e. g. a genus to its co-ordinate
species. For animal belongs to every horse and man, and

20 no man is a horse. If then it is assumed that animal
belongs to all of the one, and none of the other, the one
premiss will be wholly false, the other wholly true, and the
conclusion will be true whichever term the negative state
ment concerns.

(3) Also if one premiss is partially false, the other wholly
true. For it is possible that A should belong to some B

25 and to all C, though B belongs to no C, e.g. animal to
some white things and to every raven, though white belongs
to no raven. If then it is assumed that A belongs to no B,
but to the whole of C, the premiss AB is partially false, the
premiss A C wholly true, and the conclusion true. Similarly

30 if the negative statement is transposed : 1 the proof can be
made by means of the same terms. Also if the affirmative
premiss is partially false, the negative wholly true, a true
conclusion is possible. For nothing prevents A belonging
to some B, but not to C as a whole, 2 while B belongs to
no C, e. g. animal belongs to some white things, but to no

35 pitch, and white belongs to no pitch. Consequently if it is
assumed that A belongs to the whole of B, but to no C, the
premiss AB is partially false, the premiss AC is wholly true,
and the conclusion is true.

(4) And if both the premisses are partially false, the
conclusion may be true. For it is possible that A should

4 o belong to some B and to some C, and B to no C, e. g. animal
to some white things and to some black things, though white
g6 a belongs to nothing black. If then it is assumed that A
belongs to all B and to no C, both premisses are partially
false, but the conclusion is true. Similarly, if the negative
premiss is transposed, the proof can be made by means of
the same terms.

1 i.e. treated as minor instead of major premiss.
" i.e. not to any C.

BOOK II. 3 56*

It is clear also that our thesis holds in particular syllo- 5
gisms. For (5) nothing prevents A belonging to all B and
to some C, though B does not belong to some C, e. g. animal
to every man and to some white things, though man will
not belong to some white things. If then it is stated that
A belongs to no B and to ^some C, the universal premiss is 10
wholly false, the particular premiss is true, and the con
clusion is true. Similarly if the premiss AB is affirmative:
for it is possible that A should belong to no B, and not to
some C, though B does not belong to some C, e. g. animal
belongs to nothing lifeless, and does not belong to some
white things, and lifeless will not belong to some white 15
things. 1 If then it is stated that A belongs to all B and
not to some C, the premiss AB which is universal is wholly
false, the premiss AC is true, and the conclusion is true.
Also a true conclusion is possible when the universal premiss
is true, and the particular is false. For nothing prevents A
following - neither B nor C at all, while B does not belong to 20
some C, e. g. animal belongs to no number nor to anything
lifeless, and number does not follow some lifeless things.
If then it is stated that A belongs to no B and to some C,
the conclusion will be true, and the universal premiss true,
but the particular false. Similarly if the premiss which is 25
stated universally is affirmative. For it is possible that A
should belong both to B and to C as wholes, though B does
not follow some C, e. g. a genus in relation to its species
and difference : for animal follows every man and footed
things as a whole, but man does not follow every footed
thing. Consequently if it is assumed that A belongs to the
whole of B, but does not belong to some C, the universal 30
premiss is true, the particular false, and the conclusion
true.

(6) It is clear too that though both premisses are false
they may yield a true conclusion, since it is possible that A

1 Read ou for nvx v-napxei in 1. 15 with C.,. The sense requires
a negative, though this has little MS. support.

All B (lifeless) is A (animal). (False.)
Some C (white) is not A (animal). (True.)
. . Some C (white) is not B (lifeless). (True.)

2 See note 43 b 3-

646.24-3 II

5 6 a ANALYTICA PRIORA

should belong both to B and to C as wholes, 1 though B

35 does not follow some C. For if it is assumed that A belongs

to no B and to some C, the premisses are both false, but the

conclusion is true. Similarly if the universal premiss is

affirmative and the particular negative. For it is possible

that A should follow no B and all C, though B does not

40 belong to some C, e. g. animal follows no science but every

man, though science does not follow every man. If then A

56 b is assumed to belong to the whole of /?, and not to follow

some C, the premisses are false but the conclusion is true.

In the last figure a true conclusion may come through 4
5 what is false, alike when both premisses are wholly false,
when each is partly false, when one premiss is wholly true,
the other false, when one premiss is partly false, the other
wholly true, and vice versa, and in every other way in which it
is possible to alter the premisses. 2 For(i) nothing prevents

10 neither A nor B from belonging to any C, while A belongs
to some , e.g. neither man nor footed follows anything
lifeless, though man belongs to some footed things. If then
it is assumed that A and B belong to all C, the premisses
will be wholly false, but the conclusion true. Similarly if
one premiss is negative, the other affirmative. For it is

15 possible that B should belong to no C, but A to all C, and that
A should not belong to some B, e. g. black belongs to no
swan, animal to every swan, and animal not to everything
black. Consequently if it is assumed that B belongs to

1 The sense requires something like the reading implied in 1. 34 by
Boethius translation, viz. rw/^eV 6 Xa> TO> 8e /nr;Sw , in place of oA&>.

No Sis A. (False.)
Some C is A. (False.)
. . Some C is not B. (True.)
But the confusion may be in Aristotle.

2 The following cases are discussed in the sequel :

Both premisses tiniversal.

56 b 9-20 Both premisses wholly false, conclusion true.
56 b 20-33 Both premisses partly false, conclusion true.
56^33-57*9 One premiss true, the other wholly false, conclusion

true.
57*9-28 One premiss true, the other partly false, conclusion

true.

One premiss particular.
57*29-35 Same situation as when both premisses are universal.

BOOK IT. 4 56

all C, and A to no C, A will not belong to some B : and the
conclusion is true, though the premisses are false. 2 o

(2) Also if each premiss is partly false, the conclusion
may be true. For nothing prevents both A and B from
belonging to some C while A belongs to some B, e. g. white
and beautiful belong to some animals, and white to some
beautiful things. If then it is stated that A and B belong
to all C, the premisses are partially false, but the conclusion 25
is true. Similarly if the premiss AC is stated as negative.
For nothing prevents A from not belonging, and B from
belonging, to some C, while A does not belong to all B,

c. g. white does not belong to some animals, beautiful
belongs to some animals, and white does not belong to 30
everything beautiful. Consequently if it is assumed that A
belongs to no C, and B to all C, both premisses are partly
false, but the conclusion is true.

(3) Similarly if one of the premisses assumed is wholly
false, the other wholly true. For it is possible that both A and
B should follow all C t though A does not belong to some B, 35
e.g. animal and white follow every swan, though animal
does not belong to everything white. Taking these then as
terms, if one assumes that B belongs to the whole of C, but

A does not belong to C at all, the premiss EC will be
wholly true, the premiss AC wholly false, and the conclu
sion true. Similarly if the statement BC is false, the 40
statement AC true, the conclusion may be true. The
same terms will serve for the proof. 1 Also if both the 57
premisses assumed are affirmative, the conclusion may
be true. For nothing prevents B from following all C,
and A from not belonging to C at all, though A belongs to
some B } e. g. animal belongs to every swan, 2 black to no
swan, and black to some animals. Consequently if it is .-
assumed that A and B belong to every C, the premiss BCis
wholly true, the premiss ACis wholly false, and the conclu-

1 Black swan lifeless , which follow in the MSS. at 1. I, nre not
the same terms , and owe their origin to the (lost) commentary of
Alexander, who saw that the same terms animal, white, swan
will not serve Aristotle s turn i.e. if they are as before respectively
major, minor, and middle term.

2 Omit fifv in 1. 4 with B and \Vaitz.

II 2

57 a ANALYTICA PRIORA

sion is true. Similarly if the premiss A C which is assumed
is true : the proof can be made through the same terms.

(4) Again if one premiss is wholly true, the other partly
10 false, the conclusion may be true. For it is possible that B

should belong to all C, and A to some C, while A belongs
to some B, e. g. biped belongs to every man, beautiful not
to every man, and beautiful to some bipeds. If then it
is assumed that both A and B belong to the whole of C,
the premiss BC is wholly true, the premiss A C partly false,

! 5 the conclusion true. Similarly if of the premisses assumed
ACis true and BC partly false, a true conclusion is possible :
this can be proved, if the same terms as before are trans
posed. Also the conclusion may be true if one premiss
is negative, the other affirmative. For since it is possible
that B should belong to the whole of C, and A to some C,

20 and, when they are so, that A should not belong to all B,
therefore if it is assumed that B belongs to the whole of
C, and A to no C, the negative premiss is partly false, the
other premiss wholly true, and the conclusion is true.
Again since it has been proved that if A belongs to no C
and B to some C, it is possible that A should not belong to

- ; some C, it is clear that if the premiss A C is wholly true,
and the premiss BC partly false, it is possible that the
conclusion should be true. For if it is assumed that A
belongs to no C, and B to all C, the premiss A C is wholly
true, and the premiss BC is partly false.

(5) It is clear also in the case of particular syllogisms ] that
30 a true conclusion may come through what is false, in every

possible way. For the same terms must be taken as have
been taken when the premisses are universal, positive terms
in positive syllogisms, negative terms in negative. For it
makes no difference to the setting out of the terms, whether
one assumes that what belongs to none belongs to all or
35 that what belongs to some belongs to all. The same applies
to negative statements.

It is clear then that if the conclusion is false, the pre
misses of the argument must be false, either all or some
of them ; but when the conclusion is true, it is not necessary
1 i.e. syllogisms having one premiss particular.

BOOK II. 4 57"

that the premisses should be true, either one or all, yet it is
possible, though no part of the syllogism is true, that the
conclusion may none the less be true ; but it is not neces- 40
sitated. The reason is that when two things are so related 57 b
to one another, that if the one is, the other necessarily is,
then if the latter is not, the former will not be cither, but if
the latter is, it is not necessary that the former should be.
But it is impossible that the same thing should be neces
sitated by the being and by the not-being of the same
thing. I mean, for example, that it is impossible that B
should necessarily be great since A is white and that B 5
should necessarily be great since A is not white. For
whenever since this, A, is white it is necessary that that, />,
should be great, and since B is great that C should not be
white, then it is necessary if A is white that C should not
be white. And whenever it is necessary, since one of two
things is, that the other should be, it is necessary, if the >o
latter is not, that the former (viz. A) should not be. If
then B is not great A cannot be white. But if, when A is
not white, it is necessary that B should be great, it neces
sarily results that if B is not great, B itself is great. (But
this is impossible.) For if B is not great, A will necessarily
not be white. If then when this is not white B must be 15
great, it results that if B is not great, it is great, just as if it
were proved through three terms.

5 Circular and reciprocal proof means proof by means of
the conclusion, i. e. by converting one of the premisses
simply and inferring the other premiss which was assumed 20
in the original syllogism : 1 e. g. suppose it has been
necessary to prove that A belongs to all C, and it has
been proved through B ; suppose that A should now be
proved to belong to B by assuming that A belongs to
C, and C to B so A belongs to /?: but in the first
syllogism the converse was assumed, viz. that B belongs 25
to C. Or suppose it is necessary to prove that B belongs
to C, and A is assumed to belong to C, which was the
conclusion of the first syllogism, and B to belong to A:
but the converse was assumed in the earlier syllogism,
1 The sentence would be clearer if we could read \afr~iv in 1. 20.

57 b ANALYTICA PRIOR A

viz. that A belongs to B. In no other way is reciprocal
proof possible. If another term is taken as middle, the

30 proof is not circular : for neither of the propositions assumed
is the same as before : if one of the accepted terms is taken
as middle, only one of the premisses of the first syllogism
can be assumed in the second : for if both of them are
taken the same conclusion as before will result : but it
must be different. If the terms are not convertible, one
of the premisses from which the syllogism results must be
undemonstrated : for it is not possible to demonstrate
through these terms that the third belongs to the middle

35 or the middle to the first. If the terms are convertible,
it is possible to demonstrate everything reciprocally, e. g. if
A and B and C are convertible with one another. Suppose
the proposition AC has been demonstrated through B as
middle term, and again the proposition AB through the
conclusion and the premiss .Z>6~ con verted, and similarly the

qo proposition BC through the conclusion and the premiss AB
tj8 a converted. But it is necessary to prove both the premiss
CB> and the premiss BA : for we have used these alone
without demonstrating them. If then it is assumed that B
belongs to all C, and C to all A, we shall have a syllogism
5 relating B to A. Again if it is assumed that C belongs to
all A y and A to all B, C must belong to all B, In both
these syllogisms the premiss CA has been assumed without
being demonstrated : the other premisses had ex hypotliesi
been proved. Consequently if we succeed in demonstrating
this premiss, all the premisses will have been proved

10 reciprocally. If then it is assumed that C belongs to all B,
and B to all A, both the premisses assumed have been
proved, and C must belong to A. It is clear then that only
if the terms are convertible is circular and reciprocal
demonstration possible (if the terms are not convertible,

15 the matter stands as we said above). But it turns out in
these also that we use for the demonstration the very thing
that is being proved: for C is proved of B, and B of A,
by assuming that C is said of A, and C is proved of A
through these premisses, so that we use the conclusion for

20 the demonstration.

BOOK II. 5 5 8 a

In negative syllogisms reciprocal proof is as follows. Let
B belong to all C, and A to none of the Bs : we conclude
that A belongs to none of the Cs. If again it is necessary
to prove that A belongs to none of the >s (which was
previously assumed) A must belong to no C, and C to all B: 25
thus the previous premiss is reversed. If it is necessary to
prove that B belongs to C, the proposition AB must no
longer be converted as before : for the premiss B belongs to
no A is identical with the premiss A belongs to no B . But
we must assume that B belongs to all of that to none of
which A belongs. Let A belong to none of the Cs (which 30
was the previous conclusion) and assume that B belongs to
all of that to none of which A belongs. It is necessary then
that B should belong to all C. Consequently each of the
three propositions has been made a conclusion, and this
is circular demonstration, to assume the conclusion and the
converse of one of the premisses, and deduce the remaining 35
premiss.

In particular syllogisms it is not possible to demonstrate
the universal premiss through the other propositions, but
the particular premiss can be demonstrated. Clearly it is
impossible to demonstrate the universal premiss : for what
is universal is proved through propositions which are
universal, but the conclusion is not universal, and the proof 4
must start from the conclusion and the other premiss.
Further a syllogism cannot be made at all if the other
premiss is converted : for the result is that both premisses 58 b
are particular. But the particular premiss may be proved.
Suppose that A has been proved of some C through B. If
then it is assumed that B belongs to all A, and the conclu
sion is retained, B will belong to some C: for we obtain the 5
first figure and A is middle. But if the syllogism is nega
tive, it is not possible to prove the universal premiss, for
the reason l given above. But it is possible to prove the
particular premiss, if the proposition AB is converted as in
the universal syllogism, 2 i. e. B belongs to some of that to 10

1 Read 81 5 in 1. 7 with Buhle.

2 Cf. a 29. Omit with A, 13, and \Yaitz in 1. 8 ptv and in I. 9 OVK <

8l<\ TTOO \i f(t)S 6 fCTTlV.

58 b ANALYTICA PRIORA

some of which A does not belong : otherwise no syllogism
results because the particular premiss is negative.

In the second figure it is not possible to prove an affir- 6
mative proposition in this way, but a negative proposition

15 may be proved. An affirmative proposition is not proved
because both premisses of the new syllogism are not affirma
tive (for the conclusion is negative) but an affirmative
proposition is (as we saw) proved from premisses which are
both affirmatiVe. The negative is proved as follows. Let
A belong to all B, and to no C: we conclude that .5 belongs

20 to no C. If then it is assumed that B belongs to all A, 1 it
is necessary that A should belong to no C: for we get the
second figure, with B as middle. But if the premiss AB
was negative, and the other affirmative, we shall have the
first figure. For C belongs to all A. and B to no C,

2.; consequently B belongs to no A : neither then does A
belong to B. Through the conclusion, therefore, and one
premiss, we get no syllogism, but if another premiss is
assumed in addition, a syllogism will be possible. But,
if the syllogism is not universal, the universal premiss
cannot be proved, for the same reason as we gave above, 2 but

30 the particular premiss can be proved whenever the universal
statement is affirmative. Let A belong to all B, and not to
all C: the conclusion is EC. If then it is assumed that B
belongs to all A, but not to all C, A will not belong to some
C, B being middle. But if the universal premiss is negative,
the premiss A C will not be demonstrated by the conversion

5? of AB : for it turns out that either both or one of the
premisses is negative ; consequently a syllogism will not be
possible. But the proof will proceed as in the universal
syllogisms, 3 if it is assumed that A belongs to some of that
to some of which B does not belong.

In the third figure, when both premisses are taken 7
40 universally, it is not possible to prove them reciprocally : for
that which is universal is proved through statements which
59 a are universal, but the conclusion in this figure is always

1 Omit rw 8f r /nqSeiu in 1. 20 with A, B, and Waitz.

2 a 38. 3 Cf. a 29.

BOOK II. 7 59

particular, so that it is clear that it is not possible at all to
prove through this figure the universal premiss. But if one
premiss is universal, the other particular, proof of the latter
will sometimes be possible, sometimes not. When both the
premisses assumed are affirmative, and the universal concerns 5
the minor extreme, proof will be possible, but when it concerns
the other extreme, impossible. Let A belong to all C and
B to some C : the conclusion is the statement AB. If then
it is assumed that C belongs to all A, it has been proved
that C belongs to some B, but that B belongs to some C has

O O

not been proved. And yet it is necessary, if C belongs to 10
some B, that B should belong to some C. But it is not the
same that this should belong to that, and that to this : but
we must assume besides that if this belongs to some of that,
that belongs to some of this. But if this is assumed the
syllogism no longer results from the conclusion and the
other premiss. But if B belongs to all C, and A to some C, \?
it will be possible to prove the proposition AC, when it
is assumed that C belongs to all B, and A to some B. For
if C belongs to all B and A to some B, it is necessary that
A should belong to some C, B being middle. And when
ever one premiss is affirmative, the other negative, and the
affirmative is universal, the other premiss can be proved.
Let B belong to all C, and A not to some C : the conclusion 20
is that A does not belong to some B. If then it is assumed
further that C belongs to all B, it is necessary that A should
not belong to some C, B being middle. But when the
negative premiss is universal, the other premiss is not
proved, except as before, 1 viz. if it is assumed that that 25
belongs to some of that, to some of which this does not
belong, e.g. if A belongs to no C, and B to some C: the
conclusion is that A does not belong to some C. If then
it is assumed that C belongs to some of that to some of which
A does not belong, it is necessary that C should belong to
some of the Bs. In no other way is it possible by
converting the universal premiss to prove the other : for 30
in no other way can a syllogism be formed.

It is clear then that in the first figure reciprocal proof is
58*9.

59 a ANALYTICA PRIORA

made both through the third and through the first figure if
the conclusion is affirmative through the first ; if the con-

35 elusion is negative through the last. For it is assumed
that that belongs to all of that to none of which this belongs.
In the middle figure, when the syllogism is universal, proof
is possible through the second figure and through the first,
but when particular through the second and the last. In
the third figure all proofs are made through itself. It

40 is clear also that in the third figure and in the middle figure
those syllogisms which are not made through those figures
themselves ] either are not of the nature of circular proof or
arc imperfect.

59 b To convert a syllogism means to alter the conclusion and 8
make another syllogism to prove that either the extreme "
cannot belong to the middle or the middle to the last 3 term.
For it is necessary, if the conclusion has been changed into
its opposite and one of the premisses stands, that the other
5 premiss should be destroyed. For if it should stand, the
conclusion also must stand. It makes a difference whether
the conclusion is converted into its contradictory or into its
contrary. For the same syllogism does not result whichever
form the conversion takes. This will be made clear by the
sequel. By contradictory opposition I mean the opposition
of to all to not to all , and of to some to to none ;

10 by contrary opposition I mean the opposition of to all to
to none , and of to some to not to some . Suppose that
A has been proved of C, through B as middle term. If then
it should be assumed that A belongs to no C, but to all /?,
B will belong to no C. And if A belongs to no C, and B to
all C, A will belong, not to no B at all, but not to all B. For

15 (as we saw) the universal is not proved through the last
figure. 4 In a word it is not possible to refute universally by
conversion the premiss which concerns the major extreme :
for the refutation always proceeds through the third figure ;
since it is necessary to take both premisses in reference to

20 the minor extreme. Similarly if the syllogism is negative.

1 Cf. 58 22-7, 59 a 6-14. 2 Major term. 3 Minor. 4 i. 6.

ROOK II. 8 59

Suppose it has been proved that A belongs to no C through
B. Then if it is assumed that A belongs to all C, and to no
B, B will belong to none of the Cs. And if A and B belong
to all C, A will belong to some B : but in the original
premiss it belonged to no B.

If the conclusion is converted into its contradictory, the 2=,
syllogisms will be contradictory and not universal. For one
premiss is particular, so that the conclusion also will
be particular. Let the syllogism be affirmative, and let it
be converted as stated. Then if A belongs not to all C, but
to all B, B will belong not to all C. And if A belongs not ?,o
to all C, but B belongs to all C, A will belong not to all B.
Similarly if the syllogism is negative. For if A belongs to
some C, and to no B, B will belong, not to no C at all, but
not to some C. And if A belongs to some C, and B to
all 7, as was originally assumed, A will belong to some />. 35

In particular syllogisms when the conclusion is converted
into its contradictory, both premisses may be refuted, but
when it is converted into its contrary, neither. For
the result is no longer, as in the universal syllogisms, 1 40
a refutation in which the conclusion reached by conversion
lacks universality, but no refutation at all. Suppose that A 6o n
has been proved of some C. If then it is assumed that A
belongs to no C, and B to some C, A will not belong to some
B : and if A belongs to no C, but to all //, B will belong to
no C. Thus both premisses are refuted. But neither can
be refuted if the conclusion is converted into its contrary. .=
For if A does not belong to some C, but to all B, then B
will not belong to some C. But the original premiss is not
yet refuted : for it is possible that B should belong to some
C, and should not belong to some C. The universal premiss
AB cannot be affected by a syllogism at all : for if A does
not belong to some of the Cs, but B belongs to some of the 10
Cs, neither of the premisses is universal. Similarly if the
syllogism is negative: for if it should be assumed that A
belongs to all C, both premisses are refuted: but if the
assumption is that A belongs to some C, neither premiss is
refuted. The proof is the same as before.
1 11. 13-20, 23-4.

6o a ANALYTICA PRIORA

15 In the second figure it is not possible to refute the premiss 9
which concerns the major extreme by establishing something
contrary to it, whichever form the conversion of the conclusion
may take. For the conclusion of the refutation will always
be in the third figure, and in this figure (as we saw l ) there is no
universal syllogism. The other premiss can be refuted in a
manner similar to the conversion : I mean, if the conclusion of

20 the first syllogism is converted into its contrary, the conclusion
of the refutation will be the contrary of the minor premiss
of the first, if into its contradictory, the contradictory. Let A
belong to all B and to no C : conclusion BC. If then it is
assumed that B belongs to all C, and the proposition AB
stands, A will belong to all C, since the first figure is pro-

2? duced. If B belongs to all C, and A to no C. then A belongs
not to all B : the figure is the last. But if the conclusion BC
is converted into its contradictory, the premiss AB will be
refuted as before, 2 the premiss AC by its contradictory.
For if B belongs to some C, and A to no C, then A will not
belong to some B. Again if B belongs to some C, and A to

30 all B, A will belong to some C, so that the syllogism results
in the contradictory of the minor premiss. A similar proof
can be given if the premisses are transposed in respect
of their quality.

If the syllogism is particular, when the conclusion is
converted into its contrary neither premiss can be refuted,
as also happened in the first figure, 3 but if the conclusion is

?,:-, converted into its contradictory, both premisses can be
refuted. Suppose that A belongs to no B, and to some C:
the conclusion is BC. If then it is assumed that B belongs
to some C, and the statement AB stands, the conclusion
will be that A does not belong to some C. But the original
statement has not been refuted : for it is possible that A
should belong to some 7 and also not to some C. Again if

4 B belongs to some Cand A to some C, no syllogism will be

possible : for neither of the premisses taken is universal.

6o h Consequently the proposition AB is not refuted. But

if the conclusion is converted into its contradictory, both

1 i. 6. 2 i.e. by its contradictory.

3 59 b 39~6o a I, 6o a 5-i4.

BOOK II. 9 60

premisses can be refuted. For if B belongs to all C, and A
to no B, A will belong to no C: but it was assumed to
belong to some C. Again if B belongs to all C and A to
some C, A will belong to some B. The same proof can be
given if the universal statement is affirmative. 5

lo In the third figure when the conclusion is converted into
its contrary, neither of the premisses can be refuted in any
of the syllogisms, but when the conclusion is converted into
its contradictory, both premisses may be refuted and in all
the moods. Suppose it has been proved that A belongs to
some B, C being taken as middle, and the premisses being 10
universal. If then it is assumed that A does not belong to
some B, but B belongs to all C, no syllogism is formed about
A and C. Nor if A does not belong to some B, but belongs
to all C, will a syllogism be possible about B and C.
A similar proof can be given if the premisses are not universal. 15
For either both premisses arrived at by the conversion must
be particular, or the universal premiss must refer to the minor
extreme. But we found that no syllogism is possible thus
either in the first or in the middle figure. 1 But if the
conclusion is converted into its contradictory, both the
premisses 2 can be refuted. For if A belongs to no />, and 20
B to all C, then A belongs to no C: again if A belongs to
no B, and to all C, B belongs to no C. And similarly if one
of the premisses is not universal. For if A belongs to no B,
and B to some C, A will not belong to some C: if A
belongs to no B, and to all C, B will belong to no C. 2=;

Similarly if the original syllogism is negative. Suppose
it has been proved that A does not belong to some B, BC
being affirmative, A C being negative : for it was thus that, as
we saw, 3 a syllogism could be made. Whenever then the
contrary of the conclusion is assumed a syllogism will not
be possible. For if A belongs to some B, and B to all C, 30
no syllogism is possible (as we saw 4 ) about A and C. Nor,
if A belongs to some /?, and to no C, was a syllogism

1 26 a 17-21, 27 a 4-I2.

2 Read di/Ttor/je^ijTai in 1. 19 (which Phil, seems to have read), and
place the comma before m Trporao-ei? with Waitz.

3 28 b i-4, l5-29 a io. " 26*30-6.

6o b ANALYTICA PRIORA

possible concerning B and C.^ Therefore the premisses are
not refuted. But when the contradictory of the conclusion is
assumed, they are refuted. For if A belongs to all B, and

35 B to C, A belongs to all C: but A was supposed originally
to belong to no C. Again if A belongs to all B, and to no
C, then B belongs to no C : but it was supposed to belong
to all C. A similar proof is possible if the premisses are
not universal. For A C becomes universal and negative, the
other premiss particular and affirmative. If then A belongs

40 to all B, and B to some C, it results that A belongs to some
C: but it was supposed to belong to no C. Again if A
6l a belongs to all /?, and to no C, then B belongs to no C: but
it was assumed to belong to some C. If A belongs to some
B and B to some C, no syllogism results : nor yet if A
belongs to some B, and to no C. Thus in one way the
premisses are refuted, in the other way they are not.
5 From what has been said it is clear how a syllogism
results in each figure when the conclusion is converted ;
when a result contrary to the premiss, and when a result
contradictory to the premiss, is obtained. It is clear that in
the first figure 2 the syllogisms are formed through the
middle and the last figures, and the premiss which concerns

10 the minor extreme is always refuted through the middle
figure, the premiss which concerns the major through
the last figure. In the second figure syllogisms proceed
through the first and the last figures, and the premiss which
concerns the minor extreme is always refuted through the
first figure, the premiss which concerns the major extreme
through the last. In the third figure the refutation proceeds
through the first and the middle figures ; the premiss which

15 concerns the major is always refuted through the first figure,
the premiss which concerns the minor through the middle
figure.

It is clear then what conversion is, how it is effected in n
each figure, and what syllogism results. The syllogism
per impossibile is proved when the contradictory of the con-
20 elusion is stated and another premiss is assumed ; it can be

! ?7 b 6-8.

" i.e. in refutation of the premisses of a syllogism in the first figure.

BOOK II. ii 61"

made in all the figures. For it resembles conversion, differing
only in this : conversion takes place after a syllogism has
been formed and both the premisses have been taken, but
a reduction to the impossible takes place not because the
contradictory has been agreed to already, but because it is 25
clear that it is true. 1 The terms are alike in both, and the
premisses of both are taken in the same way. For example
if A belongs to all B, C being middle, then if it is supposed
that A does not belong to all B or belongs to no B, but to
all C (which was admitted to be true), it follows that C
belongs to no B or not to all B. But this is impossible : 30
consequently the supposition is false : its contradictory then
is true. Similarly in the other figures : for whatever moods
admit of conversion admit also of the reduction per im-
possibile.

All the problems can be proved per impossibile in all the
figures, excepting the universal affirmative, which is proved 3?
in the middle and third figures, but not in the first. Suppose
that A belongs not to all B, or to no B, and take besides
another premiss concerning either of the terms, viz. that C
belongs to all A. or that B belongs to all D\ thus we get
the first figure. If then it is supposed that A does not 40
belong to all B, no syllogism results whichever term the
assumed premiss concerns ; but if it is supposed that A 6i b
belongs to no B, when the premiss BD is assumed as well
we shall prove syllogistically what is false, but not the
problem proposed. For if A belongs to no />, and B belongs
to all D, A belongs to no D. Let this be impossible : it is ;
false then that A belongs to no B. But the universal affirma
tive is not necessarily true if the universal negative is false.
But if the premiss CA is assumed as well, no syllogism
results, nor does it do so when it is supposed that A does
not belong to all B. Consequently it is clear that the
universal affirmative cannot be proved in the first figure
per impossibile.

1 i.e. in conversion we explicitly assume one premiss and the
opposite of the conclusion, and thus form a syllogism ; in reduction ad
impossibile we need not explicitly assume the original premiss which is
the opposite of the conclusion of the new syllogism ; we may treat its
truth as obvious.

6i b

10 But the particular affirmative and the universal and par
ticular negatives can all be proved. Suppose that A belongs
to no B, and let it have been assumed that B belongs to all
or to some C. Then it is necessary that A should belong
to no C or not to all C. But this is impossible (for let it be
true and clear that A belongs to all C) : l consequently if

15 this is false, it is necessary that A should belong to some B.
But if the other premiss assumed relates to A, no syllogism
will be possible. Nor can a conclusion be drawn when the
contrary of the conclusion is supposed, e. g. that A does not
belong to some B. Clearly then we must suppose the
contradictory.

Again suppose that A belongs to some B, and let it have

20 been assumed that C belongs to all A. It is necessary then
that C should belong to some B. But let this be impossible,
so that the supposition is false : in that case it is true that A
belongs to no B. We may proceed in the same way if the
proposition CA has been taken as negative. But if the
premiss assumed concerns B, no syllogism will be possible.
If the contrary is supposed, we shall have a syllogism and

25 an impossible conclusion, but the problem in hand is not
proved. Suppose that A belongs to all B, and let it have
been assumed that C belongs to all A. It is necessary then
that C should belong to all B. But this is impossible, so
that it is false that A belongs to all B. But we have not
yet shown it to be necessary that A belongs to no B, if it

30 does not belong to all B. Similarly if the other premiss
taken concerns B ; we shall have a syllogism and a con
clusion which is impossible, but the hypothesis is not refuted.
Therefore it is the contradictory that we must suppose.

To prove that A does not belong to all /?, we must suppose
that it belongs to all B : for if A belongs to all B, and C to

35 all A, then C belongs to all B ; so that if this is impossible,
the hypothesis is false. Similarly if the other premiss
assumed concerns B. The same results if the original
proposition CA was negative : for thus also we get a
syllogism. But if the negative proposition concerns />,

1 Read eWo) ... A 11. 13, 14 in brackets, and omit the comma after
a-Xijdts, with Waitz.

BOOK II. H 6i b

nothing is proved. If the hypothesis is that A belongs
not to all but to some B, it is not proved that A belongs 4 o
not to all B, but that it belongs to no B. For if A belongs
to some B t and C to all A, then C will belong to some B.
If then this is impossible, it is false that A belongs to some B ;
consequently it is true that A belongs to no B. But if this 6a a
is proved, the truth is refuted as well ; for the original con
clusion was that A belongs to some B, and does not belong
to some B. Further the impossible does not result from
the hypothesis : for then the hypothesis would be false, 5
since it is impossible to draw a false conclusion from true
premisses : but in fact it is true : for A belongs to some B.
Consequently we must not suppose that A belongs to some
B, but that it belongs to all B. Similarly if we should be
proving that A does not belong to some B : for if not to
belong to some and to belong not to all have the same
meaning, the demonstration of both will be identical. 10

It is clear then that not the contrary but the contradictory
ought to be supposed in all the syllogisms. For thus we shall
have necessity of inference, and the claim we make is one
that will be generally accepted. For if of everything one or
other of two contradictory statements holds good, then if it
is proved that the negation does not hold, the affirmation
must be true. Again if it is not admitted that the affirma- 15
tion is true, the claim that the negation is true will be
generally accepted. But in neither way does it suit to
maintain the contrary : for it is not necessary that if the
universal negative is false, the universal affirmative should
be true, nor is it generally accepted that if the one is false-
the other is true.

12 It is clear then that in the first figure all problems except 20
the universal affirmative are proved per impossibile. But in
the middle and the last figures this also is proved. Suppose
that A does not belong to all B, and let it have been assumed
that A belongs to all C. If then A belongs not to all B, but 25
to all C, C will not belong to all B. But this is impossible
(for suppose it to be clear that C belongs to all B) : conse
quently the hypothesis is false. It is true then that A belongs

62 a ANALYTICA PRIORA

to all B. But if the contrary is supposed, we shall have a
syllogism and a result which is impossible : but the problem

30 in hand is not proved. For if A belongs to no B, and to
all C, C will belong to no B. This is impossible ; so that it
is false that A belongs to no B. But though this is false,
it does not follow that it is true that A belongs to all B.

When A belongs to some B, suppose that A belongs to
no B, and let A belong to all C. It is necessary then that C

35 should belong to no B. Consequently, if this is impossible,
A must belong to some B. But if it is supposed that A
does not belong- to some B, we shall have the same results l

o

as in the first figure. 2

Again suppose that A belongs to some B, and let A

belong to no C. It is necessary then that C should not

belong to some B. But originally it belonged to all B,

4 o consequently the hypothesis is false: A then will belong to

no.

When A does not belong to all B, suppose it does belong

62 b to all B, and to no C. It is necessary then that C should

belong to no B. But this is impossible : so that it is true

that A does not belong to all B. It is clear then that all

the syllogisms can be formed in the middle figure.

5 Similarly they can all be formed in the last figure. 13
Suppose that A does not belong to some B, but C belongs
to all B : then A does not belong to some C. If then this
is impossible, it is false that A does not belong to some B ;
so that it is true that A belongs to all B. But if it is supposed
. that A belongs to no B, we shall have a syllogism and a con
clusion which is impossible : but the problem in hand is not

10 proved : for if the contrary is supposed, we shall have the
same results as before."

But to prove that A belongs to some B, this hypothesis
must be made. If A belongs to no Z> , and C to some B,
A will belong not to all C. If then this is false, it is true
that A belongs to some B.

15 When A belongs to no B, suppose A belongs to some B,
and let it have been assumed that C belongs to all B. Then

1 Read TCIVT ea-rai in 1. 36. 2 6i r> 39-62 a 8.

3 a 28-32. Read ravr" ea-rm in 1. lo with cod. n.

BOOK II. 13 62 b

it is necessary that A should belong to some C. But
ex hypothesi it belongs to no C, so that it is false that A
belongs to some B. But if it is supposed that A belongs
to all B, the problem is not proved.

But this hypothesis must be made if we are to prove
that A belongs not to all B. For if A belongs to all B 20
and C to some B, then A belongs to some C. But this we
assumed not to be so, so it is false that A belongs to all B.
But in that case it is true that A belongs not to all B.
If however it is assumed that A belongs to some />, we shall
have the same result as before. 1

It is clear then that in all the syllogisms which proceed 25
per impossibile the contradictory must be assumed. And it
is plain that in the middle figure an affirmative conclusion,
and in the last figure a universal conclusion, are proved in
a way.

14 Demonstration per impossibile differs from ostensive proof
in that it posits what it wishes to refute by reduction - to 30
a statement admitted to be false ; whereas ostensive proof
starts from admitted positions." Both, indeed, take two
premisses that are admitted, but the latter takes the pre
misses from which the syllogism starts, the former takes
one of these, along with the contradictory of the original
conclusion. Also in the ostensive proof it is not necessary 35
that the conclusion should be known, nor that one should
suppose beforehand that it is true or not : in the other it is
necessary to suppose beforehand that it is not true. It makes
no difference whether the conclusion is affirmative or nega
tive ; the method is the same in both cases. Everything
which is concluded ostensively can be proved per impossibile,
and that which is proved per impossibile can be proved 40
ostensively, through the same terms. 4 Whenever the syllo
gism 5 is formed in the first figure, the truth will be found 63"
in the middle or the last figure, if negative in the middle.

1 6i b 39-62 a 8. Read ralr eW<u in 1. 23 with cod. n.

- Omit the comma after CWII/JH> in 1. 30.

* Omit u\T)6S>v in 1. 32 with B, C, and Waitz.

1 Omit OVK . . . (rxt iUfuriv in 1. 41 with the MSS. and Waitz.

5 i.e. the reduction ad impossibile.

i.e. the ostensive syllogism.

I 2

63 a ANALYTICA PRIORA

if affirmative in the last. Whenever the syllogism is formed
in the middle figure, the truth will be found in the first,
whatever the problem may be. Whenever the syllogism is
5 formed in the last figure, the truth will be found in the first
and middle figures, if affirmative in the first, if negative in
the middle. Suppose that A has been proved to belong to
no B, or not to all />, through the first figure. Then the
hypothesis must have been that A belongs to some >, and

to the original premisses that C belongs to all A and to no B.
For thus the syllogism was made and the impossible con
clusion reached. But this is the middle figure, if C belongs
to all A and to no B. And it is clear from these premisses
that A belongs to no B. Similarly if A has been proved

15 not to belong to all B. For the hypothesis is that A
belongs to all B ; and the original premisses are that C
belongs to all A but not to all B. Similarly too, if the
premiss CA should be negative : for thus also we have
the middle figure. Again suppose it has been proved that
A belongs to some B. The hypothesis here is that A

20 belongs to no B ; and the original premisses that B belongs
to all C, and A either to all or to some C: for in this way
we shall get what is impossible. But if A and B belong to
all C, we have the last figure. And it is clear from these
premisses that A must belong to some ./>. Similarly if B
or A should be assumed to belong to some C.

25 Again suppose it has been proved in the middle figure
that A belongs to all B. Then the hypothesis must have
been that A belongs not to all B, and the original premisses
that A belongs to all C, and C to all B : for thus we shall
get what is impossible. But if A belongs to all C. and C to
all B, we have the first figure. Similarly if it has been

30 proved that A belongs to some B : for the hypothesis then
must have been that A belongs to no B. and the original
premisses that A belongs to all C, and C to some B. If the
syllogism is negative, the hypothesis must have been that A
belongs to some >, and the original premisses that A belongs
to no C, and C to all B, so that the first figure results. If the

?,5 syllogism is not universal, but proof has been given that A
does not belong to some B, we may infer in the same way.

BOOK II. 14 6a

The hypothesis is that A belongs to all B, the original pre
misses that A belongs to no C, and C belongs to some B :
for thus we get the first figure.

Again suppose it has been proved in the third figure that 40
A belongs to all B. Then the hypothesis must have been
that A belongs not to all B, and the original premisses that C 63
belongs to all B, and A belongs to all C: for thus we shall
get what is impossible. And the original premisses form
the first figure. Similarly if the demonstration establishes
a particular proposition : the hypothesis then must have
been that A belongs to no B, and the original premisses
that C belongs to some B, and A to all C. If the syllogism 5
is negative, the hypothesis must have been that A belongs
to some B, and the original premisses that C belongs to
no A and to all B, and this is the middle figure. Similarly
if the demonstration is not universal. The hypothesis will
then be that A belongs to all B, the premisses that C belongs 10
to no A and to some B : and this is the middle figure.

It is clear then that it is possible through the same terms
to prove each of the problems ostensively as well. 1 Similarly
it will be possible if the syllogisms are ostensive to reduce
them ad impossibile in the terms which have been taken, 15
whenever the contradictory of the conclusion of the ostensive
syllogism is taken as a premiss. For the syllogisms become
identical with those which are obtained by means of con
version, so that we obtain immediately the figures through
which each problem will be solved. It is clear then that
every thesis can be proved in both ways, i. e. per impossibile
and ostensively, and it is not possible to separate one method 20
from the other.

15 In what figure it is possible to draw a conclusion from
premisses which are opposed, and in what figure this is not
possible, will be made clear in this way. Verbally four kinds
of opposition are possible, viz. universal affirmative to uni
versal negative, universal affirmative to particular negative, 25
particular affirmative to universal negative, and particular
affirmative to particular negative : but really there are only

1 Omit KO . . . dSvvdrov in 1. 13 with A, C, and Waitz.

6s b ANALYTICA PRIORA

three : for the particular affirmative is only verbally opposed

to the particular negative. Of the genuine opposites I call
those which are universal contraries, the universal affirma
tive and the universal negative, e. g. every science is good ,

30 no science is good ; the others I call contradictories^-

In the first figure no syllogism whether affirmative or
negative can be made out of opposed premisses : no affirma
tive syllogism is possible because both premisses must be
affirmative, but opposites are, the one affirmative, the other

35 negative : no negative syllogism is possible because opposites
affirm and deny the same predicate of the same subject,
and the middle term in the first figure is not predicated
of both extremes, but one thing is denied of it, and it is
affirmed of something else : but such premisses are not
opposed.

4 o In the middle figure a syllogism can be made both of
contradictories and of contraries. Let A stand for good, let
64 a B and C stand for science. If then one assumes that every
science is good, and no science is good, A belongs to all B
and to no C, so that B belongs to no C: no science then is
a science. Similarly if after taking every science is good
5 one took the science of medicine is not good ; for A
belongs to all B but to no C, so that a particular science
will not be a science. Again, a particular science will not
be a science if A belongs to all C but to no B, and B is
science, C medicine, and A supposition : for after taking
no science is supposition , one has assumed that a par-

10 ticular science is supposition. This syllogism differs from
the preceding because the relations between the terms are
reversed : before, the affirmative statement concerned B,
now it concerns C. Similarly if one premiss is not uni
versal : for the middle term is always that which is stated
negatively of one extreme, and affirmatively of the other.

15 Consequently it is possible that contradictories may lead to
a conclusion, though not always or in every mood, but only
if the terms subordinate to the middle are such that they
are either identical or related as whole to part. Otherwise

1 Elsewhere Aristotle sometimes expresses this by ai>Ti<jniTiK.u>s UVTI-

BOOK II. 15 6 4

it is impossible : for the premisses cannot anyhow be either
contraries or contradictories.

In the third figure an affirmative syllogism can never be 20
made out of opposite premisses, for the reason given in
reference to the first figure; 1 but a negative syllogism is
possible whether the terms are universal or not. Let B
and C stand for science, A for medicine. If then one should
assume that all medicine is science and that no medicine is 25
science, he has assumed that B belongs to all A and C to
no A, so that a particular science will not be a science.
Similarly if the premiss BA 2 is not assumed universally :
For if some medicine is science and again no medicine is
science, it results that some science is not science. The 30
premisses are contrary if the terms are taken universally ;
if one is particular, they are contradictory.

We must recognize that it is possible to take opposites in
the way we said, viz. all science is good ancl no science is
good or some science is not good . This does not usually 35
escape notice. But it is possible to establish one part of
a contradiction through other premisses, or to assume it in
the way suggested in the Topics? Since there are three
oppositions to affirmative statements, it follows that opposite
statements may be assumed as premisses in six ways ; we
may have either universal affirmative and negative, or uni
versal affirmative and particular negative, or particular 40
affirmative and universal negative, and the relations between
the terms may be reversed ; e. g. A may belong to all B and 64 b
to no C, or to all C and to no />, or to all of the one, not to
all of the other ; here too the relation between the terms
may be reversed. Similarly in the third figure. So it is
clear in how many ways and in what figures a syllogism can 5
be made by means of premisses which are opposed.

It is clear too that from false premisses it is possible to
draw a true conclusion, as has been said before, 4 but it is
not possible if the premisses are opposed. For the syllogism
is always contrary to the fact, e. g. if a thing is good, it is 10
proved that it is not good, if an animal, that it is not an

1 63 33. - Read BA in 1. 28 with A, J3, C, and \Vaitz.

3 viii. I. 4 cc. 2-4.

64 b ANALYTICA PRIORA

animal, because the syllogism springs out of a contradiction
and the terms presupposed arc either identical or related
as whole and part. It is evident also that in fallacious
reasonings nothing prevents a contradiction to the hypo
thesis from resulting, e. g. if something is odd, it is not odd.

J 5 For the syllogism owed its contrariety to its contradictory
premisses ; if we assume such premisses we shall get a result
that contradicts our hypothesis. But we must recognize
that contraries cannot be inferred from a single syllogism
in such a way that we conclude that what is not good is
good, or anything of that sort, 1 unless a self-contradictory

20 premiss is at once assumed, e.g. every animal is white and
not white , and we proceed man is an animal . Either we
must introduce the contradiction by an additional assump
tion, assuming, e. g., that every science is supposition, 2 and
then assuming Medicine is a science, but none of it is
supposition (which is the mode in which refutations are

2 5 made), or we must argue from two syllogisms. In no other
way than this, as was said before, 3 is it possible that the
premisses should be really contrary.

To beg and assume the original question is a species 16
of failure to demonstrate the problem proposed ; but this

30 happens in many ways. A man may not reason syllogisti-
cally at all, or he may argue from premisses which are less
known or equally unknown, or he may establish the ante
cedent by means of its consequents ; for demonstration pro
ceeds from what is more certain and is prior. Now begging
the question is none of these : but since we get to know
some things naturally through themselves, and other things

35 by means of something else (the first principles through
themselves, what is subordinate to them through something
else), whenever a man tries to prove what is not 4 self-
evident by means of itself, then he begs the original
question. This may be done by assuming what is in

1 i.e. in such a way that our conclusion is formally affirmative.

2 Omit KO.\ oi>x vir6\r)^is in 1. 23 with B, n, and Waitz.

3 It has been shown that contrary premisses will not yield an affirma
tive self-contradictory conclusion in the first figure (63 b 33) or in the
third (64 a 20). In the second of course all conclusions are negative.

4 Read pf) TO in 1. 36 with A, B, C, and Waitz.

BOOK II. 16 64*

question at once ; it is also possible to make a transition to
other things which would naturally be proved through the 40
thesis proposed, and demonstrate it through them, e.g. if A 65*
should be proved through >, and B through C, though it
was natural that C should be proved through A : for it
turns out that those who reason thus are proving A by
means of itself. This is what those persons do who suppose
that they are constructing parallel straight lines : for they 5
fail to see that they are assuming facts which it is impossible
to demonstrate unless the parallels exist. So it turns out
that those who reason thus merely say a particular thing is,
if it is: in this way everything will be self-evident. But
that is impossible.

If then it is uncertain whether A belongs to C, and also 10
whether A belongs to B, and if one should assume that A
does belong to B t it is not yet clear whether he begs the
original question, but it is evident that he is not demonstra
ting : for what is as uncertain as the question to be answered
cannot be a principle of a demonstration. If however B
is so related to C that they are identical, or if they are
plainly convertible, or the one belongs to the other, 1 the 15
original question is begged. For one might equally well
prove that A belongs to B through those terms if they are
convertible. But if they are not convertible, it is the fact
that they are not that prevents such a demonstration, not
the method of demonstrating. But if one were to make the
conversion, then he would be doing what we have described 2
and effecting a reciprocal proof with three propositions. 11

Similarly if he should assume that B belongs to C, this
being as uncertain as the question whether A belongs to C, 20
the question is not yet begged, but no demonstration is
made. If however A and B are identical either because
they are convertible or because A follows B, then the
question is begged for the same reason as before. For we
have explained the meaning of begging the question, viz.
proving that which is not self-evident by means of itself.

If then begging the question is proving what is not self-

1 As genus to species. 1 ! I- 4-

3 Omit is in 1. 19 with A, B, C, and Waitz.

6s a ANALYTICA PRIORA

evident by means of itself, in other words failing to prove
when the failure is due to the thesis to be proved and
the premiss through which it is proved being equally
uncertain, either because predicates which are identical
belong to the same subject, or because the same predicate
belongs to subjects which are identical, the question may

30 be begged in the middle and third figures in both ways, 1
though, if the syllogism is affirmative, only in the third and
first figures. If the syllogism is negative, the question is
begged when identical predicates are denied of the same
subject ; 2 and both premisses do not beg the question
indifferently (in a similar way the question may be begged
in the middle figure 3 ), because the terms in negative syllo-

35 gisms are not convertible. 4 In scientific demonstrations
the question is begged when the terms are really related in
the manner described, in dialectical arguments when they
are according to common opinion so related.

The objection that this is not the reason why the result 17

is false , which we frequently make in argument, is made

4 primarily in the case of a reductio ad impossibile, to rebut

the proposition which was being proved by the reduction.

65 For unless a man has contradicted this proposition he will

not say, False cause , but urge that something false has

been assumed in the earlier parts of the argument ; nor

will he use the formula in the case of an ostensive proof;

for here what one denies 5 is not assumed as a premiss.

1 TUVTH T( avrat and TUVTOV TO LS avTols sa& explained by 11. 14-23 ; they
refer to petitio principii in the minor and major premiss respectively.
Now from the forms and rules of the figures it follows that the former
can arise only in fig. I (affirmatively) and fig. II (negatively), the latter
in figs. I and III (affirmatively and negatively). Thus the statement
that both can occur in figs. II and III is not, in its natural meaning,
true.

2 TU avTa nnb rnv nvrov is apparently meant to cover the case of TUVTOV
(mo T&V avruiv, the stress being on a-nn. Strictly ra aura TTO TOV avroO is
found only in the second figure.

3 wo-aiTws- . . . pf<Ta> in 1. 34 is parenthetical.

4 i.e. terms negatively related are not convertible, therefore it must
be the terms in the affirmative premiss that are convertible, and the
petitio principii must be in the negative premiss.

It will be noticed that both in accuracy and in form this paragraph
falls below the general level of the Prior Analytics. It bears clear
marks of haste.

6 Read ridija-i b avrtyrjo-tv in 1. 3 with A 2 , B, C, and Waitz.

BOOK II. 17 6s 1

Further when anything is refuted ostensively by the terms
ABC, it cannot be objected that the syllogism does not ?
depend on the assumption laid down. For we use the
expression false cause , when the syllogism is concluded in
spite of the refutation of this position; but that is not
possible in ostensive proofs: since if an assumption is
refuted, a syllogism can no longer be drawn in reference to
it. It is clear then that the expression false cause can
only be used in the case of a reductio ad impossible, and 10
when the original hypothesis is so related to the impossible
conclusion, that the conclusion results indifferently whether
the hypothesis is made or not. The most obvious case of
the irrelevance of an assumption to a conclusion which is
false is when a syllogism drawn from middle terms to an
impossible conclusion is independent of the hypothesis, as 15
we have explained in the Topics}- For to put that which
is not the cause as the cause, is just this: e.g. if a man,
wishing to prove that the diagonal of the square is incom
mensurate with the side, should try to prove Zeno s theorem
that motion is impossible, and so establish a reductio ad
impossibile : for Zeno s false theorem has no connexion at 20
all with the original assumption. Another case is where
the impossible conclusion is connected with the hypothesis,
but does not result from it. This may happen whether one
traces the connexion upwards or downwards, e.g. if it is laid
down that A belongs to B, B to C, and 7 to D, and it should 25
be false that B belongs to D : for if we eliminated A and
assumed all the same that B belongs to C and C to D, the
false conclusion would not depend on the original hypo
thesis. Or again trace the connexion upwards ; e. g. sup
pose that A belongs to B, E to A y and F to E, it being 30
false that F belongs to A. In this way too the impossible
conclusion would result, though the original hypothesis
were eliminated. But the impossible conclusion ought to
be connected with the original terms: in this way it will
depend on the hypothesis, e. g. when one traces the con
nexion downwards, the impossible conclusion must be
connected with that term which is predicate in the hypo- 35
1 Soph. El. i6y b 21-36.

6s b ANALYTICA PRIORA

thesis : for if it is impossible that A should belong to D, the
false conclusion will no longer result after A has been
eliminated. If one traces the connexion upwards, the im
possible conclusion must be connected with that term
which is subject in the hypothesis : for if it is impossible
that F should belong to B, the impossible conclusion will
disappear if B is eliminated. Similarly when the syllogisms

40 are negative.

66 a It is clear then that when the impossibility is not related
to the original terms, the false conclusion does not result on
account of the assumption. Or perhaps even so it may
sometimes be independent. 1 For if it were laid down that
A belongs not to B but to K, and that K belongs to C and
? C to Z>, the impossible conclusion 2 would still stand.
Similarly if one takes the terms in an ascending series.
Consequently since the impossibility results whether the
first assumption is suppressed or not, it would appear to be
independent of that assumption. Or perhaps we ought
not to understand the statement that the false conclusion
results independently of the assumption, in the sense that
if something else were supposed the impossibility would

10 result ; but rather we mean that when the first assumption
is eliminated, the same impossibility results through the
remaining premisses ; since it is not perhaps absurd that
the same false result should follow from several hypotheses,
e. g. that parallels meet, both on the assumption that the
interior angle is greater than the exterior and on the
assumption that a triangle contains more than two right

15 angles.

A false argument depends on the first false statement in 18
it. Every syllogism is made out of two or more premisses.
If then the false conclusion is drawn from two premisses,
one or both of them must be false : for (as was proved :; )
a false syllogism cannot be drawn from true premisses.
20 But if the premisses are more than two, e. g. if C is estab
lished through A and B, and these through D, E, F, and G,

1 Mark of interrogation after \lstv8os in 1. 3 (Waitz).

2 i.e. that A belongs to D. 3 53 b 11-25.

BOOK II. 18 66 a

one of these higher propositions must be false, and on this
the argument depends : for A and B are inferred by means
of D, E, F t and G. Therefore the conclusion and the error
results from one of them.

19 In order to avoid having a syllogism drawn against us, ^5
we must take care, whenever an opponent asks us to admit
the reason without the conclusions, not to grant him the
same term twice over in his premisses, since we know that

a syllogism cannot be drawn without a middle term, and
that term which is stated more than once is the middle.
How we ought to watch the middle in reference to each
conclusion, is evident from our knowing what kind of thesis 30
is proved in each figure. This will not escape us since we
know how we are maintaining the argument.

That which we urge men to beware of in their admissions,
they ought in attack to try to conceal. This will be pos
sible first, if, instead of drawing the conclusions of pre- 35
liminary syllogisms, they take the necessary premisses and
leave the conclusions in the dark ; secondly if instead of
inviting assent to propositions which are closely connected
they take as far as possible those that are not connected by
middle terms. 1 For example suppose that A is to be
inferred to be true of F ; B, C, D, and E being middle
terms. One ought then to ask whether A belongs to B,
and next whether D belongs to E, instead of asking
whether B belongs to C ; after that he may ask whether B 4
belongs to C, and so on. If the syllogism is drawn through 66 b
one middle term, he ought to begin with that : in this way
he will most likely deceive his opponent.

20 Since we know when a syllogism can be formed and how
its terms must be related, it is clear when refutation will 5
be possible and when impossible. A refutation is possible
whether everything is conceded, or the answers alternate
(one, I mean, being affirmative, the other negative). For as
has been shown a syllogism is possible whether the terms
are related in affirmative propositions or one proposition is

1 Read piXuTra .7 M r in 1. 37 with A, B. C,, and Waitz, and perhaps
Phil.

66 b ANALYTICA PRIORA

affirmative, the other negative : consequently, if what is laid
10 down is contrary to the conclusion, a refutation must take
place : for a refutation is a syllogism which establishes the
contradictory. But if nothing is conceded, a refutation is
impossible : for no syllogism is possible (as we saw 2 ) when
all the terms are negative : therefore no refutation is pos
sible. For if a refutation were possible, a syllogism must
15 be possible ; although if a syllogism is possible it does not
follow that a refutation is possible. Similarly refutation is
not possible if nothing is conceded universally : since the
fields of refutation and syllogism are defined in the same
way.

It sometimes happens that just as we are deceived in the 21
arrangement of the terms, :i so error may arise in our thought

20 about them, e. g. if it is possible that the same predicate
should belong to more than one subject immediately, 4 but
although knowing the one, a man may forget the other and
think the opposite true. Suppose that A belongs to B and
to C in virtue of their nature, and that B and C belong to
all D in the same way. If then a man thinks that A
belongs to all B, and B to D, but A to no C, and C to all

25 D, he will both know and not know the same thing 5 in
respect of the same thing. 6 Again if a man were to make a
mistake about the members of a single series; e.g. suppose
A belongs to B, B to C, and C to D, but some one thinks
that A belongs to all B, but to no C : he will both know

30 that A belongs to I), and think that it does not. Does he
then maintain after this simply that what he knows, he
does not think? For he knows in a way that A belongs
to C through B, since the part is included in the whole ; so
that what he knows in a way, this he maintains he does not
think at all : but that is impossible.

35 In the former case, where the middle term does not
belong to the same series, it is not possible to think both
the premisses with reference to each of the two middle
terms : c. g. that A belongs to all />, but to no C, and both

1 Read e; in 1. 10 with cod. m, n L >, and Waitz. 2 41 6.

3 Cf. i. 32 ff. 4 Read irpanois in 1. 20 with A, B, C, and Waitz.

r> i.e. subject. c i.e. attribute.

BOOK II. 21 66

B and C belong to all D. For it turns out that the first
premiss of the one syllogism is either wholly or partially
contrary to the first premiss of the other. For if he thinks
that A belongs to everything to which B belongs, and he 40
knows that B belongs to D, then he knows that A belongs 6y a
to D. Consequently if again he thinks that A belongs to
nothing to which C belongs, he thinks that A does not
belong to some of that to which B belongs ; ] but if he
thinks that A belongs to everything to which B belongs,
and again thinks that A does not belong to some of that to
which B belongs, these beliefs are wholly or partially con- 5
trary. In this way then it is not possible to think ; but
nothing prevents a man thinking one premiss of each
syllogism or both premisses of one of the two syllogisms :
e. g. A belongs to all B, and B to D, and again A belongs
to no C. An error of this kind is similar to the error into
which we fall concerning particulars : e. g. if A belongs to
all B, and B to all C, A will belong to all C. If then :o
a man knows that A belongs to everything to which B
belongs, he knows that A belongs to C. But nothing
prevents his being ignorant that 6" exists ; e.g. let A stand
for two right angles, B for triangle, C for a particular
diagram of a triangle. A man might think that C did not
exist, though he knew that every triangle contains two 15
right angles ; consequently he will know and not know the
same thing at the same time. For the expression to know
that every triangle has its angles equal to two right angles
is ambiguous, meaning to have the knowledge either of the
universal or of the particulars. Thus then he knows that C
contains two right angles with a knowledge of the universal,
but not with a knowledge of the particulars ; consequently 20
his knowledge will not be contrary to his ignorance.
The argument in the Meno- that learning is recollection
may be criticized in a similar way. For it never happens
that a man starts with a foreknowledge of the particular,
but along with the process of being led to see the general

1 w TO # vjrupxfi, rivl rovro) would be more correct, but perhaps the
text may stand.
- Si.

6y a ANALYTICA PRIORA

principle he receives a knowledge of the particulars, by an
act (as it were) of recognition. For we know some things
directly; e.g. that the angles are equal to two right angles,

25 if we know that the figure is a triangle. Similarly in all
other cases.

By a knowledge of the universal then we see the particu
lars, but we do not know them by the kind of knowledge
which is proper to them ; consequently it is possible that
we may make mistakes about them, but not that we should
have the knowledge and error that are contrary to one
another : rather we have the knowledge of the universal

30 but make a mistake in apprehending the particular. Simi
larly in the cases stated above. 1 The error in respect of
the middle term is not contrary to the knowledge obtained
through the syllogism, nor is the thought in respect of one
middle term contrary to that in respect of the other.
Nothing prevents a man who knows both that A belongs to
the whole of B, and that B again belongs to C, thinking

35 that A does not belong to C, e. g. knowing that every mule
is sterile and that this is a mule, and thinking that this
animal is with foal : for he does not know that A belongs

o

to C, unless he considers the two propositions together.
So it is evident that if he knows the one and does not
know the other, he will fall into error. And this is the
relation of knowledge of the universal to knowledge of the
67** particular. For we know no sensible thing, once it has
passed beyond the range of our senses, even if we happen
to have perceived it, except by means of the universal and
the possession of the knowledge which is proper to the
particular, but without the actual exercise of that know
ledge. For to know is used in three senses : it may mean
either to have knowledge of the universal or to have
5 knowledge proper to the matter in hand or to exercise
such knowledge : consequently three kinds of error also
are possible. Nothing then prevents a man both knowing
and being mistaken about the same thing, provided that
his knowledge and his error are not contrary. And this
happens also to the man whose knowledge is limited to each
1 66 b 20-6, 26-30.

BOOK II. 21 67*

of the premisses and who has not previously considered the
particular question. For when he thinks that the mule is
with foal he has not the knowledge in the sense of its
actual exercise, nor on the other hand has his thought 10
caused an error contrary to his knowledge : for the error
contrary to the knowledge of the universal would be a
syllogism.

But he who thinks the essence of good is the essence of
bad will think the same thing to be the essence of good and
the essence of bad. Let A stand for the essence of good
and B for the essence of bad, and again C for the essence of
good. Since then he thinks B and C identical, he will 15
think that C is B, and similarly that B is A, consequently
that C is A. For just as we saw that if B is true of all
of which C is true, and A is true of all of which B is true,
A is true of C, similarly with the word think . Similarly
also with the word is ; for we saw that if C is the same as 20
B, and as A, C is the same as A. Similarly therefore with
opine . Perhaps then this l is necessary if a man will grant
the first point. 2 But presumably that is false, that any one
could suppose the essence of good to be the essence of bad,
save incidentally. For it is possible to think this in many 25
different ways. But we must consider this matter better. 3

22 Whenever the extremes are convertible it is necessary that
the middle should be convertible with both. For if A
belongs to C through , then if A and C are convertible and
C belongs to everything to which A belongs, B is convertible
with A, and B belongs to everything to which A belongs, 30
through C as middle, and C is convertible with B through A
as middle. 4 Similarly if the conclusion is negative, e. g. if
B belongs to C, but A does not belong to B, neither will A
belong to C. If then B is convertible with A, C will

1 That a man should think the same thing to be the essence of good
and to be the essence of bad.

2 That the essence of good is the essence of bad.

3 The reference may be to Met. r. 4.

4 All B is A

All C is B All C is B

.-. All C is A All AisC All A is C

. .-. All A is B All B is A

.-. All B is C

K

6; b ANALYTICA PRIORA

35 be convertible with A. Suppose B does not belong to A ;
neither then will C\ for ex hypothesi B belonged to all C. 1
And if C is convertible with B, B is convertible also with
A : 2 for C is said of that of all of which B is said. 3 And if
C is convertible in relation to A and to B^ B also is
convertible in relation to A. For C belongs to that to
68 a which B belongs : but C does not belong to that to which
A 5 belongs. 6 And this alone starts from the conclusion ;
the preceding moods do not do so as in the affirmative
syllogism. Again if A and B are convertible, and similarly

5 C and D, and if A or C must belong to anything whatever,
then B and D will be such that one or other belongs
to anything whatever. For since B belongs to that to
which A belongs, and D belongs to that to which C belongs,
and since A or C belongs to everything, but not together,
it is clear that B or D belongs to everything, but not together.
For example if that which is uncreated is incorruptible and
that which is incorruptible is uncreated, it is necessary that

10 what is created should be corruptible and what is corruptible
should have been created. For two syllogisms have been
put together. Again if A or B belongs to everything and
if C or D belongs to everything, but they cannot belong
together, then when A and C are convertible B and D are
convertible. For if B does not belong to something to
which D belongs, it is clear that A belongs to it. But if A

i? then C\ for they are convertible. Therefore 7 and D belong
together. But this is impossible. When A belongs to the

1 No B is A

All C is B All C is B

:. No C is A No A is B

. . No A is C

2 Read TO> A TO B for rw A in 1. 37 with Pacius.

3 No B is A
All C is B

:. No C is A No C\s A

All B is C

.-. No^ is A

.-. No A is B

4 Read di/no-rp^a (nal TO B), KU\ TO B az/ricrrpe(pfi in 1. 39.
6 Read TO A, TO r in 1. I with A 9 , B 2 , Phil., and Pacius.

No B is A

All C is B All B is C

.: No C is A No A is C

. . No A is B

BOOK II. 22 68 a

whole of B and to C and is affirmed of nothing else, and B
also belongs to all C, it is necessary that A and B should be
convertible : for since A is said of B and C only, and B
is affirmed both of itself and of C, it is clear that B will be 20
said of everything of which A is said, except A itself.
Again when A and B belong to the whole of (7, and C is
convertible with B, it is necessary that A should belong to
all B : for since A belongs to all C, and C to B by conversion,
A will belong to all B.

When, of two opposites A and B, A is preferable to B, 25
and similarly D is preferable to C, then if A and 67 together are
preferable to B and D together, A must be preferable to D.
For A is an object of desire to the same extent as B is
an object of aversion, since they are opposites : and C is
similarly related to D, since they also are opposites. If then
A is an object of desire to the same extent as D, B is an 30
object of aversion to the same extent as C (since each is to
the same extent as each the one an object of aversion, the
other an object of desire). Therefore both A and C together,
and B and D together, will be equally objects of desire
or aversion. But since A and C arc preferable to B and D
A cannot be equally desirable with D ; for then B along
with D would be equally desirable with A along with C.
But if D is preferable to A, then B must be less an object 35
of aversion than C : for the less is opposed to the less. But
the greater good and lesser evil are preferable to the lesser
good and greater evil : the whole BD then is preferable to
the whole A C. But ex hypothesi this is not so. A then is
preferable to D, and C consequently is less an object of
aversion than B. If then every lover in virtue of his love
would prefer A, viz. that the beloved should be such as 40
to grant a favour, and yet should not grant it (for which C
stands), to the beloved s granting the favour (represented by
D} without being such as to grant it (represented by B), it is 68 b
clear that A (being of such a nature) is preferable to granting
the favour. To receive affection then is preferable in love to
sexual intercourse. Love then is more dependent on friend
ship than on intercourse. And if it is most dependent
on receiving affection, then this is its end. Intercourse then 5

K a

68 b ANALYTICA PRIORA

either is not an end at all or is an end relative to the further
end. the receiving of affection. And indeed the same is true
of the other desires and arts.

It is clear then how the terms are related in conversion, 23
and in respect of being in a higher degree objects of aversion

10 or of desire. 1 * We must now state that not only dialectical and
demonstrative syllogisms are formed by means of the afore
said figures, but also rhetorical syllogisms and in general any
form of persuasion, however it may be presented. For every
belief comes either through syllogism or from induction.

15 Now induction, or rather the syllogism which springs out
of induction, consists in establishing syllogistically a relation
between one extreme and the middle by means of the other
extreme, e. g. if B is the middle term between A and C, it
consists in proving through C that A belongs to B. For
this is the manner in which we make inductions. For
example let A stand for long-lived, B for bileless, and C

20 for the particular long-lived animals, e.g. man, horse,
mule. A then belongs to the whole of C\ for whatever is
bileless is long-lived. But B also ( not possessing bile )
belongs to all C. If then C is convertible with 2>, and the
middle term is not wider in extension, it is necessary that A
should belong to B. For it has already been proved 2 that

2 ? if two things belong to the same thing, and the extreme 3 is
convertible with one of them, then the other predicate will
belong to the predicate that is converted. But we must
apprehend 7 as made up of all the particulars. For induction
proceeds through an enumeration of all the cases.

30 Such is the syllogism which establishes the first and

1 Read (frevKTorepoi Jj (r) KM C) aipfTMrepoi in 1. 9 with A, B, C, and
Waitz.

2 a 2l-25-

3 i.e. the subject of both predicates, which, being a particular thing,
is of the nature of a minor term, and would be minor term in the first
figure, though as subject of both premisses it actually serves as middle
term in the supposed syllogism in the third figure. The transition from
the syllogism in the third figure which yields only a particular conclusion
to that in the first figure, which yields a universal conclusion, may be
represented thus :

All C is A All C is A

All C is B All B is C

. . Some B is A . . All is A

BOOK IT. 23 68 1

immediate premiss: for where there is a middle term
the syllogism proceeds through the middle term ; when
there is no middle term, through induction. And in a way
induction is opposed to syllogism : for the latter proves the
major term to belong to the third term by means of the
middle, the former proves the major to belong to the middle
by means of the third. In the order of nature, syllogism ?,;
through the middle term is prior and better known, but
syllogism through induction is clearer to us.

24 We have an example when the major term is proved to
belong to the middle by means of a term which resembles the
third. It ought to be known both that the middle belongs
to the third term, and that the first belongs to that which 4 o
resembles the third. For example let A be evil, B making
war against neighbours, C Athenians against Thebans, D 6g f
Thebans against Phocians. If then we wish to prove that
to fight with the Thebans is an evil, we must assume that
to fight against neighbours is an evil. Evidence of this is
obtained from similar cases, e.g. that the war against
the Phocians was an evil to the Thebans. Since then to 5
fight against neighbours is an evil, and to fight against the
Thebans is to fight against neighbours, it is clear that
to fight against the Thebans is an evil. Now it is clear that
B belongs to C and to D (for both are cases of making war
upon one s neighbours) and that A belongs to D (for the
war against the Phocians did not turn out well for the 10
Thebans) : but that A belongs to B will be proved through
D. Similarly if the belief in the relation of the middle term
to the extreme should be produced by several similar cases.
Clearly then to argue by example is neither like reasoning
from part to whole, nor like reasoning from whole to part,
but rather reasoning from part to part, when both particulars I5
are subordinate to the same term, and one of them is known.
It differs from induction, because induction starting from all
the particular cases proves (as we saw T ) that the major term
belongs to the middle, and does not apply the syllogistic
conclusion to the minor term, whereas argument by example

1 ch. 23.

6g a ANALYTICA PRIORA

does make this application and does not draw its proof from
all the particular cases.

20 By reduction we mean an argument in which the first term 25
clearly belongs to the middle, but the relation of the middle
to the last term is uncertain though equally or more probable
than the conclusion ; or again an argument in which the
terms intermediate between the last term and the middle are
few. For in any of these cases it turns out that we approach
more nearly to knowledge. For example let A stand for

25 what can be taught, B for knowledge, C for justice. Now it
is clear that knowledge can be taught : but it is uncertain
whether virtue is knowledge. If now the statement C l is
equally or more probable than A C, we have a reduction : for
we are nearer to knowledge, since we have taken a new
term, 2 being so far without knowledge that A belongs to C
Or again suppose that the terms intermediate between Z> and

30 C are few : for thus too we are nearer knowledge. For
example let D stand for squaring, E for rectilinear figure,
F for circle. If there were only one term intermediate
between E and F (viz. that the circle is made equal to a
rectilinear figure by the help of lunules), we should be near
to knowledge. But when BC is not more probable than A C,

35 and the intermediate terms are not few, I do not call this
reduction : nor again when the statement BC is immediate :
for such a statement is knowledge.

An objection is a premiss contrary to a premiss. It differs 26

from a premiss, because it may be particular, but a premiss

either cannot be particular at all or not in universal syllogisms.

6g b An objection is brought in two ways and through two

figures ; in two ways because every objection is either

universal or particular, by two figures because objections are

brought in opposition to the premiss, and opposites can be

5 proved only in the first and third figures. If a man maintains

a universal affirmative, we reply with a universal or a

particular negative ; the former is proved from the first

1 See note 26* 29.

3 viz. B, thus obtaining a certain premiss AB, and a premiss BC, on
which the inquiry now turns.

BOOK II. 26 6g c

figure, the latter from the third. For example let A stand
for there being a single science, B for contraries. If a man
premises that contraries are subjects of a single science, the
objection may be either that opposites are never subjects of 10
a single science, and contraries are opposites. so that we get
the first figure, or that the knowable and the unknowable
are not subjects of a single science : this proof is in the third
figure : for it is true of C (the knowable and the unknowable)
that they are contraries, and it is false that they are the
subjects of a single science.

Similarly if the premiss objected to is negative. For if a 15
man maintains that contraries are not subjects of a single
science, we reply either that all opposites or that certain
contraries, e. g. what is healthy and what is sickly, are
subjects of the same science : the former argument issues
from the first, the latter from the third figure.

In general if a man urges a universal objection he must
frame his contradiction with reference to the universal of 20
the terms taken by his opponent, e. g. if a man maintains
that contraries are not subjects of the same science, his
opponent must reply that there is a single science of all
opposites}- Thus we must have the first figure : for the
term which embraces the original subject becomes the middle
term.

If the objection is particular, the objector must frame his
contradiction with reference to a term relatively to which
the subject of his opponent s premiss is universal, e. g. he
will point out that the knowable and the unknowable are 25
not subjects of the same science : contraries is universal
relatively to these. And we have the third figure : for the
particular term assumed is middle, e. g. the knowable and
the unknowable. Premisses from which it is possible to draw
the contrary conclusion are what we start from when we try
to make objections. Consequently we bring objections in 3
these figures only : for in them only are opposite syllogisms
possible, since the second figure cannot produce an affirmative
conclusion.

1 Read a comma before, not after, TTMTUV, I 22.

6g b ANALYTICA PRIORA

Besides, an objection in the middle figure would require a
fuller argument, e. g. if it should not be granted that A
belongs to B, because C does not follow B. 1 This can
35 be made clear only by other premisses. But an objection
ought not to turn off into other things, but have its new
premiss quite clear immediately. For this reason also this
is the only figure from which proof by signs cannot be
obtained. 2

We must consider later the other kinds of objection, namely

the objection from contraries, from similars, and from com-

7O a mon opinion, and inquire whether a particular objection

cannot be elicited from the first figure or a negative

objection from the second. 3

A probability and a sign are not identical, but a probability 27
is a generally approved proposition : what men know to

5 happen or not to happen, to be or not to be ; for the most
part thus and thus, is a probability, e. g. the envious hate ,
the beloved show affection . A sign means a demonstrative
proposition necessary or generally approved : for anything
such that when it is another thing is, or when it has come
into being the other has come into being before or after, is a
sign of the other s being or having come into being. Now

10 an enthymeme is a syllogism starting from probabilities or
signs, and a sign may be taken in three ways, corresponding
to the position of the middle term in the figures. For
it may be taken as in the first figure or the second or
the third. For example the proof that a woman is with
child because she has milk is in the first figure : for to have

15 milk is the middle term. Let A represent to be with child,
B to have milk, C woman. The proof that wise men are

1 i. e. if the objection takes the form

All A is C.

No B is C.

:. No B is A.

2 It may be conjectured that this sentence is a gloss (so Susemihl),
or that it should come after Kara^aTiKtas in 1. 32. The fact that the
second figure is necessarily negative is in effect the reason given in 70*
35-7 for the invalidity of proof by signs in that figure.

3 This sentence is inconsistent with what precedes, and is perhaps,
as Cook Wilson has pointed out, a gloss added by some one who was
familiar with the treatment of fvarncris in Rhet. ii. 25.

BOOK II. 27 7 o a

good, since Pittacus is good, comes through the last figure.
Let A stand for good, B for wise men, C for Pittacus. It is
true then to affirm both A and B of C: only men do not
say the latter, because they know it. though they state the
former. The proof that a woman is with child because she 20
is pale is meant to come through the middle figure: for
since paleness follows women with child and is a concomitant
of this woman, people suppose it has been proved that she
is with child. Let A stand for paleness, B for being with
child, C for woman. Now if the one proposition is stated,
we have only a sign, but if the other is stated as well, ^
a syllogism, e.g. Pittacus is generous, since ambitious men
are generous and Pittacus is ambitious. Or again Wise
men are good, since Pittacus is not only good but wise. In
this way then syllogisms are formed, only that which pro
ceeds through the first figure is irrefutable if it is true (for
it is universal), that which proceeds through the last figure 30
is refutable even if the conclusion is true, since the syllogism
is not universal nor correlative to the matter in question : for
though Pittacus is good, it is not therefore necessary that all
other wise men should be good. But the syllogism which
proceeds through the middle figure is always refutable in any
case : for a syllogism can never be formed when the terms 35
are related in this way : for though a woman with child is
pale, and this woman also is pale, it is not necessary that she
.should be with child. Truth then may be found in signs
whatever their kind, but they have the differences we have
stated.

We must either divide signs in the way stated, and 7 b
among them designate the middle term as the index l (for
people call that the index which makes us know, and the
middle term above all has this character), or else we must
call the arguments derived from the extremes signs, that
derived from the middle term the index : for that which is
proved through the first figure is most generally accepted 5
and most true.

It is possible to infer character from features, if it is

1 This points to the argument in the first figure, whose middle term
is a genuine middle term.

7o b ANALYTICA PRIORA

granted that the body and the soul are changed together by
the natural affections : I say natural , for though perhaps
by learning music a man has made some change in his soul,

10 this is not one of those affections which are natural to us ;
rather I refer to passions and desires when I speak of
natural motions. If then this were granted and also that
for each change there is a corresponding sign, and we could
state the affection and sign proper to each kind of animal,
we shall be able to infer character from features. For
if there is an affection which belongs properly to an

1 5 individual kind, e.g. courage to lions, it is necessary that
there should be a sign of it : for ex hypothesi body and soul
are affected together. Suppose this sign is the possession
of large extremities : this may belong to other kinds also
though not universally. For the sign is proper in the sense
stated, because the affection is proper to the whole kind,
though not proper to it alone, according to our usual

20 manner of speaking. The same thing then will be found in
another kind, and man may be brave, and some other kinds
of animal as well. They will then have the sign : for ex
hypothesi there is one sign corresponding to each affection.
If then this is so, and \ve can collect signs of this sort in these
animals which have only one affection proper to them but
each affection has its sign, since it is necessary that it

25 should have a single sign we shall then be able to infer
character from features. But if the kind as a whole has
two properties, e. g. if the lion is both brave and generous,
how shall we know which of the signs which are its proper
concomitants is the sign of a particular affection ? Perhaps
if both belong to some other kind though not to the whole
of it, and if, in those kinds in which each is found though
not in the whole of their members, some members possess
one of the affections and not the other : e. g. if a man

30 is brave but not generous, but possesses, of the two signs,
large extremities, it is clear that this is the sign of courage
in the lion also. To judge character from features, then, is
possible in the first figure if 1 the middle term is convertible
with the first extreme, but is wider than the third term and
1 Read r for TU>V in 1. 32 with codd. c, d, m, (TO C), and Waitz.

BOOK II. 27 7o b

not convertible with it : e. g. let A stand for courage, B for
large extremities, and C for lion. B then belongs to every- 35
thing to which C belongs, but also to others. But A belongs
to everything to which B belongs, and to nothing besides,
but is convertible with B : otherwise, there would not be a
single sign correlative with each affection.

ANALYTICA POSTERIORA

BY

G. R. G. MURE, M.A.

FELLOW AND TUTOR OF MERTON COLLEGE

Oxford University Press

London Edinburgh Glasgow Copenhagen

New York Toronto Melbourne Cape Town

Bombay Calcutta Madras Shanghai
Humphrey Milford Publisher to the UNIVERSITY

PREFACE

I DOUBT whether I should have undertaken to translate
the Posterior Analytics had I not been encouraged by a
promise of assistance from Professor Joachim. That promise
he has most generously fulfilled, and if this translation has
any value it is largely because it embodies an amount of
his constructive criticism far too great for detailed acknow
ledgement. I have, however, also received a number of
valuable suggestions from the Editor, and the errors from
which these two scholars were unable to save me probably
constitute the remainder of the book.

I have taken Bekker s text as a foundation, noting
departures from it, and in this connexion I have to thank
Professor J. A. Smith for the gift of a photograph of
Cod. A of the Posterior Analytics. The notes are perhaps
too numerous for a translation, certainly too few to form
anything resembling a commentary. I have not known
how to avoid this compromise.

Finally my thanks are due to the late Mr. H. Beighton,
who read about half the proofs and made several suggestions
which I have adopted, and to Mr. Joseph of New College
for the loan of his notes on Professor Cook Wilson s lectures
on the Posterior Analytics.

October 5, 1925.

B 2

CONTENTS
BOOK I

CHAP.

1. The student s need of pre-existent knowledge. Its nature.

2. The nature of scientific knowledge. The conditions of demonstra

tion. The meaning of Contradiction, Enunciation, Proposition,
Basic truth, Thesis, Axiom, Hypothesis, Definition.

3. Two erroneous views of scientific knowledge. The futility of

circular demonstration.

4. Types of attribute : True in every instance , Essential , Com

mensurate and universal , Accidental .

5. Causes through which we erroneously suppose a conclusion com

mensurate and universal when it is not. How to avoid this
error.

6. The premisses of demonstration must be necessary and essential.

7. The premisses and conclusion of a demonstration must fall within

a single genus. The three constituent elements of demonstration.

8. Only eternal connexions can be demonstrated.

9. Demonstration must proceed from the basic premisses peculiar to

each science, except in the case of subalternate sciences.
10. The different sorts of basic truth,
u. The function of the common axioms in demonstration.

12. The scientific premiss in interrogative form. Formal fallacy.

The growth of a science.

13. The difference between knowledge of the fact and knowledge of

the reasoned fact.

14. The first figure is the true type of scientific syllogism.

15. Immediate negative propositions.

16. Ignorance as erroneous inference when the premisses are im

mediate.

17. Ignorance as erroneous inference when the premisses are mediate.

1 8. Ignorance as the negation of knowledge, e.g. such as must result

from the lack of a sense.

19. Can demonstration develop an indefinite regress of premisses,

(i) supposing the primary attribute fixed? (2) supposing the
ultimate subject fixed ? (3) supposing both primary attribute
and ultimate subject fixed ?

20. If (i) and (2) are answered negatively, the answer to (3) must be

in the negative.

21. If affirmative demonstration cannot develop an indefinite regress,

then negative demonstration cannot.

CONTENTS

CHAP.

22. Dialectical and analytic proofs that the answer to both (i) and

(2) is in the negative.

23. Corollaries.

24. The superiority of universal to particular demonstration.

25. The superiority of affirmative to negative demonstration.

26. The superiority of affirmative and negative demonstration to

reductio ad impossibile.

27. The more abstract science is the prior and the more accurate science.

28. What constitutes the unity of a science.

29. How there may be several demonstrations of one connexion.

30. Chance conjunctions are not demonstrable.

31. There can be no demonstration through sense-perception.

32. Different sciences must possess different basic truths.

33. The relation of opinion to knowledge.

34. Quick wit : the faculty of instantaneously hitting upon the middle

term.

BOOK II

1. The four possible forms of inquiry.

2. They all concern the middle term.

3. The difference between definition and demonstration.

4. Essential nature cannot be demonstrated.

5. Essential nature cannot be inferred by division.

6. Attempts to prove a thing s essential nature either hypothetically

or through the definition of its contrary beg the question.

7. Definition does not touch the question of existence; demonstration

proves existence. Hence definition cannot demonstrate.

8. Yet only demonstration can reveal the essential nature of things

which have a cause other than themselves i.e. attributes.

9. That which is self-caused the basic premisses is grasped im

mediately.

10. Types of definition.

11. The several causes as middle terms.

12. The question of time in causal inference.

13. How to obtain the definition of a substance. The use of division

for this purpose.

14. How to select a connexion for demonstration.

15. One middle will often serve to prove several connexions.

16. If the effect is present, is the cause also present? Plurality of

causes is impossible where cause and effect are commensurate.

17. Different causes may produce the same effect, but not in things

specifically identical.

1 8. The true cause of a connexion is the proximate and not the more

universal cause.

19. How the individual mind comes to know the basic truths.

ANALYTICA POSTERLORA

BOOK I

I ALL instruction given or received by way of argument 71
proceeds from pre-existent knowledge. This becomes
evident upon a survey of all the species of such instruction.
The mathematical sciences and all other speculative disci
plines are acquired in this way, and so are the two forms of
dialectical reasoning, syllogistic and inductive ; for each 5
of these latter makes use of old knowledge to impart new,
the syllogism assuming an audience that accepts its premisses,
induction : exhibiting the universal as implicit in the clearly
known particular. Again, the persuasion exerted by rhe
torical arguments is in principle the same, since they use
either example, a kind of induction, or enthymeme, a form 10
of syllogism.

The pre-existent knowledge required is of two kinds.
In some cases admission of the fact must be assumed, in
others comprehension of the meaning of the term used, and
sometimes both assumptions are essential. Thus, we assume
that every predicate can be either truly affirmed or truly
denied of any subject, 2 and that triangle 3 means so and
so ; as regards unit we have to make the double assump
tion of the meaning of the word and the existence of the 15
thing. The reason is that these several objects are not equally
obvious to us. Recognition of a truth may in some cases

1 The sense of tirdydv implied in the use of eVaywyi} by Aristotle is
probably that of leading the pupil on from the particular to the
universal by making him recognize the latter as implicit in the former.

2 i. e. the law of excluded middle.

3 Elsewhere Tpiyavov as a rule appears as one of the subjects of which
the geometer assumes the meaning and being and demonstrates pro
perties: here it seems to be instanced as a property, of which only
the meaning is assumed. This chapter is, however, preliminary, and
probably Aristotle is only drawing the distinction, which appears in
ch. 10, 76 b l6ff., between tacit and explicit assumptions. Possibly,
however, Aristotle is thinking of triangular as an attribute of number,
cf. note on 73*40, or as a particular modification of arj^tla KOI y^a^ai,
the Trpwra of space.

7i a ANALYTICA POSTERIORA

contain as factors both previous knowledge and also know
ledge acquired simultaneously with that recognition
knowledge, this latter, of the particulars actually falling
under the universal and therein already virtually known.
For example, the student knew beforehand that the angles

20 of every triangle are equal to two right angles ; but it was
only at the actual moment at which he was being led on to
recognize this as true in the instance before him that he
came to know this figure inscribed in the semicircle to be
a triangle. 1 For some things (viz. the singulars finally reached
which are not predicable of anything else as subject) are
only learnt in this way, i.e. there is here no recognition
through a middle of a minor term as subject to a major.
Before he was led on to recognition or before he actually

25 drew a conclusion, we should perhaps say that in a manner
he knew, in a manner not.

If he did not in an unqualified sense of the term know
the existence of this triangle, how could he know without
qualification that its angles were equal to two right angles ?
No : clearly he knows not without qualification but only in
the sense that he knows universally. If this distinction is
not drawn, we are faced with the dilemma in the Meno : 2
either a man will learn nothing or what he already knows ;

30 for we cannot accept the solution which some people offer.
A man is asked, Do you, or do you not, know that every
pair is even ? He says he does know it. The questioner
then produces a particular pair, of the existence, and so a
fortiori of the evenness, of which he was unaware. The
solution which some people offer is to assert that they do
not know that every pair is even, but only that everything

1 Though he uses syllogistic terms, Aristotle is hardly describing
syllogism, but rather the conversion of a universal known eei into
actual knowledge. The major premiss here is a previously known
universal (in Aristotle s example the angles of all triangles are together
equal to two right angles ), the minor is the recognition of a singular
(in the example, this is a triangle ), and the conclusion , with which
the minor is simultaneous, is the recognition of this singular as an
instance embodying the universal ( the angles of this triangle in the
semi-circle are equal to two right angles ). Hence lav e ^ei TT]V yv&aiv in
a 19 refers to Sera, and means the singulars of which he has knowledge
as a f^is in that he knows the universal .

2 Plato, Meno, 80 E.

BOOK I. i 7 i b

which they know to be a pair is even : yet what they know 7i b
to be even is that of which they have demonstrated evenness,
i.e. what they made the subject of their premiss, viz. not
merely every triangle or number which they know to be
such, but any and every number or triangle without reserva
tion. For no premiss is ever couched in the form every
number which you know to be such , or every rectilinear
figure which you know to be such : the predicate is always
construed as applicable to any and every instance of the 5
thing. On the other hand, I imagine there is nothing to
prevent a man in one sense knowing what he is learning, in
another not knowing it. The strange thing would be, not
if in some sense he knew what he was learning, but if he
were to know it in that precise sense and manner in which
he was learning it. 1

2 We suppose ourselves to possess unqualified scientific
knowledge of a thing, as opposed to knowing it in the
accidental way in which the sophist knows, when we think 10
that we know the cause on which the fact depends, as the
cause of that fact and of no other, and, further, that the fact
could not be other than it is. Now that scientific knowing is
something of this sort is evident witness both those who
falsely claim it and those who actually possess it, since the
former merely imagine themselves to be, while the latter are
also actually, in the condition described. Consequently the
proper object of unqualified scientific knowledge is something 15
which cannot be other than it is.

There may be another manner of knowing as well that
will be discussed later. 2 What I now assert is that at all
events we do know by demonstration. By demonstration
I mean a syllogism productive of scientific knowledge, a
syllogism, that is, the grasp of which is eo ipso such knowledge.
Assuming then that my thesis as to the nature of scientific
knowing is correct, the premisses of demonstrated knowledge 20
must be true, primary, immediate, better known than and
prior to the conclusion, which is further related to them as
effect to cause. Unless these conditions are satisfied, the

1 Cf. An. Pr. ii, ch. 21.

2 Cf. the following chapter and more particularly n, ch. 19.

7i b ANALYTICA POSTERIORA

basic truths will not be appropriate l to the conclusion.
Syllogism there may indeed be without these conditions,
but such syllogism, not being productive of scientific know
ledge, will not be demonstration. The premisses must be

25 true : for that which is non-existent cannot be known we
cannot know, e.g., that the diagonal of a square is commen
surate with its side. 2 The premisses must be primary and
indemonstrable ; otherwise they will require demonstration
in order to be known, since to have knowledge, if it be not
accidental knowledge, of things which are demonstrable,
means precisely to have a demonstration of them. The
premisses must be the causes of the conclusion, better known

30 than it, and prior to it ; its causes, since we possess scientific
knowledge of a thing only when we know its cause ; prior,
in order to be causes ; antecedently known, this antecedent
knowledge being not our mere understanding of the meaning,
but knowledge of the fact as well. 3 Now prior and better
known are ambiguous terms, for there is a difference
between what is prior and better known in the order of
72 a being and what is prior and better known to man. I mean
that objects nearer to sense are prior and better known to
man ; objects without qualification prior and better known
are those further from sense. Now the most universal
causes 4 are furthest from sense and particular causes are

5 nearest to sense, and they are thus exactly opposed to one
another. In saying that the premisses of demonstrated
knowledge must be primary, I mean that they must be the
appropriate basic truths, for I identify primary premiss
and basic truth. A basic truth in a demonstration is an
immediate proposition. An immediate proposition is one
which has no other proposition prior to it. A proposition
is either part of an enunciation, i.e. it predicates a single

1 i.e. within the same genus. Cf. i, ch. 7.

a Within the conditions of anoSagis here laid down, false premisses
would give a false conclusion corresponding to a ^17 bv $ ^evdos such
as Std/nerpoy 0-v/j.fj.tTpos, which is not anything fVTolsnpdyfjiaa-ii . Such
a ^17 ov cannot be the object of demonstration.

3 Cf. 7l a n ff. False anodfi^is is a contradiction in terms. Though
false premisses may yield a true conclusion, a syllogism in which this
occurs is not anoddgis but gives only the on : cf. An. Pr. ii. 2. 53 b 7-lo.

4 Magis universalia in causando , Zabarella. Cf. 76 a 19 and 85 b 24.

BOOK I. 2 72 a

attribute of a single subject. If a proposition is dialectical,
it assumes either part indifferently ; if it is demonstrative, it 10
lays down one part to the definite exclusion of the other
because that part is true. The term enunciation denotes
either part of a contradiction indifferently. A contra
diction is an opposition which of its own nature excludes
a middle. The part of a contradiction which conjoins a
predicate with a subject is an affirmation ; the part
disjoining them is a negation. I call an immediate
basic truth of syllogism a thesis when, though it is not 15
susceptible of proof by the teacher,, yet ignorance of it does
not constitute a total bar to progress on the part of the
pupil : one which the pupil must know if he is to learn any
thing whatever is an axiom. I call it an axiom because
there are such truths and we give them the name of axioms
par excellence?- If a thesis assumes one part or the other
of an enunciation, i.e. asserts either the existence or the 20
non-existence of a subject, it is a hypothesis ; 2 if it does not
so assert, it is a definition. Definition is a thesis or a laying
something down , since the arithmetician lays it down that
to be a unit is to be quantitatively indivisible ; but it is not
a hypothesis, for to define what a unit is is not the same as
to affirm its existence.

Now since the required ground of our knowledge i.e. of 25
our conviction 3 of a fact is the possession of such a syllogism
as we call demonstration, and the ground of the syllogism is
the facts constituting its premisses, we must not only know
the primary premisses some if not all of them beforehand,
but know them better than the conclusion : for the cause
of an attribute s inherence in a subject always itself inheres
in the subject more firmly than that attribute; e.g. the
cause of our loving anything is dearer to us than the object
of our love. So since the primary premisses are the cause 3

1 sc. because the quantitative axioms ignorance of which is a bar
only to 7)iathematical knowledge are also called axioms.

2 Hypothesis to Aristotle and Plato means an assumption not
calling for proof within the sphere of the special science in which it
functions, not a working hypothesis .

3 For Aristotle s view of the relation of belief to knowledge see i,
ch. 33.

72 a ANALYTICA POSTERIORA

of our knowledge i. e. of our conviction it follows that we
know them better that is, are more convinced of them
than their consequences, precisely because our knowledge
of the latter is the effect of our knowledge of the premisses.
Now a man cannot believe in anything more than in the
things he knows, unless he has either actual knowledge of it
or something better than actual knowledge. But we are
35 faced with this paradox if a student whose belief rests on
demonstration has not prior knowledge ; l a man must
believe in some, if not in all, of the basic truths more than
in the conclusion. Moreover, if a man sets out to acquire
the scientific knowledge that comes through demonstration,
he must not only have a better knowledge of the basic
truths and a firmer conviction of them than of the connexion
72 b which is being demonstrated : more than this, nothing must
be more certain or better known to him than these basic
truths in their character as contradicting the fundamental
premisses which lead to the opposed and erroneous con
clusion. 2 For indeed the conviction of pure science must
be unshakable.

5 Some hold that, owing to the necessity of knowing the 3
primary premisses, there is no scientific knowledge. Others
think there is, but that all truths are demonstrable. Neither
doctrine is either true or a necessary deduction from the
premisses. The first school, assuming that there is no way

1 I take TLS . . . TU>V 8C an68fi^iv iri<TTev6vTa>v in a 35 as a periphrasis
meaning a man convinced by demonstration (the traditional interpre
tation), though the construction is harsh. Zabarella suggests that in
1.37 -rbv 8e nfXXovra . . . Aristotle passes from a dialectical proof applicable
to all syllogisms to a strict proof confined to d-rr68eits, observing that
fTriaraaOai, eTrtoT^p; do not occur in the immediately preceding passage.
Prof. Joachim suggests to me that et pf) TIS . . . trio-revoi Tcw may mean
unless a man knows the premisses before those who believe them
owing to a demonstration i. e. before anyone demonstrates them to
him but suspects the text. Aristotle clearly intends a contrast
between (a) those convinced e. g. of a particular truth di dirodfi&v,
and (b} those who set out to acquire the scientific knowledge that
comes by demonstration. The former to be convinced by demonstra
tion must be more convinced of the premisses than of the conclusion,
but of the latter even more is required, since their conviction must be
unshakable.

2 To read alrS>v with M in 72 b I and a>s for T>I> in ^ 2 would assist
this interpretation.

BOOK I. 3 72*

of knowing other l than by demonstration, maintain that an
infinite regress is involved, on the ground that if behind the
prior stands no primary, we could not know the posterior
through the prior (wherein they are right, for one cannot
traverse an infinite series) : if on the other hand they
say the series terminates and there are primary premisses,
yet these are unknowable because incapable of demonstra
tion, which according to them is the only form of knowledge.
And since thus one cannot know the primary premisses,
knowledge of the conclusions which follow from them is not
pure scientific knowledge nor properly knowing at all, but
rests on the mere supposition that the premisses are true.
The other party agree with them as regards knowing, 15
holding that it is only possible by demonstration, but they
see no difficulty in holding that all truths are demonstrated,.
on the ground that demonstration may be circular and
reciprocal.

Our own doctrine is that not all knowledge is demonstra
tive : on the contrary, knowledge of the immediate premisses
is independent of demonstration. (The necessity of this is 20
obvious ; for since we must know the prior premisses from
which the demonstration is drawn, and since the regress
must end in immediate truths, those truths must be
indemonstrable.) Such, then, is our doctrine, and in addi
tion we maintain that besides scientific knowledge there is
its originative source which enables us to recognize the
definitions. 2

Now demonstration must be based on premisses prior to 25
and better known than the conclusion ; and the same things
cannot simultaneously be both prior and posterior to one
another : so circular demonstration is clearly not possible in
the unqualified sense of demonstration , but only possible
if demonstration be extended to include that other method
of argument which rests on a distinction between truths
prior to us and truths without qualification prior, i. e. the

1 Reading dXXwj with A, B, C.

2 Zabarella takes opoi as meaning definitions = middle terms ,
which in demonstratio potissima are elements in the definition of the
subjects.

72 b ANALYTICA POSTERIORA

30 method by which induction produces knowledge. 1 But if
we accept this extension of its meaning, our definition of
unqualified knowledge will prove faulty ; for there seem to
be two kinds of it. Perhaps, however, the second form of
demonstration, that which proceeds from truths better known
to us, is not demonstration in the unqualified sense of the
term. 2

The advocates of circular demonstration are not only
faced with the difficulty we have just stated : in addition
their theory reduces to the mere statement that if a thing
exists, then it does exist an easy way of proving anything.
35 That this is so can be clearly shown by taking three terms, 3
for to constitute the circle it makes no difference whether
many terms or few or even only two are taken. Thus by
direct proof, if A is, B must be ; if B is, C must be ; there
fore if A is, C must be. Since then by the circular
73 a proof if A is, B must be, and if B is, A must be, A may
be substituted for C above. Then if B is, A must be =
if B is, C must be , which above gave the conclusion if A
is, C must be : but C and A have been identified. 4 Con-

1 Placing a comma after yvapiiiuTtpuv in b 27, and taking eZ fif) . . . in
b 28 ff. as qualifying aftvvarov in b 25. Aristotle seems to mean that cir
cular demonstration is impossible unless demonstration is taken to in
clude a type of argument based on truths prior only in the sense of prior
to us , such as induction, where we grasp the particular and recognize in
it the universal, which is however dn-Xwy Trporepov. The next sentence,
6i 8 ourwr . . . , seems to confirm this interpretation, which does, however,
involve a verbal contradiction, olov TU nei> irpbs }/^a?, ru 8 cnr\5>s may
be a marginal gloss crept into the text. The Greek would be less
harsh without it.

2 sc. and therefore our definition is not faulty .

3 sc. to constitute the valid syllogism which Aristotle sets up in b 37-9
to illustrate the tautology of the circular demonstration when reduced
to explicit syllogism.

4 TOVTO 6 on TOV A ovros TU F eori seems to mean that B implies C
taken in conjunction with A implies B gave the conclusion A implies
C . Aristotle tries to show the circular proof tautologous by reducing
it to syllogism, apparently arguing thus : B implies C , 1 A implies B ,
., A implies C is valid syllogism (a schema for comparison) : while
according to the circular proof A necessitates B and B necessitates A.
If A-B, B-A ( A implies , B implies A ) are to be made the
premisses of a syllogism, there is nothing but A to take the place of C
in the schema no major term different from the minor : . . B-A is all
we have to fill the place of the major premiss B-C. Now, in the schema,
B-C (taken in conjunction with the minor premiss A-B, which is com
mon to both syllogisms) gave the conclusion A-C. But C is now A
(a restatement of the fact that B-C has become B-A). Therefore the
conclusion is A-A.

BOOK I. 3 73*

sequently the upholders of circular demonstration are in the
position of saying that if A is, A must be a simple way of 5
proving anything. Moreover, even such circular demonstra
tion is impossible except in the case of attributes that imply
one another, viz. peculiar l properties.

Now, it has been shown that the positing of one thing
be it one term or one premiss never involves a necessary
consequent : 2 two premisses constitute the first and smallest 10
foundation for drawing a conclusion at all and therefore
a fortiori for the demonstrative syllogism of science. If,
then, A is implied in B and C, and B and C are reciprocally
implied in one another and in A, it is possible, as has been
shown in my writings on the syllogism," to prove all the
assumptions on which the original conclusion rested, by
circular demonstration in the first figure. But it has also i 5
been shown that in the other figures either no conclusion is
possible, or at least none which proves both the original
premisses.* Propositions the terms of which are not con
vertible cannot be circularly demonstrated at all, and since
convertible terms occur rarely in actual demonstrations, it is
clearly frivolous and impossible to say that demonstration
is reciprocal and that therefore everything can be demon
strated.

4 Since the object of pure scientific knowledge cannot be
other than it is, the truth obtained by demonstrative know
ledge will be necessary. And since demonstrative know
ledge is only present when \ve have a demonstration, it
follows that demonstration is an inference from necessary
premisses. So we must consider what are the premisses of
demonstration i. e. what is their character : and as a 25
preliminary, let us define what we mean by an attribute
true "in every instance of its subject , an essential

1 r<> uW is defined in Top. i. 102* 18 as 6 /^} 8ijXoi^V TO rirjv tlvat,
p.6vu> 8 inrtipxet KO\ avTmarriyopelrai TOV irpdyfJiaTos. ra iota in this sense
are in fact ra naff avra irv^e^Kora as Aristotle elsewhere calls them :
but Aristotle often uses idiov more widely to include also elements in
the TI ffv elvai and even as in An. Post, ii, ch. 6. 92* 8 to differentiate
these from other characters of a substance.

~ 2 An. Pr. i, ch. 25. s Ibid, ii, ch. 5.

4 Ibid, ii, cc. 5 and 6.

73 a ANALYTICA POSTERIORA

attribute, and a f commensurate and universal 1 attribute.
I call true in every instance what is truly predicable of
all instances not of one to the exclusion of others and at
all times, not at this or that time only ; e. g. if animal is

30 truly predicable of every instance of man, then if it be true
to say this is a man , this is an animal is also true, and
if the one be true now the other is true now. A corre
sponding account holds if point is in every instance predi
cable as contained in line. There is evidence for this in
the fact that the objection we raise against a proposition
put to us as true in every instance is either an instance in
which, or an occasion on which, it is not true. Essential
attributes are (i) such as belong to their subject as elements

35 in its essential nature (e. g. line thus belongs to triangle,
point to line ; for the very being or substance of triangle
and line is composed of these elements, which are contained
in the formulae denning triangle and line) : (2) such that,
while they belong to certain subjects, the subjects to which
they belong are contained in the attribute s own defining
formula. Thus straight and curved belong to line, odd and

4 even, prime and compound, square and oblong, to number; 2
73 and also the formula defining any one of these attributes
contains its subject e. g. line or number as the case
may be.

Extending this classification to all other attributes, I
distinguish those that answer the above description as
belonging essentially to their respective subjects ; whereas
attributes related in neither of these two ways to their
subjects I call accidents or coincidents ; 3 e. g. musical or
white is a coincident of animal.

5 Further (a) that is essential which is not predicated of a
subject other than itself: e. g. the walking [thing] walks

1 Ka66\ov is not always used by Aristotle in the strict sense here
defined. It has therefore seemed advisable to add commensurate in
translating it where it is used in the strict sense.

2 The reference is to a method of naming numbers according to the
geometrical arrangements of which their units are capable. Cf. Plato,
Theaetetus, 147 -148 B.

3 o-vufteftiiKos is elsewhere except in i, cc. 19 and 22 translated acci
dent , which less adequately covers the sense of the word here and in
that chapter. For the meaning expressed by coincident cf. 8i b 28-29.

BOOK I. 4 73 b

and is white in virtue of being something else besides ; 1
whereas substance, in the sense of whatever signifies a this
somewhat , 2 is not what it is in virtue of being something
else besides. Things, then, not predicated of a subject I
call essential ; things predicated of a subject I call acci
dental or coincidental .

In another sense again (b] a thing consequentially 3 con- 10
nected with anything is essential ; one not so connected is
coincidental . An example of the latter is While he was
walking it lightened : the lightning was not due to his
walking ; it was, we should say, a coincidence. If, on the
other hand, there is a consequential connexion, the predica
tion is essential ; e. g. if a beast dies when its throat is being
cut, then its death is also essentially connected with the
cutting, because the cutting was the cause of death, not 15
death a coincident of the cutting.

So far then as concerns the sphere of connexions scienti
fically known in the unqualified sense of that term, all
attributes which (within that sphere) are essential either in
the sense that their subjects are contained in them, or in
the sense that they are contained in their subjects, are
necessary as well as consequentially connected with their
subjects. 4 For it is impossible for them not to inhere in
their subjects either simply or in the qualified sense that
one or other of a pair of opposites must inhere in the
subject ; e. g. in line must be either straightness or curvature, 20
in number either oddness or evenness. For within a single
identical genus the contrary of a given attribute is either
its privative or its contradictory ; e. g. within number what
is not odd is even, inasmuch as within this sphere even is a

1 sc. the unexpressed subject. Aristotle s point cannot be rendered
in English, which seldom uses an adjective or participle substantially.
Cf. Met. z, ch. 10, where Aristotle distinguishes TO XWKOV from the Trdffos

XfVKOT^?.

2 i.e. any this which is designable as characterized under the
Category of Substance. Cf. Prof. J. A. Smith in Class. Rev., vol. xxxv,
p. 19.

3 fit avro implies a connexion really wider than causation, and would
include e. g. the inherence of mathematical properties.

4 So Zabarella and Pacius, taking Aristotle s meaning to be that only
types (i) and (2) have the degree of necessity requisite for scientific
knowledge a view borne out by i, ch. 22, 84* 7-28.

7 3 b ANALYTICA POSTERIORA

necessary consequent of not-odd. So, since any given
predicate must be either affirmed or denied of any subject, 1
essential attributes must inhere in their subjects of
necessity. 2

25 Thus, then, we have established the distinction between
the attribute which is true in every instance and the
f essential attribute.

I term commensurately universal an attribute which
belongs to every instance of its subject, and to every
instance essentially and as such ; from which it clearly
follows that all commensurate universals inhere necessarily
in their subjects. The essential attribute, and the attribute
that belongs to its subject as such, are identical. E. g. point

30 and straight belong to line essentially, for they belong to
line as such ; and triangle as such has two right angles, for
it is essentially equal to two right angles.

An attribute belongs commensurately and universally to
a subject when it can be shown to belong to any random
instance of that subject and when the subject is the first
thing to which it can be shown to belong. Thus, e. g., (i)
the equality of its angles to two right angles is not a com
mensurately universal attribute of figure. For though it

35 is possible to show that a figure has its angles equal to two
right angles, this attribute cannot be demonstrated of any
figure selected at haphazard, nor in demonstrating does one
take a figure at random a square is a figure but its angles
are not equal to two right angles. On the other hand, any
isosceles triangle has its angles equal to two right angles,
yet isosceles triangle is not the primary subject of this
attribute but triangle is prior. So whatever can be shown

1 i. e. the law of excluded middle.

2 Aristotle argues as follows : Essential attributes of type (2) which
inhere in their subjects as disjunctive pairs of opposites are necessary
because the disjunction covers the whole ground of the subject. The
disjunction covers the whole ground because the subject is within a
single genus, and the law of excluded middle here invests the contrary
with the character of the contradictory or privative i.e. though this
law only entitles you either to affirm or deny a predicate, yet here the
affirmation of one predicate is ip so facto the denial of its opposite and
vice versa: number is odd or not-odd must mean number is odd
or even ; animal is seeing or not-seeing is identical with animal
is seeing or blind .

BOOK I. 4 73 b

to have its angles equal to two right angles, or to possess 40
any other attribute, in any random instance of itself and
primarily that is the first subject to which the predicate in
question belongs commensurately and universally, and the 74*
demonstration, in the essential sense, of any predicate is
the proof of it as belonging to this first subject commen
surately and universally: while the proof of it as belonging
to the other subjects to which it attaches is demonstration
only in a secondary and unessential sense. Nor again (2)
is equality to two right angles a commensurately universal
attribute of isosceles ; it is of wider application. 1

5 We must not fail to observe that we often fall into error
because our conclusion is not in fact primary and commen- 5
surately universal in the sense in which we think we prove
it so. We make this mistake (i) when the subject is an
individual or individuals above which there is no universal
to be found : (2) when the subjects belong to different
species and there is a higher universal, but it has no name :
(3) when the subject which the demonstrator takes as
a whole is really only a part of a larger whole ; for then
the demonstration will be true of the individual instances 10
within the part and will hold in every instance of it, yet the
demonstration will not be true of this subject primarily and
commensurately and universally. When a demonstration
is true of a subject primarily and commensurately and
universally, that is to be taken to mean that it is true of
a given subject primarily and as such. Case (3) may be
thus exemplified. If a proof were given that perpendiculars
to the same line are parallel, it might be supposed that lines
thus perpendicular were the proper subject of the demon
stration because being parallel is true of every instance
of them. But it is not so, for the parallelism depends not 15
on these angles being equal to one another because each is
a right angle, but simply on their being equal to one
another. An example of (i) would be as follows : if
isosceles were the only triangle, it would be thought to

1 If oi>8f in a 2 is the right reading, it seems necessary to regard
KaiYot (73 b 34) . . . Aca0 aiiro (74*2) as a parenthesis, however clumsy.
In b 36 I place a comma after a-x^aros.

C 2

74 a ANALYTICA POSTERIORA

have its angles equal to two right angles qua isosceles.
An instance of (2) would be the law that proportionals
alternate. 1 Alternation used to be demonstrated separately
of numbers, lines, solids, and durations, 2 though it could

20 have been proved of them all by a single demonstration.
Because there was no single name to denote that in which
numbers, lengths, durations, and solids are identical, and
because they differed specifically from one another, this
property was proved of each of them separately. To-day,
however, the proof is commensurately universal, for they do
not possess this attribute qua lines or qua numbers, but qua
manifesting this generic character which they are postulated

25 as possessing universally. Hence, even if one prove of each
kind of triangle that its angles are equal to two right angles,
whether by means of the same or different proofs ; still, as
long as one treats separately equilateral, scalene, and isos
celes, one does not yet know, except sophistically, that
triangle has its angles equal to two right angles, nor does
one yet know that triangle has this property commen
surately and universally, even if there is no other species

30 of triangle but these. For one does not know that triangle
as such has this property, nor even that all triangles have
it unless all means each taken singly : if all means
4 as a whole class , then, though there be none in which one
does not recognize this property, one does not know it of
all triangles .

When, then, does our knowledge fail of commensurate
universality, and when is it unqualified knowledge ? If
triangle be identical in essence with equilateral, i. e. with
each or all equilaterals, then clearly we have unqualified
knowledge : 3 if on the other hand it be not, and the
attribute belongs to equilateral qua triangle ; then our

35 knowledge fails of commensurate universality. But , it will
be asked, does this attribute belong to the subject of which

1 i.e. the law by which if A : B :: C : D, then A : C :: B : D.

2 The reference is perhaps to xp vot as tne time-units of music and
metre.

s sc. of the attribute equal to two right angles which, known to
inhere in equilateral, would then be known to inhere in a primary
subject, i. e. fully known.

BOOK I. 5 74"

it has been demonstrated qua triangle or qua isosceles?
What is the point at which the subject to which it belongs
is primary ? (i. e. to what subject can it be demonstrated as
belonging commensurately and universally ?) Clearly this
point is the first term in which it is found to inhere as
the elimination of inferior differentiae proceeds. Thus the
angles of a brazen isosceles triangle are equal to two right
angles : but eliminate brazen and isosceles and the attribute
remains. But you may say eliminate figure or limit, 74 b
and the attribute vanishes. True, but figure and limit are
not the first differentiae whose elimination destroys the
attribute. Then what is the first ? If it is triangle, it
will be in virtue of triangle that the attribute belongs to all
the other subjects of which it is predicable, and triangle
is the subject to which it can be demonstrated as belonging
commensurately and universally.

6 Demonstrative knowledge must rest on necessary basic 5
truths ; for the object of scientific knowledge l cannot be
other than it is. Now attributes attaching essentially to
their subjects attach necessarily to them : for essential attri
butes are either elements in the essential nature of their
subjects, or contain their subjects as elements in their own
essential nature. (The pairs of opposites which the latter
class includes are necessary because one member or the
other necessarily inheres.) It follows from this that pre- 10
misses of the demonstrative syllogism must be connexions
essential in the sense explained : for all attributes must
inhere essentially or else be accidental, and accidental
attributes are not necessary to their subjects.

We must either state the case thus, or else premise that
the conclusion of demonstration is necessary 2 and that
a demonstrated conclusion cannot be other than it is, and
then infer that the conclusion must be developed from 15
necessary premisses. For though you may reason from true
premisses without demonstrating, yet if your premisses are
necessary you will assuredly demonstrate in such necessity

1 i. e. that which is known by demonstration.
J Reading avayKaiov.

74 b ANALYTICA POSTERIORA

you have at once a distinctive character of demonstration.
That demonstration proceeds from necessary premisses is
also indicated by the fact that the objection we raise
against a professed demonstration is that a premiss of it

20 is not a necessary truth whether we think it altogether
devoid of necessity, or at any rate so far as our opponent s
previous argument goes. This shows how naive it is to
suppose one s basic truths rightly chosen if one starts with
a proposition which is (i) popularly accepted and (2) true,
such as the sophists assumption that to know is the same
as to possess knowledge. 1 For (i) popular acceptance or
rejection is no criterion of a basic truth, which can only be
the primary law of the genus constituting the subject matter

25 of the demonstration; and (2) not all truth is appropriate . 2
A further proof that the conclusion must be the develop
ment of necessary premisses is as follows. Where demon
stration is possible, one who can give no account which
includes the cause has no scientific knowledge. If, then, we
suppose a syllogism in which, though A necessarily inheres
in C, yet B, the middle term of the demonstration, is not
necessarily connected with A and C, then the man who argues

30 thus has no reasoned knowledge of the conclusion, since this
conclusion does not owe its necessity to the middle term ;
for though the conclusion is necessary, the mediating link is
a contingent fact. Or again, if a man is without knowledge
now, though he still retains the steps of the argument,
though there is no change in himself or in the fact and no
lapse of memory on his part ; then neither had he knowledge
previously. But the mediating link, not being necessary,

35 may have perished in the interval ; and if so, though there
be no change in him nor in the fact, and though he will still
retain the steps of the argument, yet he has not knowledge,
and therefore had not knowledge before. Even if the link
has not actually perished but is liable to perish, this
situation is possible and might occur. But such a condition
cannot be knowledge.

75 a When the conclusion is necessary, the middle through
which it was proved may yet quite easily be non-necessary.
1 Plato, Euthydennts, 2778. 2 Cf. note on 7i b 23.

BOOK I. 6 75

You can in fact infer the necessary even from a non-neces
sary premiss, just as you can infer the true from the not true.
On the other hand, when the middle is necessary the
conclusion must be necessary ; just as true premisses always 5
give a true conclusion. Thus, if A is necessarily predicated
of B and B of C, then A is necessarily predicated of C.
But when the conclusion is non-necessary the middle cannot
be necessary either. Thus : let A be predicated non-
necessarily of C but necessarily of B, and let B be a 10
necessary predicate of C\ then A too will be a necessary
predicate of C, which by hypothesis it is not.

To sum up, then : demonstrative knowledge must be
knowledge of a necessary nexus, and therefore must clearly
be obtained through a necessary middle term ; otherwise its
possessor will know neither the cause nor the fact that his
conclusion is a necessary connexion. Either he will mistake 15
the non-necessary for the necessary and believe the necessity
of the conclusion without knowing it, or else he will not even
believe it in which case he will be equally ignorant,
whether he actually infers the mere fact through middle
terms or the reasoned fact and from immediate premisses. 1

Of accidents that are not essential according to our
definition of essential there is no demonstrative knowledge ;
for since an accident, in the sense in which I here speak of it, 20
may also not inhere, it is impossible to prove its inherence
as a necessary conclusion. A difficulty, however, might be
raised as to why in dialectic, if the conclusion is not a
necessary connexion, such and such determinate premisses
should be proposed in order to deal with such and such
determinate problems. Would not the result be the same
if one asked any questions whatever and then merely stated
one s conclusion ? The solution is that determinate questions 25
have to be put, not because the replies to them affirm facts
which necessitate facts affirmed by the conclusion.but because
these answers are propositions which if the answerer affirm,

1 So Zabarella, taking Aristotle to mean that you may construct a
formally perfect syllogism, inferring the fact, or even the reasoned fact,
from what are actually true and necessary premisses ; yet because you
do not realize their necessity, you have not knowledge. One would,
however, have expected o-vAXoyio-qrai for tldfj in * 16.

75 a ANALYTICA POSTERIORA

he must affirm the conclusion and affirm it with truth if
they are true.

Since it is just those attributes within every genus which
are essential and possessed by their respective subjects as
such that are necessary, it is clear that both the conclusions

30 and the premisses of demonstrations which produce scientific
knowledge are essential. 1 For accidents are not necessary :
and, further, 2 since accidents are not necessary one does not
necessarily have reasoned knowledge of a conclusion drawn
from them (this is so even if the accidental premisses are
invariable but not essential, as in proofs through signs ; 3 for
though the conclusion be actually essential, one will not
know it as essential nor know its reason) ; but to have

35 reasoned knowledge of a conclusion is to know it through
its cause. We may conclude that the middle must be
consequentially connected with the minor, and the major
with the middle.

It follows that we cannot in demonstrating pass from one 7
genus to another. We cannot, for instance, prove geome
trical truths by arithmetic. For there are three elements in
40 demonstration : (i) what is proved, the conclusion an
attribute inhering essentially in a genus ; (2) the axioms, 5
75 b i. e. axioms which are premisses of demonstration ; (3) the
subject-genus whose attributes, i.e. essential properties, are
revealed by the demonstration. The axioms which are
premisses of demonstration may be identical 6 in two or

1 The implied minor premiss required for this conclusion is the
already proved fact that the conclusions and premisses of demonstra
tion are necessary. I take oi>8 fl a 32 8i6n a 34 as a parenthesis.

J A further reason for excluding accidental premisses from demonstra
tion : they cannot give reasoned knowledge of a conclusion, i. e. ( a 35)
knowledge of it through its cause (and this, Aristotle implies, was one
of the first conditions of demonstration. Cf. 7i b 10, n).

8 Usually proofs from effect to cause, cf. i, ch. 13, 78*30 ff.

4 Zabarella begins ch. 7 at 75* 28 perhaps a better division.

5 It is not clear whether by e &v Aristotle implies that the quantita
tive axioms can be premisses of demonstration a view perhaps
supported by i, ch. 9, 7S b 4O, 41 if the interpretation of Bryson s
quadrature of the circle suggested in my note on 76 a 3 is correct or
whether, like such axioms as the laws of contradiction and excluded
middle, they are implied as canons regulating all mathematical
demonstrations but do not serve as premisses. I have with hesitation
adopted the former alternative here and in ch. 10, 76^ 14.

6 SC. Kar" dvaXoyiav

BOOK I. 7 75 b

more sciences : but in the case of two different genera such
as arithmetic and geometry you cannot apply arithmetical
demonstration to the properties of magnitudes unless the 5
magnitudes in question are numbers. 1 How in certain
cases transference is possible I will explain later. 2

Arithmetical demonstration and the other sciences likewise
possess, each of them, their own genera ; so that if the
demonstration is to pass from one sphere to another, the
genus must be either absolutely or to some extent 3 the
same. If this is not so, transference is clearly impossible, i
because the extreme and the middle terms must be drawn
from the same genus : 4 otherwise, as predicated, they will
not be essential and will thus be accidents. That is why it
cannot be proved by geometry that opposites fall under one
science, nor even that the product of two cubes is a cube.
Nor can the theorem of any one science be demonstrated by
means of another science, unless these theorems are related 15
as subordinate to superior (e. g. as optical theorems to
geometiy or harmonic theorems to arithmetic). Geometry
again 5 cannot prove of lines any property which they do
not possess qua lines, i. e. in virtue of the fundamental
truths of their peculiar genus : it cannot show, for example,
that the straight line is the most beautiful of lines or the
contrary of the circle ; for these qualities do not belong
to lines in virtue of their peculiar genus, but through some
property which it shares with other genera. ao

8 It is also clear that if the premisses from which the
syllogism proceeds are commensurately universal, the
conclusion of such demonstration demonstration, i. e., in
the unqualified sense must also be eternal. Therefore no
attribute can be demonstrated nor known by strictly scien
tific knowledge to inhere in perishable things. The proof
can only be accidental, because the attribute s connexion 25
with its perishable subject is not commensurately universal

1 Cf. Met. 1039*9. 2 Cf. i, cc. 9 and 13.

3 i. e. in the case of subalternate sciences : cf. e. g. 75 b 15 ff.

4 sc. in all the demonstrations of the science.

5 Aristotle has given two examples of the vicious transference of a
middle term from one science to another : he now gives two examples
of the vicious transference of a complete major premiss.

75 b ANALYTICA POSTERIORA

but temporary and special. If such a demonstration is
made, one premiss must be perishable and not commensur-
ately universal (perishable l because only if it is perishable will
the conclusion be perishable ; not commensurately universal,
because the predicate will be predicable of some instances
of the subject and not of others) ; so that the conclusion can
only be that a fact is true at the moment not commen-

30 surately and universally. The same is true of definitions,
since a definition is either a primary premiss 2 or a conclusion
of a demonstration, or else only differs from a demonstration
in the order of its terms. Demonstration and science of
merely frequent occurrences e. g. of eclipse as happening to
the moon are, as such, 3 clearly eternal : whereas so far as
they are not eternal they are not fully commensurate. 4

35 Other subjects too have properties attaching to them in the
same way as eclipse attaches to the moon.

It is clear that if the conclusion is to show an attribute 9
inhering as such, nothing can be demonstrated except from
its appropriate 5 basic truths. Consequently a proof even
from true, indemonstrable, and immediate premisses does

40 not constitute knowledge. Such proofs are like Bryson s
method of squaring the circle ; for they operate by taking
as their middle a common character a character, therefore,

6 a which the subject may share with another and consequently
they apply equally to subjects different in kind. They
therefore afford knowledge of an attribute only as inhering
accidentally, not as belonging to its subject as such : other
wise they would not have been applicable to another genus. 6

1 Taking (f)0apTrjv pev . . . {<$> &v as a parenthesis.

2 i.e. the minor premiss in a basic syllogism of a science. Cf. ii.
ch. 10.

3 sc. f as far as they are demonstration and science the thesis which
the chapter establishes. In so far as eclipse, demonstrated through
its proximate cause, is regarded as embodying an unalterable nexus of
cause and effect, the demonstration is genuine demonstration.

4 In so far as the eclipse so demonstrated is a particular event, the
demonstration is not fully commensurate and so not truly universal.

6 Cf. note on 7i b 23-

6 The usual explanation of Bryson s method, viz. that he argued
that a circle is the mean area between the areas of the circumscribed
and inscribed squares, renders it improbably futile. A more probable
account (cf. Heath, Greek Mathematics, vol. i. 223-5) ls as follows :
Bryson circumscribed regular polygons about a circle and inscribed

BOOK I. 9 76*

Our knowledge of any attribute s connexion with a
subject is accidental unless we know that connexion through
the middle term in virtue of which it inheres, and as an 5
inference from basic premisses essential and appropriate to
the subject unless we know, e. g., the property of possess
ing angles equal to two right angles as belonging to that
subject in which it inheres essentially, and as inferred from
basic premisses essential and appropriate to that subject :
so that if that middle term also belongs essentially to the
minor, the middle must belong to the same kind as the
major and minor terms. The only exceptions to this rule
are such cases as theorems in harmonics which are demon
strable by arithmetic. Such theorems are proved by the 10
same middle terms as arithmetical properties, but with a
qualification the fact falls under a separate science (for the
subject genus is separate), but the reasoned fact concerns
the superior science, to which the attributes essentially
belong. Thus, even these apparent exceptions show that
no attribute is strictly demonstrable except from its
appropriate basic truths, \vhich, however, in the case of 15
these sciences have the requisite identity of character.

It is no less evident that the peculiar basic truths of each
inhering attribute are indemonstrable ; for basic truths from
which they might be deduced would be basic truths of all

regular polygons within it, in each case increasing the number of sides
so that the area of the resulting polygon more and more nearly
approached that of the circle, arguing that eventually the external
and internal polygons would approximate so closely that there could
be only one polygon mean in area between them, which would con
sequently coincide in area with the circle. He may then have
reasoned thus : Things which are greater and less than the same
things respectively are equal. The mean polygon is greater than all
the internal polygons and less than all the external polygons; so is the
circle : therefore they are equal. Now the axiom contained by the
major premiss is true, but requires specification within each science
to be effective ; e. g. in arithmetic it can only prove a number equal to
itself, while in geometry it must be stated as Commensurate magni
tudes &c. . The difficulty of this explanation is that in Soph. Elench.
I72 a 2~7 Aristotle condemns Bryson s quadrature as eristic , because
it can be extended outside the sphere of geometry altogether ; leaving
one to suppose that had Bryson reduced the application of the axiom to
geometry and stated it as Magnitudes which are, &c. , the proof
would have been valid, whereas in fact it requires a further reduction
within geometry to connect it with the minor premiss. It is also
highly questionable whether Aristotle held that a quantitative axiom
could serve as major premiss of demonstration, cf. note on 75* 42.

?6 a ANALYTICA POSTERIORA

that is, and the science to which they belonged would possess
universal sovereignty. 1 This is so because he knows better
whose knowledge is deduced from higher causes, for his

20 knowledge is from prior premisses when it derives from
causes themselves uncaused : hence, if he knows better than
others or best of all, his knowledge would be science in a
higher or the highest degree. But, as things are, demonstra
tion is not transferable to another genus, with such exceptions
as we have mentioned of the application of geometrical
demonstrations to theorems 2 in mechanics or optics, or of

a 5 arithmetical demonstrations to those of harmonics.

It is hard to be sure whether one knows or not ; for it is
hard to be sure whether one s knowledge is based on the
basic truths appropriate to each attribute the differentia
of true knowledge. We think we have scientific knowledge
if we have reasoned from true and primary premisses. But
that is not so : the conclusion must be homogeneous with

30 the basic facts of the science.

I call the basic truths of every genus those elements in it 10
the existence of which cannot be proved. As regards both
these primary truths and the attributes dependent on them
the meaning of the name is assumed. The fact of their
existence as regards the primary truths must be assumed ;
but it has to be proved of the remainder, 3 the attributes.
Thus we assume the meaning alike of unity, straight, and
35 triangular; but while as regards unity and magnitude 4 we
assume also the fact of their existence, in the case of the
remainder proof is required.

1 Cf. Met. B, cc. 2 and 3. Aristotle must surely mean that there is
no such dominant science. This interpretation, however, leaves the
relation of science to metaphysics to which a reference is clearly
implied obscure. Zabarella : notandum est Aristotelem non negare
metaphysicum posse probare aliarum scientiarum principia, id namque
non negari potest ; sed solum negare quod in illis scientiis quarum sunt
principia, id fieri queat : ex principiis enim metaphysicis possunt
probari principia geometrica, non tamen in ipsa geometria sed in
metaphysica ; i. e. as opposed to the relation of subalternate sciences.
Pacius retains the discussion within the limits of a single science, but
not without violence to the text.

2 pr)xaviK.as, dnriKas, and ap/j.oviKas should almost certainly be neuter
plurals. 3 sc. the remainder of the genus ; vide 75* 42- b i.

4 Unless neyedos stands for the genus of which f I6v and Tpiyu>i>ov are
species, the insertion of it is odd though not without parallel. For
as apparently an attribute vide note on 71* 15.

BOOK I. 10 76*

Of the basic truths used in the demonstrative sciences
some are peculiar to each science, and some are common,
but common only in the sense of analogous, being of use
only in so far as they fall within the genus constituting the
province of the science in question.

Peculiar truths are, e.g., the definitions of line and straight ; 40
common truths are such as take equals from equals and
equals remain . Only so much of these common truths is
required as falls within the genus in question : for a truth
of this kind will have the same force even if not used 76 b
generally but applied by the geometer only to magnitudes,
or by the arithmetician only to numbers. Also peculiar to
a science are the subjects the existence as well as the meaning
of which it assumes, and the essential attributes of which it
investigates, e. g. in arithmetic units, in geometry points and 5
lines. Both the existence and the meaning of the subjects
are assumed by these sciences ; but of their essential attributes
only the meaning is assumed. For example arithmetic as
sumes the meaning of odd and even, square and cube, geo
metry that of incommensurable, or of deflection or verging l
of lines, whereas the existence of these attributes is demon
strated by means of the axioms and from previous conclusions 10
as premisses. Astronomy too proceeds in the same way.
For indeed every demonstrative science has three elements :
(i) that which it posits, the subject genus whose essential
attributes it examines ; (2) the so-called axioms, which are
primary premisses 2 of its demonstration ; (3) the attributes, 15
the meaning of which it assumes. Yet some sciences may
very well pass over some of these elements ; e. g. we might
not expressly posit the existence of the genus if its existence
were obvious (for instance, the existence of hot and cold is
more evident than that of number) ; or we might omit to
assume expressly the meaning of the attributes if it were
well understood. In the same way the meaning of axioms, 20
such as Take equals from equals and equals remain , is
well known and so not expressly assumed. 2 Nevertheless in
the nature of the case the essential elements of demonstration
are three: the subject, the attributes, and the basic premisses. 2

1 Vide Heath, Euclid, vol. i, p. 150. 2 Cf. note on 75* 42.

76 b ANALYTICA POSTERIORA

That which expresses necessary self-grounded fact, and
which we must necessarily believe, 1 is distinct both from the
hypotheses 2 of a science and from illegitimate postulate
I say must believe , because all syllogism, and therefore
a fortiori demonstration, is addressed not to the spoken

25 word, but to the discourse within the soul, 3 and though we
can always raise objections to the spoken word, to the
inward discourse we cannot always object. That which is
capable of proof but assumed by the teacher without proof
is, if the pupil believes and accepts it, hypothesis, though
only in a limited sense hypothesis that is, relatively to the

30 pupil ; if the pupil has no opinion or a contrary opinion on
the matter, the same assumption is an illegitimate postulate.
Therein lies the distinction between hypothesis and illegiti
mate postulate : the latter is the contrary of the pupil s
opinion, 4 demonstrable, but assumed and used without
demonstration.

35 The definitions viz. those which are not expressed as
statements that anything is or is not 5 are not hypotheses :
but it is in the premisses of a science that its hypotheses are
contained. Definitions require only to be understood, and
this is not hypothesis unless it be contended that the pupil s
hearing is also an hypothesis required by the teacher.
Hypotheses, on the contrary, postulate facts on the being
of which depends the being of the fact inferred. Nor are

4 the geometer s hypotheses false, as some have held, urging
that one must not employ falsehood and that the geometer
is uttering falsehood in stating that the line which he draws
is a foot long or straight, when it is actually neither. The
77 a truth is that the geometer does not draw any conclusion from
the being of the particular line of which he speaks, but from
what his diagrams symbolize. A further distinction is
that all hypotheses and illegitimate postulates are either
universal or particular, whereas a definition is neither. 6

1 sc. axioms. 2 Cf. note on 72* 20.

3 Cf. Plato, Theaetetus, 18QE ff. * Omitting i) after Sofa

5 It seems easier to read ovdev for ouSe with Waitz, but one would then

expect \eyovcriv.

* A opof is not strictly a judgement at all ; it is the unify of the
constitutive moments of an UTO/IOJ/ eiSoj set out as a formula or Xoyoy.

BOOK I. ii 77

II So l demonstration does not necessarily imply the being 5
of Forms nor a One beside a Many, but it does necessarily
imply the possibility of truly predicating one of many ;
since without this possibility we cannot save the universal,
and if the universal goes, the middle term goes with it, and
so demonstration becomes impossible. We conclude, then,
that there must be a single identical term unequivocally
predicable of a number of individuals.

The law that it is impossible to affirm and deny simul- 10
taneously the same predicate of the same subject is not
expressly posited by any demonstration except when the
conclusion also has to be expressed in that form ; in which
case the proof lays down as its major premiss that the
major is truly affirmed of the middle but falsely denied.
It makes no difference, however, if we add to the middle, or
again to the minor term, the corresponding negative. For
grant a minor term of which it is true to predicate man 15
even if it be also true to predicate not-man of it still grant
simply that man is animal and not not-animal, and the
conclusion follows : for it will still be true to say that
Callias even if it be also true to say that not-Callias is
animal and not not-animal. 2 The reason is that the major

1 Zabarella inserts the first paragraph of this chapter down to fj.f/
6fi<awfj.ov in a 9 at 75 b 30.

2 i. e. if the required conclusion is Callias is animal and not not-
animal , the syllogism is adequate in the form

Man is animal and not not-animal,

Callias is man,

. . Callias is animal and not not-animal.

There is no need to add and not not-man to the middle or and not
not-Callias to the minor, for even if the opposites which these
additions would exclude were taken as true, the same conclusion would
follow :

Man and also not-man (cat, dog, &c.) is animal and not not-
animal,

Callias and also not-Callias (Plato, Socrates, &c.) is man-and-
also-not-man (i. e. belongs to a genus wider than man and
narrower than animal).
. . Callias is animal and not not-animal.

The major once made definite, the width of the middle, provided it is
narrower than the major, does not matter, and the width of the minor,
provided it is narrower than the middle, .is unimportant.

The construction in a 15-17 perhaps presents two anacolutha : (a) the
antecedent to KU# ov seems to be the subject to an unexpressed verb,
presumably tivai (could dvai have dropped out between stTmc and et

a

77 a ANALYTICA POSTERIORA

term is predicable not only of the middle, but of something
other than the middle as well, being of wider application ;

20 so that the conclusion is not affected even if the middle is
extended to cover the original middle term and also what
is not the original middle term. 1

The law that every predicate can be either truly affirmed
or truly denied of every subject is posited by such demonstra
tion as uses redtictio ad impossibile, and then not always
universally, but so far as it is requisite ; within the limits,
that is, of the genus the genus, I mean (as I have already

35. explained 2 ), to which the man of science applies his demon
strations. In virtue of the common elements of demonstra
tion I mean the common axioms which are used as
premisses of demonstration, 3 not the subjects nor the
attributes demonstrated as belonging to them all the
sciences have communion with one another, and in commu
nion with them all is dialectic and any science which might
attempt a universal proof of axioms such as the law of

30 excluded middle, the law that the subtraction of equals from
equals leaves equal remainders, or other axioms of the same
kind. Dialectic has no definite sphere of this kind, not
being confined to a single genus. Otherwise its method
would not be interrogative ; for the interrogative method is
barred to the demonstrator, who cannot use the opposite
facts to prove the same nexus. This was shown in my work

35 on the syllogism. 4

If a syllogistic question 5 is equivalent to a proposition 12
embodying one of the two sides of a contradiction, and if

Kai ?), and (&) a main clause, the conclusion follows , must be supplied.
To avoid (a) I have with hesitation taken the antecedent to *a# ov as
subject to { Or? in the first et clause, and f866r) as followed by the
infinitive flvai in the third clause.

1 Lit. even if the middle is itself and also what is not itself; i.e.
you may pass from the middle term man to include not-man without
affecting the conclusion. Cf. previous note.

2 Cf. 75 a 42 ff. and ;6 b 13. s Cf. note on 75* 42.

4 An. Pr. I. i. The opposite facts are those which would be
expressed in the alternatively possible answers to the dialectical
question, the dialectician s aim being to refute his interlocutor whether
the latter answers the question first put to him affirmatively or in the
negative.

5 i. e. a premiss put in the form of a question.

BOOK I. 12 77 a

each science has its peculiar propositions from which its
peculiar conclusion is developed, then there is such a thing
as a distinctively scientific question, and it is the interroga
tive form of the premisses from which the appropriate
conclusion of each science is developed. Hence it is clear 40
that not every question will be relevant to geometry, nor to
medicine, nor to any other science : only those questions
will be geometrical which form premisses for the proof of 77 b
the theorems of geometry or of any other science, 1 such as
optics, which uses the same basic truths as geometry. Of
the other sciences the like is true. Of these questions the
geometer is bound to give his account, using the basic
truths of geometry in conjunction with his previous conclu
sions ; of the basic truths the geometer, as such, is not 5
bound to give any account. The like is true of the other
sciences. There is a limit, then, to the questions which we
may put to each man of science ; nor is each man of science
bound to answer all inquiries on each several subject, but
only such as fall within the defined field of his own science.
If, then, in controversy with a geometer qua geometer the
disputant confines himself to geometry and proves anything
from geometrical premisses, he is clearly to be applauded ; 10
if he goes outside these he will be at fault, and obviously
cannot even refute the geometer except accidentally. 2 One
should therefore not discuss geometry among those who are
not geometers, for in such a company an unsound argument
will pass unnoticed. This is correspondingly true in the
other sciences. 15

Since there are geometrical questions, does it follow
that there are also distinctively ungeometrical questions ?
Further, in each special science geometry for instance
what kind of error 3 is it that may vitiate questions, and yet
not exclude 4 them from that science ? Again, is the erro
neous conclusion one constructed from premisses opposite to

1 Reading r\ a. (< TO>I/ with C and Bonitz.

2 Placing a colon instead of a comma after Stinvvr], a comma instead
of a full stop after *cnXo>s in b n, and a colon instead of a comma
after O-V^^KOS in b 12.

3 Reading noiav.

4 Omitting fj ayeco/urpqra with A, B, and C. So Waitz.

77 b ANALYTICA POSTERIORA

20 the true premisses, 1 or is it formal fallacy though drawn
from geometrical premisses ? 2 Or, perhaps, the erroneous
conclusion is due to the drawing of premisses from another
science; e.g. in a geometrical controversy a musical ques
tion is distinctively ungeometrical, whereas the notion that
parallels meet is in one sense geometrical, being ungeo
metrical in a different fashion : the reason being that ungeo-
metrical , like unrhythmical , is equivocal, meaning in the

35 one case not geometry at all, 3 in the other bad geometry?
It is this error, i. e. error 4 based on premisses of this kind
of the science but false that is the contrary 5 of science.
In mathematics the formal fallacy is not so common,
because it is the middle term in which the ambiguity lies, 6
since the major is predicated of the whole of the middle

30 and the middle of the whole of the minor (the predicate of
course never has the prefix all ) ; and in mathematics one
can, so to speak, see these middle terms with an intellectual
vision, while in dialectic the ambiguity may escape detec
tion. E.g. Is every circle a figure? A diagram shows
that this is so, but the minor premiss Are epics circles ? 7
is shown by the diagram to be false.

If a proof has an inductive minor premiss, one should not

35 bring an objection against it. For since every premiss
must be applicable to a number of cases (otherwise it will
not be true in every instance, which, since the syllogism
proceeds from universals, it must be), then assuredly the
same is true of an objection ; since premisses and objec
tions are so far the same that anything which can be
validly advanced as an objection must be such that it
could take the form of a premiss, either demonstrative or

40 dialectical. 8 On the other hand, arguments formally illo-

1 i. e. wrong in its matter.

2 Placing a note of interrogation after Kara yt^^trpLav 8t.

5 Omitting aHnrepro appvO/JLOf in 77 b 2J.

4 Reading avrrj KOI rj fK with A, B, C, and Waitz.
8 fi-avria : but not contradictory. The ignorance contradictory to
science is blank nescience, cf. i, ch. 18.

6 Reading del TO Sirrdi/ with A, B, and C first hand.

7 The reference is to ra KVK\tKa, the cycle of post-Homeric epics
supplementing Homer.

8 The connexion of this section 77 b 34-9 is not very clear.

b

BOOK I. 12 77

gical do sometimes occur through taking as middles mere
attributes of the major and minor terms. An instance of
this is Caeneus proof that fire increases in geometrical 78*
proportion : Fire , he argues, increases rapidly, and so
does geometrical proportion . There is no syllogism so,
but there is a syllogism if the most rapidly increasing
proportion is geometrical and the most rapidly increasing
proportion is attributable to fire in its motion. Sometimes, 5
no doubt, it is impossible to reason from premisses predicat
ing mere attributes: but sometimes it is possible, though
the possibility is overlooked. 1 If false premisses could
never give true conclusions resolution would be easy,
for premisses and conclusion would in that case inevit
ably reciprocate. 2 I might then argue thus : let A 3 be
an existing fact ; let the existence of A imply such
and such facts actually known to me to exist, which we
may call B^ I can now, since they reciprocate, infer A
from B.

Reciprocation of premisses and conclusion is more fre- 10
quent in mathematics, because mathematics takes defi
nitions, but never an accident, for its premisses a second
characteristic distinguishing mathematical reasoning from
dialectical disputations.

A science expands not by the interposition of fresh middle

Zabarella inserts it at the end of ch. 17. I take it as an obiter dictum
on fvaraats, and Aristotle as saying that the proper way to attack a
proof containing an inductive minor premiss is not to urge an eWrao-i?,
for in science an eWrao-ir, like a positive premiss of science, must be
universal and must lead to the conclusion opposite to the inference it
attacks. Hence if the fva-raa-is is another inductive premiss, it is
equally unscientific it does not demonstrate an opposite conclusion ;
if it is universal, it is gratuitous, for all one need do, Aristotle implies,
is to point out that the original proof proves nothing, because it has
a premiss which is not Ka66\ov.

1 It is possible, i.e. not of course by mere conversion to the first
figure, but when, as in the above hypothetical example, a fresh truth
ignored in the invalid argument can be brought in to amend the
paralogism and produce a syllogism in the first figure.

2 Paralogism occurs because, though true premisses must give a true
conclusion, the converse does not hold. If it did, premisses and con
clusion would reciprocate, and it would be as easy to resolve a
conclusion into its premisses as to see what conclusion must follow
from given premisses.

The premisses regarded as an antecedent.
4 The conclusion regarded as a consequent.

D 2

78 a ANALYTICA POSTERIORA

terms, but by the apposition of fresh extreme terms. 1 E.g.

15 A is predicated of B, B of C, C of D, and so indefinitely.
Or the expansion may be lateral: e.g. one major, A, may
be proved of two minors, C and E. Thus let A represent
number a number or number taken indeterminately ; B
determinate odd number ; C any particular odd number.

20 We can then predicate A of C. Next let D represent
determinate even number, and E even number. Then A is
predicable of JS. 2

Knowledge of the fact differs from knowledge of the 13
reasoned fact. To begin with, they differ within the same
science and in two ways : (i) when the premisses of the
25 syllogism are not immediate (for then the proximate cause
is not contained in them a necessary condition of know
ledge of the reasoned fact) : (2) when the premisses are
immediate, but instead of the cause the better known of
the two reciprocals is taken as the middle ; for of two
reciprocally predicable terms the one which is not the cause
may quite easily be the better known and so become the

1 i.e. the old conclusion forms one premiss of the new syllogism
and supplies the middle term :

AB That which has sensation, sleeps,
BC Animal has sensation
.. A C Animal sleeps.
Then (i) if the apposed term is a minor,
A C Animal sleeps,

C D That which expels fatigue-products is animal ;
. . A D That which expels fatigue-products sleeps.
(2) if the apposed term is a major,

D A That which sleeps expels fatigue-products,
A C Animal sleeps;
/. D C Animal expels fatigue-products.
Cf. note on An. Pr. 26* 29.

Aristotle here and in the passage immediately following, where he
speaks of lateral expansion, is thinking of the scientist as setting out
the body of his results in systematic form, as in fact writing a text
book: in passages such as i, ch. 22, 8s a i ff. which regard the ex
pansion of a science as proceeding by the insertion of fresh middle
terms between the terms of a 7rpo|3A^a, he has in mind actual
scientific discovery or at any rate a systematization of results prior
to the final setting out of the science in its logical order.

2 i.e. A A Sand A D are the two major

/\ premisses with A for predicate which

, ^ produce respectively the conclusions

A C and A E -

BOOK I. 13 78 a

middle term of the demonstration. Thus (2) (a) you might
prove as follows that the planets are near because they do 30
not twinkle : let C be the planets, B not twinkling, A proxi
mity. Then B is predicable of C ; for the planets do not
twinkle. But A is also predicable of B, since that which
does not twinkle is near we must take this truth as having
been reached by induction or sense-perception. Therefore 35
A is a necessary predicate of C\ so that we have demon
strated that the planets are near. This syllogism, then,
proves not the reasoned fact but only the fact ; since they
are not near because they do not twinkle, but. because
they are near, do not twinkle. The major and middle of
the proof, however, may be reversed, and then the demon
stration will be of the reasoned fact. Thus : let C be the 40
planets, B proximity, A not twinkling. Then B is an 78 b
attribute of C, and A not twinkling of B. Consequently
A is predicable of C, and the syllogism proves the reasoned
fact, since its middle term is the proximate cause. Another
example is the inference that the moon is spherical from its
manner of waxing. Thus : since that which so waxes is 5
spherical, and since the moon so waxes, clearly the moon
is spherical. Put in this form, the syllogism turns out to be
proof of the fact, but if the middle and major be reversed it
is proof of the reasoned fact; since the moon is not spheri
cal because it waxes in a certain manner, but waxes in such
a manner because it is spherical. (Let C be the moon, B 10
spherical, and A waxing.) Again (b], in cases where the
cause and the effect are not reciprocal and the effect is
the better known, the fact is demonstrated but not the
reasoned fact. This also occurs (i) when the middle falls
outside the major and minor, 1 for here too the strict cause
is not given, and so the demonstration is of the fact, not of
the reasoned fact. For example, the question Why does 15
not a wall breathe? might be answered, Because it is not an
animal ; but that answer would not give the strict cause,
because if not being an animal causes the absence of respira
tion, then being an animal should be the cause of respiration,

1 sc. in the second figure (vide 78 b 24), in which the middle is predi
cate in both premisses. Cf. An. Pr. i, ch. 5, 26 b 39.

78 b ANALYTICA POSTERIORA

according to the rule that if the negation of x causes the

ao non-inherence of j, the affirmation of x causes the inherence
of y ; e.g. if the disproportion of the hot and cold elements is
the cause of ill health, their proportion is the cause of health ;
and conversely, if the assertion of x causes the inherence of
y, the negation of x must cause ys non-inherence. But in
the case given this consequence does not result; for not
every animal breathes. A syllogism with this kind of cause
takes place in the second figure. Thus : let A be animal,

25 B respiration, C wall. Then A is predicable of all B (for
all that breathes is animal), but of no C; and consequently
B is predicable of no C; that is, the wall does not breathe.
Such causes are like far-fetched explanations, which precisely
consist in making the cause too remote, as in Anacharsis

30 account of why the Scythians have no flute-players ; namely
because they have no vines. 1

Thus, then, do the syllogism of the fact and the syllogism
of the reasoned fact differ within one science and according
to the position of the middle terms. But there is another
way too in which the fact and the reasoned fact differ, and
that is 2 when they are investigated respectively by different

35 sciences. This occurs in the case of problems related to
one another as subordinate and superior, as when optical
problems are subordinated to geometry, mechanical pro
blems to stereometry, harmonic problems to arithmetic,

40 the data of observation to astronomy. (Some of these
7Q a sciences bear almost the same name ; e. g. mathematical
and nautical astronomy, mathematical and acoustical har
monics.) Here it is the business of the empirical observers
to know the fact, of the mathematicians to know the
reasoned fact ; for the latter are in possession of the demon
strations giving the causes, and are often ignorant of the
5 fact : just as we have often a clear insight into a universal,
but through lack of observation are ignorant of some of its
particular instances. These connexions ;! have a perceptible
existence though they are manifestations of forms. For

1 i.e. they have no flute-players, v they do not indulge in wine, v
they have no grapes, v they have no vines.

2 In 7& b 35 read TW 81 a\\rjs for TO fit aXX^y with n and p.

3 sc. which require two sciences for their proof. Cf.

BOOK I. 13 79

the mathematical sciences concern forms : they do not
demonstrate properties of a substratum, since, even though
the geometrical subjects are predicable as properties of
a perceptible substratum, it is not as thus predicable that
the mathematician demonstrates properties of them. 1 As 10
optics is related to geometry, so another science is related
to optics, namely the theory of the rainbow. Here know
ledge of the fact is within the province of the natural philo
sopher, knowledge of the reasoned fact within that of the
optician, either qua optician or 2 qua mathematical optician.
Many sciences not standing in this mutual relation enter
into it at points; e.g. medicine and geometry: it is the
physician s business to know that circular wounds heal more 15
slowly, the geometer s to know the reason why. 3

*4 Of all the figures the most scientific is the first. Thus,
it is the vehicle of the demonstrations of all the mathe
matical sciences, such as arithmetic, geometry, and optics,
and practically of all sciences that investigate causes : for 20
the syllogism of the reasoned fact is either exclusively or
generally speaking and in most cases in this figure a
second proof that this figure is the most scientific ; for grasp
of a reasoned conclusion is the primary condition of know
ledge. Thirdly, the first is the only figure which enables
us to pursue knowledge of the essence of a thing. In the 25
second figure no affirmative conclusion is possible, and
knowledge of a thing s essence must be affirmative ; while
in the third figure the conclusion can be affirmative, but
cannot be universal, and essence must have a universal
character : e. g. man is not two-footed animal in any quali
fied sense, but universally. Finally, the first figure has no
need of the others, while it is by means of the first that the 30
other two figures are developed, and have their intervals

1 Cf. 8i b 2-5 and note thereon.

2 Reading r? roO KUTU for 17 mi in 79* 12, with the MSS. Bekker s
omission of TOV is an obvious misprint.

3 Perhaps because they expose the maximum amount of raw surface,
or possibly because a wound forming an acute angle heals most easily
i.e. by first or second intention ( granulation and therefore a circular
wound least easily.

79 a ANALYTICA POSTERIORA

close-packed l until immediate premisses are reached.
Clearly, therefore, the first figure is the primary condition
of knowledge.

Just as an attribute A may (as we saw) be atomically 15
connected with a subject B, so its disconnexion may be
atomic. I call atomic connexions or disconnexions which
35 involve no intermediate term ; since in that case the con
nexion or disconnexion will not be mediated by something
other than the terms themselves. It follows that if either
A or B, or both A and By have a genus, their disconnexion
cannot be primary. Thus: let C be the genus of A. Then,
if C is not the genus of B for A may well have a genus
40 which is not the genus of B there will be a syllogism

proving A s disconnexion from B thus :
79 b all A is C,

no B is Cy
/. no B is A.

Or if it is B which has a genus D, we have
all B is D,
no D is A,

/. no B is A, by syllogism ;

5 and the proof will be similar if both A and B have a genus.
That the genus of A need not be the genus of B and vice
versa, is shown by the existence of mutually exclusive co
ordinate series of predication. If no term in the series
A CD ... is predicable of any term in the series BEF . . .,
and if G a term in the former series is the genus of A,
10 clearly G will not be the genus of B \ since, if it were, the
series would not be mutually exclusive. So also if B has
a genus, it will not be the genus of A. If, on the other
hand, neither A nor B has a genus and A does not inhere
in B y this disconnexion must be atomic. If there be
a middle term, one or other of them is bound to have

1 Cf. i, ch. 23, 84 b 19 ff., and also note on 78 a 14. TTVKI OHTIS means
the filling up with middle terms of the mediable loosely connected
8tdoTi?/ua or interval between the terms of a Trpo/SX^/za or proposition
requiring proof a process which continues until each term is imme
diately connected with its neighbour, and basic premisses are reached.
Then only is the original irp6fi\r)pa. genuinely proved.

BOOK I. 15 79 b

a genus, for the syllogism will be either in the first or the 15
second figure. If it is in the first, B will have a genus for
the premiss containing it must be affirmative ; T if in the
second, either A or B indifferently, since syllogism is pos
sible if either is contained in a negative premiss, 2 but not if
both premisses are negative.

Hence it is clear that one thing may be atomically
disconnected from another, 3 and we have stated when and
how this is possible.

16 Ignorance defined not as the negation of knowledge but
as a positive state of mind is error produced by inference.

(i) Let us first consider propositions asserting a predicate s 25
immediate connexion with or disconnexion from a subject.
Here, 4 it is true, positive error may befall one in alternative
ways ; for it may arise where one directly believes a con
nexion or disconnexion as well as where one s belief is
acquired by inference. The error, however, that consists
in a direct belief is without complication ; but the error
resulting from inference which here concerns us takes
many forms. Thus, let A be atomically disconnected from
all B : then the conclusion inferred through a middle term 30
C, that all B is A, will be a case of error produced by
syllogism. Now, two cases are possible. Either (a) both
premisses, or (b) one premiss only, may be false, (a) If
neither A is an attribute of any C nor C of any B, whereas
the contrary was posited in both cases, both premisses will
be false. (7 may quite well be so related to A and B that 35
C is neither subordinate to A nor a universal attribute
of B : for B, since A was said to be primarily disconnected
from B, cannot have a genus, and A need not necessarily
be a universal attribute of all things. Consequently both

1 i. e. in Celarent.

" i. e. in Cesare or Camestres.

3 Reading aXAo <"XX with MSS. and Waitz. The omission of aXXo in
Bekker is clearly a misprint.

4 fitv in b 25 is not answered till 8i a 38. It has seemed necessary
to expand the translation of b 25-39. b 26 appears to contradict
b 24; but really Aristotle begins to discuss error resulting from
inference and is led by the mention of immediate propositions to
comment in passing upon error in direct apprehension.

79 b ANALYTICA POSTERIORA

40 premisses may be false. 1 ) On the other hand, (b) one of the
premisses may be true, though not either indifferently but
8o a only the major A-C \ since, B having no genus, the premiss
C-B will always be false, while A-C may be true. This is
the case if, for example, A is related atomically to both C
and B; because when the same term is related atomically
to more terms than one, neither of those terms will belong-
to the other. 2 It is, of course, equally the case if A-C is
r not atomic. 3

Error of attribution, then, occurs through these causes
and in this form only for we found that no syllogism
of universal attribution was possible in any figure but the
first. 4 On the other hand, an error of non-attribution may
occur either in the first or in the second figure. Let us
therefore first explain the various forms it takes in the first
10 figure and the character of the premisses in each case.

(c) It may occur when both premisses are false ; e. g.
supposing A atomically connected with both C and B,

C A

1 e. g. All quantity is substance,

B C

All quality is quantity ;

B A

. . All quality is substance.

Had B a genus, A s disconnexion from B would have been mediated
by it.

C A

2 e. g. All body is substance atomic,

B C

All quality is body ;
B A

. . All quality is substance atomic.

The reference cannot be to the impossibility of predicating co-ordinate
species of one another, because B is stated to have no genus. \Ve
must therefore suppose naTijyopflv here to include negation as well as
affirmation (cf. 82* 14 and note) ; e. g. substance is primarily affirmed
of body and denied of quality, therefore quality and body cannot be
predicated either of the other. Aristotle then adds that this is only
one case, and that as long as the minor premiss is atomic the major
need not be atomic ; e. g. in the above example man or stone might
be substituted for body.

C A

3 e. g. All man is substance mediable,

B C

All quality is man ;
B A

. . All quality is substance atomic.
An. Pr. i. I.

BOOK I. 16 8o 6

if it be then assumed that no C is A, and all B is C, both
premisses are false. 1

(d) It is also possible when one is false. This may be
either premiss indifferently. A-C may be true, C-B false 15
A-C true because A is not an attribute of all things,
C-B false because C, which never has the attribute A,
cannot be an attribute of Z?; 2 for if C-B were true,
the premiss A-C would no longer be true, and besides
if both premisses were true, the conclusion would be true. 3 2 o
Or again, C-B may be true and A C false ; e. g. if both C
and A contain B as genera, one of them must be subordinate
to the other, so that if the premiss takes the form No Cis A,
it will be false. 4 This makes it clear that whether either or
both premisses are false, the conclusion will equally be 25
false.

In the second figure the premisses cannot both be wholly
false; for if all B is A, no middle term can be with truth
universally affirmed of one extreme and universally denied
of the other : but premisses in which the middle is affirmed 3 o
of one extreme and denied of the other are the necessary
condition if one is to get a valid inference at all. 5 There-

C A

1 e. g. No cat is animal,

B C

All man is cat ;
B A

/. No man is animal.

2 Reading u^vvaruv vndpxtiv with codd.

C A

3 e. g. No stone is animal, (possibly true V animal is not true of

B C all things, as is, e.g., being or one.)

All man is stone ; (false v stone, which is never animal,

B A cannot be an attribute of man.)

. . No man is animal.

C A

4 e.g. No living thing is animal,

B C

All man is living ;

B A

. . No man is animal.

Here living must be a genus of animal because both animal and
living are predicable of man as genera. If living and animal were
co-ordinate, they could not both be predicable of man.
e sc. in this figure.

8o a ANALYTICA POSTERIORA

fore if, taken in this way, they are wholly false, their
contraries conversely should be wholly true. But this is
impossible. 1 On the other hand, there is nothing to pre
vent both premisses being partially false ; e. g. if actually
35 some A is C and some B is C, then if it is premised that all
A is C and no B is C, both premisses are false, yet partially,
not wholly, false. 2 The same is true if the major is made
negative instead of the minor. Or one premiss may be
wholly false, and it may be either of them. Thus, sup
posing that actually an attribute of all A must also be an
40 attribute of all B? then if C is yet taken to be a universal
8o b attribute of all A but universally non-attributable to B,
C-A will be true but CB false. 4 Again, actually that
which is an attribute of no B will not be an attribute of all
A either ; for if it be an attribute of all A, it will also be an
attribute of all B, which is contrary to supposition ; but
if C be nevertheless assumed to be a universal attribute of
5 A, but an attribute of no B, then the premiss C-B is true

A C

1 e. g. in Camestres, All animal is immortal,

B C

No man is immortal,

B A

gives the false conclusion No man is animal : but if the contraries of
these premisses were wholly true they would form a syllogism in
Cesare A C

No animal is immortal,

B C

All men are immortal

B A

giving the same conclusion No man is animal -which would have
to be true.

A C

2 e.g. All animals are biped,

B C

No mammals are biped ;

B A

. . No mammals are animal.

3 sc. as must be the case on our initial assumption that in fact all
B is A.

A C

4 e. g. All animal is living,

B C

No man is living ;

B A

. . No man is animal.

BOOK I. 16 8o l

but the major is false. 1 The case is similar if the major
is made the negative premiss. For in fact what is an
attribute of no A will not be an attribute of any B either ;
and if it be yet assumed that C is universally non-attribu
table to A, but a universal attribute of B, the premiss C-A
is true but the minor wholly false. 2 Again, in fact it is 10
false to assume that that which is an attribute of all B
is an attribute of no A, for if it be an attribute of all B, it
must be an attribute of some A. If then 7 is nevertheless
assumed to be an attribute of all B but of no A, C-B will
be true but C-A false. :!

It is thus clear that in the case of atomic propositions
erroneous inference will be possible not only when both 15
premisses are false but also when only one is false.

17 (2) In the case of attributes not atomically connected with
or disconnected from their subjects, (a) (i) as long as the
false conclusion is inferred through the appropriate middle,
only the major and not both premisses can be false. By 20
appropriate middle I mean the middle term through which
the contradictory i.e. the true conclusion is inferrible. 4
Thus, let A be attributable to B through a middle term C:
then, since to produce a conclusion the premiss C-B must
be taken affirmatively, it is clear that this premiss must

A C

1 e. g. All animal is stone,

B C

No man is stone ;

B A

. . No man is animal.

A C

3 e.g. No animal is stone,

B C

All man is stone ;

B A

. . No man is animal.
A C

3 e. g- No animal is living,

B C

All man is living ;

33 A

. . No man is animal.

4 Cf. note on ;i b 3. This definition is a corollary of the definition
there given of appropriate .

8o b ANALYTICA POSTERIORA

35 always be true, for its quality is not changed. 1 But the
major A-C is false, for it is by a change in the quality of
A-C that the conclusion becomes its contradictory i. e.

* true. 2 Similarly (ii) if the middle is taken from another
series of predication ; e. g. suppose D to be not only contained
within A as a part within its whole but also predicable of
all B. Then the premiss D B must remain unchanged, but

30 the quality of A-D must be changed ; so that D-B is always
true, A-D always false. 3 Such error is practically identical
with that which is inferred through the appropriate middle.
On the other hand, (b] if the conclusion is not inferred
through the appropriate middle (i) when the middle is
subordinate to A but is predicable of no B, both premisses

35 must be false, because if there is to be a conclusion both
must be posited as asserting the contrary of what is actually
the fact, and so posited both become false : e.g. suppose that
actually all D is A but no B is D ; then if these premisses
are changed in quality, a conclusion will follow and both

40 of the new premisses will be false. 4 When, however, (ii)

8l a the middle D is not subordinate to A, A-D will be true,

D-B false A-D true because A was not subordinate

1 i. e. it does not become negative instead of affirmative in the false
syllogism.

C A

2 e. g. Nothing rational laughs,

B C

All man is rational ;

B A

.*. No man laughs.

Change the quality of the minor and there is no inference ; change the
quality of the major and the contradictory and true conclusion follows.

D A

3 e. g. Nothing that walks upright laughs,

B D

All men walk upright ;

B A

. . No man laughs.

Change the quality of the minor and there is no inference ; change
the quality of the major and the contradictory true conclusion follows.
D A

4 e.g. No brute is living,

B D

All men are brutes ;

B A

. . No man is living.

BOOK I. 17 81"

to D, D-B false because if it had been true, the conclu
sion too would have been true; but it is ex hypothesi
false. 1

When the erroneous inference is in the second figure, both 5
premisses cannot be entirely false ; since if B is subordinate
to A, there can be no middle predicable of all of one extreme
and of none of the other, as was stated before. 2 One premiss,
however, may be false, and it may be either of them. Thus,
if C is actually an attribute of both A and B, but is assumed 10
to be an attribute of A only and not of B, C-A will be true,
C-B false : 3 or again if C be assumed to be attributable to
B but to no A, C-B will be true, C-A false.

We have stated when and through what kinds of premisses 15
error will result in cases where the erroneous conclusion is
negative. If the conclusion is affirmative, (a) (i) it may be
inferred through the appropriate middle term. In this
case both premisses cannot be false since, as we said before, 4
C-B must remain unchanged if there is to be a conclusion,
and consequently A-C, the quality of which is changed,
will always be false. This is equally true if (ii) the middle 20
is taken from another series of predication, as was stated
to be the case also with regard to negative error ; 6 for
D-B must remain unchanged, while the quality of A-D
must be converted, and the type of error is the same as
before.

(b) The middle may be inappropriate. Then (i) if D is 25
subordinate to A, A-D will be true, but D-B false; since
A may quite well be predicable of several terms no one of

D A

1 e. g. No stone is living,

B D

All man is stone ;

B A

. . No man is living.

2 Cf. 8o a 29.

A C

8 e. g. Every living thing is substance,

B C

No man is substance ;

B A

. . No man is living.
4 Cf. 80*17-26. Cf. 8o b 26-32.

8i a ANALYTICA POSTERIORA

which can be subordinated to another. 1 If, however, (ii) D
is not subordinate to A, obviously A-D, since it is affirmed,
will always be false, while D- z may be either true or

30 false ; for A may very well be an attribute of no D, whereas
all B is D, e. g. no science is animal, all music is science.
Equally well A may be an attribute of no D, and D of no B.
It emerges, then, that if the middle term is not subordinate
to the major, not only both premisses but either singly may
be false.

35 Thus we have made it clear how many varieties of erroneous
inference are liable to happen and through what kinds of
premisses they occur, in the case both of immediate and of
demonstrable truths.

It is also clear that the loss of any one of the senses entails 18
the loss of a corresponding portion of knowledge, and that,
since we learn either by induction or by demonstration, this
40 knowledge cannot be acquired. Thus demonstration de-
8l b velops from universals, induction from particulars ; but since
it is possible to familiarize the pupil with even the so-called
mathematical abstractions only through induction i. e. only
because each subject genus possesses, in virtue of a deter
minate mathematical character, certain properties which can
be treated as separate even though they do not exist in
5 isolation 3 it is consequently impossible to come to grasp
universals except through induction. But induction is
impossible for those who have not sense-perception. For
it is sense-perception alone which is adequate for grasping
the particulars : they cannot be objects of scientific know
ledge, because neither can universals give us knowledge of

D A

1 e. g. All brutes are quadrupeds,

B D

All men are brutes ;

B A

. . All men are quadrupeds.

2 Reading rfjv Se AB with MSS.

3 Cf. 79* 6-10. Ta fjia6rjfj.aTiKd or TO. e d(fiatpecr(a>?, as Aristotle
calls them, exist only as properties of sensible objects, not per se as
separate entities, although they can be isolated by abstraction and thus
constitute the subjects of mathematical demonstration. Consequently
it is only by eVccycoy^ from sensible objects that the universal can be
elicited and known : vide Met, K. io6i a 28.

BOOK I. 18 8i b

them without induction, nor can we get it through induction
without sense-perception. 1

19 Every syllogism is effected by means of three terms. 10
One kind of syllogism serves to prove that A inheres in C
by showing that A inheres in B and B in C; the other is
negative and one of its premisses asserts one term of another,
while the other denies one term of another. It is clear, then,
that these are the fundamentals and so-called hypotheses
of syllogism. Assume them as they have been stated, and 15
proof is bound to follow proof that A inheres in C through
B, and again that A inheres in B through some other middle
term, and similarly that B inheres in C. If our reasoning
aims at gaining credence and so is merely dialectical, it is
obvious that \ve have only to see that our inference is based
on premisses as credible as possible : so that if a middle ao
term between A and B is credible though not real, one can
reason through it and complete a dialectical syllogism. If,
however, one is aiming at truth, one must be guided by the
real connexions of subjects and attributes. Thus: 2 since
there are attributes which are predicated of a subject essen
tially or naturally 3 and not coincidentally 4 not, that is, 25
in the sense in which we say That white (thing) is a man ,
which is not the same mode of predication as when we say
The man is white : the man is white not because he is
something else but because he is man, but the white is man
because being white coincides with humanity within one
substratum therefore there are terms such as are naturally
subjects of predicates. Suppose, then, C such a term not 3
itself attributable to anything else as to a subject, but the
proximate 5 subject of the attribute B i. e. so that B-C is
immediate ; suppose further E related immediately to F,
and Fio B. The first question is, must this series terminate,

1 I itfe ii, ch. 19 and notes thereon.

2 Placing a colon after ourwr.

3 i. e. predication in which the predicate is essentially adjectival ; cf.
ch. 4, 73 b 5-10. Such predication is called by the Latin commentators
predicatio naturalis , and is further discussed in ch. 22,

4 Cf. note on 73 b 4.

6 In ch. 21, 82*39 ff. Aristotle from the alternative point of view
defines such a subject as ixnarov.

8i b ANALYTICA POSTERIORA

or can it proceed to infinity? The second question is as
follows : Suppose nothing is essentially predicated of A, but

35 A is predicated primarily of H and of no intermediate prior
term, and suppose H similarly related to G and G to B ;
then must this series also terminate, or can it too proceed to
infinity? There is this much difference between the
questions : the first is, is it possible to start from that which
is not itself attributable to anything else but is the subject

40 of attributes, and ascend to infinity ? The second is the
problem whether one can start from that which is a predicate
8a a but not itself a subject of predicates, and descend to infinity ?
A third question is, if the extreme terms are fixed, can there
be an infinity of middles ? I mean this : suppose for example
that A inheres in Cand B is intermediate between them, but
5 between B and A there are other middles, and between these
again fresh middles ; can these proceed to infinity or can
they not ? This is the equivalent of inquiring, do demon
strations proceed to infinity, i.e. is everything demonstrable ?
Or do ultimate subject and primary attribute limit one
another ?

I hold that the same questions arise with regard to

10 negative conclusions and premisses : viz. if A is attributable
to no B, then either this predication will be primary, or
there will be an intermediate term prior to B to which A is
not attributable G, let us say, which is attributable to all
B and there may still be another term H prior to G, which
is attributable to all G. The same questions arise, I say,
because in these cases too either the series of prior terms to
which A is not attributable l is infinite or it terminates.

15 One cannot ask the same questions in the case of
reciprocating terms, since when subject and predicate are
convertible 2 there is neither primary nor ultimate subject,
seeing that all the reciprocals qua subjects stand in the same
relation to one another, whether we say that the subject has
an infinity of attributes or that both subjects and attributes
and we raised the question in both cases are infinite in

1 Reading o\>x vnapxu with D : or else vjrupxfiv is used generally to
include negation.
a Reading dvTiKaTr}yopovp.evois with D. So Waitz.

BOOK I. 19 82*

number. These questions then cannot be asked unless,
indeed, the terms can reciprocate by two different modes,
by accidental predication in one relation and natural 20
predication in the other. 1

20 Now, 2 it is clear that if the predications terminate in both
the upward and the downward direction (by upward I
mean the ascent to the more universal, by downward the
descent to the more particular), the middle terms cannot be
infinite in number. For suppose that A is predicated of F,
and that the intermediates call them BB B". . . are 35
infinite, then clearly you might descend from A and find one
term predicated of another ad infinitum, since you have
an infinity of terms between you and F; and equally, if
you ascend from F, there are infinite terms between you
and A. It follows that if these processes are impossible
there cannot be an infinity of intermediates between A and
F. Nor is it of any effect to urge that some terms of the 30
series AB. . . F s are contiguous 4 so as to exclude inter
mediates, while others cannot be taken into the argument

at all : 5 whichever terms of the series B . . . I take, the
number of intermediates in the direction either of A or of F
must be finite or infinite : where the infinite series starts,
whether from the first term or from a later one, is of no
moment, for the succeeding terms in any case are infinite 35
in number.

21 Further, 6 if in affirmative demonstration the series ter
minates in both directions, clearly it will terminate too

1 The possibility of unnatural predication is ruled out in ch. 22.

2 Ch. 20 consists of a hypothetical argument to the effect that if the
first and second questions asked in ch. 19 are answered in the negative,
then the answer to the third question must also be in the negative.

3 I read ABZ with Waitz. Codd. ABC read ABr, not, as Bekker
indicates, AB ; cod. M, AB.

4 Cf. note on 95 b 4.

6 The objector apparently argues that even if in fact the number of
terms between A and F is infinite, yet in thought we can reach from
A to F since some of the intermediate terms will be contiguous and
the rest the possibly infinite series of middles separating two terms
may elude our apprehension altogether, so that for our thought these
two terms constitute an immediate proposition.

6 The hypothetical argument of the last chapter is now extended to
cover negation.

E a

82 a ANALYTICA POSTERIORA

in negative demonstration. Let us assume that we cannot
proceed to infinity either by ascending from the ultimate
term (by ultimate term I mean a term such as F was,
82 b not itself attributable to a subject but itself the subject of
attributes), or by descending towards an ultimate from the
primary term (by primary term I mean a term predicable
of a subject but not itself a subject 1 ). If this assumption
is justified, the series will also terminate in the case ol
negation. For a negative conclusion can be proved in all
5 three figures. In the first figure it is proved thus : no B is

A, all Cis B. In packing the interval B-C we must reach
immediate propositions as is always the case with the
minor premiss 2 since B-C \s affirmative. As regards the
other premiss it is plain that if the major term is denied of
a term D prior to B, D will have to be predicable of all B,

10 and if the major is denied of yet another term prior to D,
this term must be predicable of all D. Consequently, since
the ascending series is finite, the descent will also terminate
and there will be a subject of which A is primarily non-
predicable. 3 In the second figure the syllogism is, all A is

B, no C is B, . . no C is A. If proof of this 4 is required,
15 plainly it may be shown either in the first figure as above,

in the second as here, or in the third. The first figure has been
discussed, and we will proceed to display the second, proof
by which will be as follows : all B is D, no C is D . . ., since
it is required that B should be a subject of which a predicate
is affirmed. Next, since D is to be proved not to belong to

C, then D has a further predicate which is denied of C.
30 Therefore, since the succession of predicates affirmed of an

1 sc. a predicate above which is no wider universal.

2 Because Celarent is the only mood of the first figure in which
negative 7roSei|u is possible.

3 Interchanging K<!r and <ivca in 82 b ll and 12 with Waitz. If we
keep the text, 17 eVi TO Kara) oSoy must mean the series of subjects
descending from the primary, i.e. most universal predicate of C, through
/?, to C; and in that case Aristotle s argument is : The minor premiss,
B-C, being affi mative, the number of s and . . of C s predicates
is finite ; but it is this series which must contain the subject of which
A is primarily denied : therefore looking at the series from the opposite
point of view as ascending towards the term of which A is primarily
denied (fj V<u 68os-), it is equally finite. So Zabarella ; but this interpre
tation is artificial, and 82 b 2i below confirms Waitz s reading.

4 sc. that no C is B \

BOOK I. 21 82 b

ever higher universal terminates, 1 the succession of predicates
denied terminates too. 2

The third figure shows it as follows : all B is A, some B
is not C, . . some A is not C. This premiss, i. e. C-B, will
be proved either in the same figure or in one of the two
figures discussed above. In the first and second figures the 25
series terminates. If we use the third figure, we shall take
as premisses, all E is B, some E is not C, and this premiss
again will be proved by a similar prosyllogism. But since
it is assumed that the series of descending subjects also
terminates, plainly the series of more universal non-predi-
cables will terminate also. Even supposing that the proof
is not confined to one method, but employs them all and is
now in the first figure, now in the second or third even so 30
the regress will terminate, for the methods are finite in
number, and if finite things are combined in a finite number
of ways, the result must be finite.

Thus it is plain that the regress of middles terminates in
the case of negative demonstration, if it does so also in the
case of affirmative demonstration. That in fact the regress
terminates in both these cases may be made clear by the 35
following dialectical considerations.

22 3 In the case of predicates constituting the essential nature
of a thing, it clearly terminates, seeing that if definition is
possible, or in other words, if essential form is knowable,

1 i. e. each of the successive prosyllogisms required to prove the
negative minors contains an affirmative major in which the middle is
affirmed of a subject successively higher or more universal than the
subject of the first syllogism. Thus :

Syllogism : All B is D Prosyllogisms : All D is E All E is F
No C is D No C is E No C is F

. . No C is B .: No C is D :. No C is E

ft, D, E, &c., are successively more universal subjects ; and the series
of affirmative majors containing them must ex hypothesi terminate.

2 Since the series of affirmative majors terminates and since an affirma
tive major is required for each prosyllogism, we shall eventually reach a
minor incapable of proof and therefore immediate.

3 This chapter attempts to answer the first and second questions
raised in ch. 19. So obscure is it that it has seemed best to add a
series of foot-notes constituting an analysis of the argument. This has
been expanded where it has appeared possible to supplement the text
of the translation, and contracted where the contrary was the case.
Direct comment has been included only in parentheses contained in
square brackets.

82 b ANALYTICA POSTERIORA

and an infinite series cannot be traversed, predicates
constituting a thing s essential nature must be finite in
83* number. 1 But as regards predicates generally we have the
following prefatory remarks to make, (i) We can affirm
without falsehood the white (thing) is walking , and that
big (thing) is a log ; or again, the log is big , and the
man walks . But the affirmation differs in the two cases.
5 When I affirm the white is a log , I mean that something
which happens to be white is a log not that white is the
substratum in which log inheres, for it was not qna white or
qua a species of white that the white (thing) came to be a log,
and the white (thing) is consequently not a log except
incidentally. On the other hand, when I affirm the log is
white , I do not mean that something else, which happens

10 also to be a log, is white (as I should if I said the musician
is white , which would mean the man who happens also to
be a musician is white ) ; on the contrary, log is here the
substratum the substratum which actually came to be
white, and did so qua wood or qua a species of wood and
qua nothing else.

If we must lay down a rule, let us entitle the latter kind

15 of statement predication, and the former not predication at
all, or not strict but accidental predication. White and
log will thus serve as types respectively of predicate and
subject.

We shall assume, then, that the predicate is invariably

a predicated strictly and not accidentally of the subject, for on
such predication demonstrations depend for their force. It
follows from this that when a single attribute is predicated
of a single subject, the predicate must affirm of the subject
either some element constituting its essential nature, or that it
is in some way qualified, quantified, essentially related, active,
passive, placed, or dated. 2

1 If the attributes in a series of predication such as we are discussing
are substantial, they must be finite in number, because they are then
the elements constituting the definition of a substance.

2 The first of three statements preliminary to a proof that predicates
which are accidental other than substantial cannot be unlimited in
number : Accidental is to be distinguished from essential or natural pre
dication [cf. i, ch. 4, 73 b 5 ff. and An. Pr. i, ch. 25, 43* 25-6]. The former
is alien to demonstration : hence, provided that a single attribute is

BOOK I. 22 83

(2) Predicates which signify substance signify that the sub
ject is identical with the pred icate or with a species of the predi
cate. Predicates not signifying substance which are predicated 25
of a subject not identical with themselves or with a species of
themselves are accidental or coincidental ; e. g. white is a
"coincident of man, seeing that man is not identical with
white or a species of white, but rather with animal, since man

is identical with a species of animal. These predicates which 3
do not signify substance must be predicates of some other
subject, and nothing can be white which is not also other
than white. The Forms we can dispense with, for they are
mere sound without sense ; and even if there are such things,
they are not relevant to our discussion, since demonstrations
are concerned with predicates such as we have defined. 1 35

(3) If A is a quality of , B cannot be a quality of A a
quality of a quality. Therefore A and B cannot be predi
cated reciprocally of one another in strict predication : they
can be affirmed without falsehood of one another, but not
genuinely predicated of each other. 2 For one alternative is
that they should be substantially predicated of one another,

i. e. B would become the genus or differentia of A the 83 b
predicate now become subject. But it has been shown that
in these substantial predications neither the ascending
predicates nor the descending subjects form an infinite
series ; e. g. neither the series, man is biped, biped is
animal, &c., nor the series predicating animal of man, man
of Callias, Callias of a further subject as an element of its

predicated of a single subject, all genuine predicates fall either under
the category of substance or under one of the adjectival categories.

1 Second preliminary statement : The precise distinction of sub
stantive from adjectival predication makes clear (implicitly) the two
distinctions, (a) that between natural and accidental predication, (b)
that between substantival and adjectival predication, which falls within
natural predication. [For coincidental , coincident , see note on
73 b 4.] This enables us to reject the Platonic Forms.

[In a 3O read Q6v n, and for rtperia-nara in a 33 cf. Probl, 918*29.]

2 Third preliminary statement merging into the beginning of the
proof proper : Reciprocal predication cannot produce an indefinite
regress because it is not natural predication.

[noiorrjs in 83*37 seems to be equivalent to character and to cover
all the categories, cf. Met. A. ioao a 33-^ 2. oZras in a 38 is most
naturally taken as meaning in strict or natural predication , but
may mean so as to produce an indefinite regress . The latter is, how
ever, an mplicit consequence of the predication being unnatural.]

8s b ANALYTICA POSTERIORA

5 essential nature, is infinite. For all such substance is
definable, and an infinite series cannot be traversed in
thought : consequently neither the ascent nor the descent is
infinite, since a substance whose predicates were infinite
would not be definable. Hence they will not be predicated
each as the genus of the other ; for this would equate a

10 genus with one of its own species. Nor (the other alterna
tive) can a quale be reciprocally predicated of a quale, nor
any term belonging to an adjectival category of another
such term, except by accidental predication ; for all such
predicates are coincidents and are predicated of substances. 1
On the other hand in proof of the impossibility of an
infinite ascending series every predication displays the
subject as somehow qualified or quantified or as characte
rized under one of the other adjectival categories, or else

15 is an element in its substantial nature: these latter are
limited in number, and the number of the widest kinds
under which predications fall is also limited, for every
predication must exhibit its subject as somehow qualified,
quantified, essentially related, acting or suffering, or in
some place or at some time. 2

I assume first that predication implies a single subject
and a single attribute, and secondly that predicates which
are not substantial are not predicated of one another. We
assume this because such predicates are all coincidents, and

1 Expansion of third preliminary statement : Reciprocals A and B
might be predicated of one another (a) substantially; but it has been
proved already that because a definition cannot contain an infinity of
elements substantial predication cannot generate infinity ; and it would
disturb the relation of genus and species : (b] as gualta or quanta &c. ;
but this would be unnatural predication, because all such predicates
are adjectival, i. e. accidents, or coincidents, of substances.

[oiSe nfjv in 83 b 10, though an anacoluthon, answers J? . . . Voi in a 39-
navra yap . . . Karriyopflrai in b ii and 12 seems to be Aristotle s proof
that the descending series in the predication of accidents terminates ;
sc. because it ends in an individual substance.]

2 The ascent of predicates is also finite ; because all predicates fall
under one or other of the categories, and (a) the series of predicates
under each category terminates when the category is reached, and (b)
the number of the categories fs limited. [(a) seems to mean that an
attribute as well as a substance is definable by genus and differentia,
and the elements in its definition must terminate in an upward direction
at the category, and can therefore no more form an infinite series than
can the elements constituting the definition of a substance.]

BOOK I. 22 83*

though some are essential coincidents, others of a different
type, yet we maintain that all of them alike are predicated 20
of some substratum and that a coincident is never a sub
stratum since we do not class as a coincident anything
which does not owe its designation to its being something
other than itself, but always hold that any coincident is
predicated of some substratum other than itself, and that
another group of coincidents may have a different substra
tum. Subject to these assumptions then, neither the
ascending nor the descending series of predication in which 25
a single attribute is predicated of a single subject is
infinite. 1 For the subjects of which coincidents are predi
cated are as many as the constitutive elements of each
individual substance, and these we have seen are not infinite
in number, while in the ascending series are contained
those constitutive elements with their coincidents both of
which are finite. 2 We conclude that there is a given
subject (D) of which some attribute (C) is primarily predic-
able ; that there must be an attribute (13) primarily pre-
dicable of the first attribute, and that the series must end
with a term (A) not predicable of any term prior to the last 3
subject of which it was predicated (/?), and of which no term
prior to it is predicable. 3

1 To reinforce this brief proof that descent and ascent are both
finite we may repeat the premisses on which it depends. These are
(i) the assumption that predication means the predication of one
attribute of one subject, and (2) our proof that accidents cannot be
reciprocally predicated of one another, because that would be unnatural
predication. It follows from these premisses that both ascent and
descent are finite. [Actually (2) only reinforces the proof that the
descent terminates.]

2 To repeat again the proof that both ascent and descent are finite :
The subjects cannot be more in number than the constituents of a de
finable form, and these, we know, are not infinite in number : hence the
descent is finite. The series regarded as an ascent contains subjects
and ever more universal accidents, and neither subjects nor accidents are
infinite in number.

3 Formal restatement of the last conclusion. [This is obscure:
apparently Aristotle here contemplates a hybrid series: category,
accident, further specified accident . . . substantial genus, subgenus
. . . infima species, individual substance.

If this interpretation of the first portion of the chapter is at all correct,
Aristotle s first proof that the first two questions of ch. 19 must be
answered in the negative is roughly as follows : The ultimate subject
of all judgement is an individual substance, a concrete singular. Of
such concrete singulars you can predicate substantially only the elements

8s b ANALYTICA POSTERIORA

The argument we have given is one of the so-called
proofs ; an alternative proof follows. Predicates so related
to their subjects that there are other predicates prior to
them predicable of those subjects are demonstrable ; but
of demonstrable propositions one cannot have something
35 better than knowledge, nor can one know them without
demonstration. Secondly, if a consequent is only known
through an antecedent (viz. premisses prior to it) and we
neither know this antecedent nor have something better
than knowledge of it, then we shall not have scientific
knowledge of the consequent. Therefore, if it is possible
through demonstration to know anything without qualifica
tion and not merely as dependent on the acceptance of certain
premisses i. e. hypothetically the series of intermediate
84* predications must terminate. If it does not terminate,
and beyond any predicate taken as higher than another
there remains another still higher, then every predicate is
demonstrable. Consequently, since these demonstrable
predicates are infinite in number and therefore cannot be
traversed, we shall not know them by demonstration. If,
therefore, we have not something better than knowledge of
5 them, we cannot through demonstration have unqualified
but only hypothetical science of anything. 1

constituting their infima species. These are limited in number because
they form an intelligible synthesis. So far, then, as substantial predicates
are concerned, the questions are answered. But these elements are
also the subjects of which accidents, or coincidents, are predicated,
and therefore as regards accidental predicates, at any rate, the descend
ing series of subjects terminates. The ascending series of attributes
also terminates, (i) because each higher attribute in the series can
only be a higher genus of the accident predicated of the ultimate sub
ject of its genus, and therefore an element in the accident s definition ;
(2) because the number of the categories is limited.

We may note that the first argument seems to envisage a series
which, viewed as an ascent, starts with a concrete individual of which
the elements of its definition are predicated successively, specific
differentia being followed by proximate genus, which latter is the
starting-point of a succession of ever more universal attributes termi
nating in a category ; and that the second argument extends the scope
of the dispute to the sum total of all the trains of accidental predication
which one concrete singular substance can beget. It is, as so often in
Aristotle, difficult to be sure whether he is regarding the infima species
or the concrete singular the Trpcorq ovuia of the Categories as the
ultimate subject of judgement. I have assumed that he means the latter.]

1 The former proof was dialectical. So is that which follows in
this paragraph. If a predicate inheres in a subject but is sub-

BOOK I. 22 84*

As dialectical proofs of our contention these may carry
conviction, but an analytic process will show more briefly
that neither the ascent nor the descent of predication can
be infinite in the demonstrative sciences which are the I0
object of our investigation. Demonstration proves the
inherence of essential attributes in things. Now attributes
may be essential for two reasons : either because they are
elements in the essential nature of their subjects, or because
their subjects are elements in their essential nature. An
example of the latter is odd as an attribute of number
though it is number s attribute, yet number itself is an 15
element in the definition of odd ; of the former, multiplicity
or the indivisible, which are elements in the definition of
number. In neither kind of attribution can the terms be
infinite. 1 They are not infinite where each is related to
the term below it as odd is to number, for this would mean
the inherence in odd of another attribute of odd in whose
nature odd was an essential element : but then number 20
will be an ultimate subject of the whole infinite chain of
attributes, and be an element in the definition of each of
them. Hence, since an infinity of attributes such as con
tain their subject in their definition cannot inhere in a single
thing, the ascending series is equally finite. 2 Note, more-

ordinate to a higher predicate also predicable of that subject [i. e. not
to a wider predicate but to a middle term giving logically prior premisses
and in that sense higher], then the inherence can be known by demon
stration and only by demonstration. But that means that it is known
as the consequent of an antecedent. Therefore, if demonstration gives
genuine knowledge, the series must terminate; i.e. every predicate is
demonstrable and known only as a consequent and therefore hypo-
thetically, unless an antecedent known per se is reached.

1 Analytic proof [i. e. a proof from the appropriate dpxni of the subject
which Aristotle is here treating, namely TO. dva\vTiK.d : cf. the frequent
corresponding use of (pva-iK&s. Note, however, that TO. UVH\VTIKU have
no proper place in Aristotle s classification of the sciences : there is no
special ytvos of reality forming their subject-matter]. Demonstration
proves the inherence in subjects of attributes essential either (i ) because
they are elements in their subject s definition, e.g. multiplicity or the
indivisible [reading in 84 a 16 adtaipfrov with the first hand of D. Number
= n\fj6os ddiaipfTav, cf. Met. io85 b 22] ; or (2) because their subjects
are elements in their definition, as e.g. odd [ntpiTrov in a 14 is really
an abbreviation for nepiTrov K<U apTiov, cf. i, ch. 4, 73 a 39] in relation to
number. Attribution of neither type of attribute can beget an infinite
series.

1 As regards type (2) [the opening of the chapter has disposed of
type (i)] : in any series of such predicates any given term will contain

84 a ANALYTICA POSTERIORA

over, that all such attributes must so inhere in the ultimate
subject e. g. its attributes in number and number in them
as to be commensurate with the subject and not of wider

25 extent. Attributes which are essential elements in the nature
of their subjects are equally finite : otherwise definition
would be impossible. Hence, if all the attributes predicated
are essential and these cannot be infinite, the ascending
series will terminate, and consequently the descending
series too. 1

If this is so, it follows that the intermediates between any
two terms are also always limited in number. 2 An imme-

30 diately obvious consequence of this is that demonstrations
necessarily involve basic truths, and that the contention of
some referred to at the outset that all truths are
demonstrable is mistaken. For if there are basic truths,
(a) not all truths are demonstrable, and (b) an infinite
regress is impossible ; since if either (a) or (b) were not a
fact, it would mean that no interval was immediate and

35 indivisible, but that all intervals were divisible. This is
true because a conclusion is demonstrated by the interposi
tion, not the apposition, of a fresh term. If such inter
position could continue to infinity there might be an infinite
number of terms between any two terms ; but this is im-
84 b possible if both the ascending and descending series of
predication terminate ; and of this fact, which before was
shown dialectically, analytic proof has now been given/

in its definition all the lower terms, and the series will therefore
terminate at the bottom in the ultimate subject. But since every
term down to and including the ultimate subject is contained in
the definition of any given term, if the series ascend infinitely there
must be a term containing an infinity of terms in its definition. But
this is impossible, and therefore the ascent terminates.

1 Note too that either type of essential attribute must be commen
surate with its subject, because the first defines, the second is defined
by, its subject ; and consequently no subject can possess an infinite
number of essential predicates of either type, or definition would be
impossible. Hence if the attributes predicated are all essential, the
series terminates in both directions. [This passage merely displays
the ground underlying the previous argument that the ascent of
attributes of type (2) is finite, and notes in passing its more obvious
and already stated application to attributes of type (l).]

2 It follows that the intermediates between a given subject and a
given attribute must also be limited in number.

3 Corollary : (a) demonstrations necessarily involve basic truths,

BOOK I. 23 84 b

23 It is an evident corollary of these conclusions that if the
same attribute A inheres in two terms C and D predicable
either not at all, or not of all instances, of one another, it 5
does not always belong to them in virtue of a common
middle term. Isosceles and scalene possess the attribute of
having their angles equal to two right angles in virtue of a
common middle ; for they possess it in so far as they are
both a certain kind of figure, and not in so far as they differ
from one another. But this is not always the case ; for,
were it so, if we take B as the common middle in virtue of
which A inheres in C and Z>, clearly B would inhere in C 10
and D through a second common middle, and this in turn
would inhere in C and D through a third, so that between
two terms an infinity of intermediates would fall an im
possibility. Thus it need not always be in virtue of a
common middle term that a single attribute inheres in
several subjects, since there must be immediate intervals.
Yet if the attribute to be proved common to two subjects 15
is to be one of their essential attributes, the middle terms
involved must be within one subject genus and be derived
from the same group of immediate premisses ; for we have
seen that processes of proof cannot pass from one genus to
another. 1

It is also clear^ that when A inheres in B, this can be
demonstrated if there is a middle term. Further, the ao
elements of such a conclusion are the premisses contain-

and therefore (/>} not all truths, as we saw [84 a 32] that some maintain,
are demonstrable [cf. 72 b 6]. If either (a) or (b) were not a fact, since
conclusions are demonstrated by the interposition of a middle and not
by the apposition of an extreme term [cf. note on 78*15], no premiss
would be an immediate indivisible interval. This closes the analytic
argument.

[Thus the nerve of the dialectical and analytic arguments is the same :
they differ only in that the former covers all syllogism. The basis of
Aristotle s contention is that predication is always a synthesis of
determinate elements, a concrete whole which is essentially not
aneipiiv. Unfortunately for Aristotle s point this contention, however
sound, involves the reciprocal interdependence of the elements of such
a synthesis and, ultimately, of all the terms of a series of predication.
It may prove that the series of predication cannot contain an infinity
of terms, but it does not prove that it is terminated by self-evident
dpxai, true within their own four corners. It is questionable how far
Aristotle s logical system can survive this chapter.]

1 i, ch. 7.

84 b ANALYTICA POSTERIORA

ing the middle in question, and they are identical in number
with the middle terms, seeing that the immediate proposi
tions or at least such immediate propositions as are univer
sal are the elements . If, on the other hand, there is no
middle term, demonstration ceases to be possible : we are
on the way to the basic truths. Similarly if A does not
inhere in B, this can be demonstrated if there is a middle

25 term or a term prior to B in which A does not inhere :
otherwise there is no demonstration and a basic truth is
reached. 1 There are, moreover, as many elements of the
demonstrated conclusion as there are middle terms, since it
is propositions containing these middle terms that are the
basic premisses on which the demonstration rests ; and as
there are some indemonstrable basic truths asserting that
this is that or that this inheres in that , so there are

30 others denying that this is that or that this inheres in
that in fact some basic truths will affirm and some will
deny being.

When we are to prove a conclusion, we must take a
primary essential predicate suppose it C of the subject
B, and then suppose A similarly predicable of C. If we
proceed in this manner, no proposition or attribute which
falls beyond A is admitted in the proof: the interval is
constantly condensed until subject and predicate become

35 indivisible, i.e. one. We have our unit when the premiss
becomes immediate, 2 since the immediate premiss alone is
a single premiss in the unqualified sense of single . And
as in other spheres the basic element is simple but not
identical in all in a system of weight it is the mina, in
music the quarter-tone, and so on so in syllogism the unit
85 a is an immediate premiss, and in the knowledge that demon
stration gives it is an intuition. 3 In syllogisms, then, which
prove the inherence of an attribute, nothing falls outside
the major term. In the case of negative syllogisms on the
other hand, (i) in the first figure nothing falls outside the

1 Placing a full stop after apx ] in b 26.

2 Placing a comma after yfvqrm in b 36.

z vovs grasps immediately an indivisible reality e.g. the ri i]v tlvai
of a substance the elements of which are not predicated of one another
Cf. 77 a 4, 88 b 35~7, and notes thereon.

BOOK I. 23 8s 8

major term whose inherence is in question ; e. g. to prove
through a middle C that A does not inhere in B the
premisses required are, all B is C, no C is A, Then if it has 5
to be proved that no C is A, a. middle must be found
between A and C ; and this procedure will never vary.

(2) If we have to show that E is not D by means of the
premisses, all D is C; no ", or not all E, 1 is C; then the
middle will never fall beyond JS, and E is the subject of
which D is to be denied in the conclusion.

(3) In the third figure the middle will never fall beyond 10
the limits of the subject and the attribute denied of it.

24 Since demonstrations may be either commensurately
universal or particular, 2 and either affirmative or negative ;
the question arises, which form is the better? And the same 15
question may be put in regard to so-called direct demon
stration and reductio od impossibile. Let us first examine
the commensurately universal and the particular forms, and
when we have cleared up this problem proceed to discuss
direct demonstration and reductio od impossibile.

The following considerations might lead some minds to 20
prefer particular demonstration.

(i) The superior demonstration is the demonstration
which gives us greater knowledge (for this is the ideal of
demonstration), and we have greater knowledge of a particu
lar individual when we know it in itself than when we know
it through something else; e.g. we know Coriscus the
musician better when we know that Coriscus is musical than 25
when we know only that man is musical, and a like argu
ment holds in all other cases. But commensurately universal
demonstration, instead of proving that the subject itself
actually is x, proves only that something else is x e.g. in
attempting to prove that isosceles is x, it proves not that
isosceles but only that triangle is x whereas particular
demonstration proves that the subject itself is x. The
demonstration, then, that a subject, as such, possesses an
attribute is superior. If this is so, and if the particular

1 Second figure, Camestres or Baroco.

2 The distinction is that of whole and part, genus and species ; not
that of universal and singular.

85 a ANALYTICA POSTERIORA

rather than the commensurately universal form so demon-

3 o strates, particular demonstration is superior.

(2) The universal has not a separate being over against
groups of singulars. Demonstration nevertheless creates
the opinion that its function is conditioned by something
like this some separate entity belonging to the real world ;
that, for instance, of triangle or of figure or number, over

35 against particular triangles, figures, and numbers. But
demonstration which touches the real and will not mislead
is superior to that which moves among unrealities and is
delusory. Now commensurately universal demonstration
is of the latter kind : if we engage in it we find ourselves
reasoning after a fashion well illustrated by the argument
that the proportionate is what answers to the definition of
some entity which is neither line, number, solid, nor plane,
8s b but a proportionate apart from all these. Since, then, such
a proof is characteristically commensurate and universal,
and less touches reality than does particular demonstration,
and creates a false opinion, it will follow that commensurate
and universal is inferior to particular demonstration.

We may retort thus, (i) The first argument applies no
more to commensurate and universal than to particular
5 demonstration. If equality to two right angles is attributable
to its subject not qua isosceles but qua triangle, he who
knows that isosceles possesses that attribute knows the
subject as qua itself possessing the attribute, to a less degree
than he who knows that triangle has that attribute. To sum
up the whole matter : if a subject is proved to possess qua
triangle an attribute which it does not in fact possess qua
triangle, that is not demonstration : but if it does possess it
qua triangle, the rule applies that the greater knowledge is
his who knows the subject as possessing its attribute qua
that in virtue of which it actually does possess it. Since,

jo then, triangle is the wider term, and there is one identical
definition of triangle i.e. the term is not equivocal and
since equality to two right angles belongs to all triangles, it
is isosceles qua triangle and not triangle qua isosceles which
has its angles so related. It follows that he who knows a
connexion universally has greater knowledge of it as it in

BOOK I. 24 85*

fact is than he who knows the particular ; and the inference
is that commensurate and universal is superior to particular
demonstration.

(2) If there is a single identical definition i.e. if the 15
commensurate universal is unequivocal then the universal
will possess being not less but more than some of the
particulars, inasmuch as it is universals which comprise
the imperishable, particulars that tend to perish.

(3) Because the universal has a single meaning, we are
not therefore compelled to suppose that in these examples
it has being as a substance apart from its particulars any
more than we need make a similar supposition in the other
cases of unequivocal universal predication, viz. where the
predicate signifies not substance but quality, essential related- 20
ness, or action. If such a supposition is entertained, the
blame rests not with the demonstration but with the
hearer.

(4) Demonstration is syllogism that proves the cause,
i. e. the reasoned fact, and it is rather the commensurate
universal than the particular which is causative (as may be
shown thus : that which possesses an attribute through its
own essential nature is itself the cause of the inherence, 25
and the commensurate universal is primary ; l hence the
commensurate universal is the cause). Consequently com-
mensurately universal demonstration is superior as more
especially proving the cause, that is the reasoned fact.

(5) Our search for the reason ceases, and we think that we
know, when the coming to be or existence of the fact before
us is not due to the coming to be or existence of some other
fact, for the last step of a search thus conducted is eo ipso
the end and limit of the problem. Thus : Why did he 30
come ? To get the money wherewith to pay a debt
that he might thereby do what was right. When in this
regress we can no longer find an efficient or final cause, we
regard the last step of it as the end of the coming or being
or coming to be and we regard ourselves as then only
having full knowledge of the reason why he came.

If, then, all causes and reasons are alike in this respect, 35
1 And therefore also essential ; cf. i, ch. 4, 73 b z6 ff.

8s b ANALYTICA POSTERIORA

and if this is the means to full knowledge in the case of
final causes such as we have exemplified, it follows that in
the case of the other causes also full knowledge is attained
when an attribute no longer inheres because of something
else. Thus, when we learn that exterior angles are equal
to four right angles because they are the exterior angles of
an isosceles, there still remains the question Why has
86 a isosceles this attribute ? and its answer Because it is a
triangle, and a triangle lias it because a triangle is a recti
linear figure. If rectilinear figure possesses the property for
no further reason, 1 at this point we have full knowledge but
at this point our knowledge has become commensurately
universal, and so we conclude that commensurately universal
demonstration is superior.

(6) The more demonstration becomes particular the more
it sinks into an indeterminate manifold, while universal

5 demonstration tends to the simple and determinate. But
objects so far as they are an indeterminate manifold are
unintelligible, so far as they are determinate, intelligible :
they are therefore intelligible rather in so far as they are
universal than in so far as they are particular. From this it
follows that univei sals are more demonstrable : but since
relative and correlative increase concomitantly, of the more
demonstrable there will be fuller demonstration. Hence
the commensurate and universal form, being more truly
I0 demonstration, is the superior.

(7) Demonstration which teaches two things is preferable
to demonstration which teaches only one. He who possesses
commensurately universal demonstration knows the parti
cular as well, but he who possesses particular demonstration
does not know the universal. So that this is an additional
reason for preferring commensurately universal demonstra
tion. And there is yet this further argument :

(8) Proof becomes more and more proof of the commen
surate universal as its middle term approaches nearer to the

15 basic truth, and nothing is so near as the immediate premiss
which is itself the basic truth. If, then, proof from the
basic truth is more accurate than proof not so derived,
1 i. c. for no reason other than its own nature.

BOOK I. 24 86 a

demonstration which depends more closely on it is more
accurate than demonstration which is less closely dependent.
But commensurately universal demonstration is characterized
by this closer dependence, and is therefore superior. Thus,
if A had to be proved to inhere in D, and the middles were
B and C,B -being the higher term would render the demon
stration which it mediated the more universal. 20

Some of these arguments, however, are dialectical. The
clearest indication of the precedence of commensurately
universal demonstration is as follows : if of two propositions,
a prior and a posterior, we have a grasp of the prior, we
havea kind of knowledge a potential grasp of the posterior
as well. For example, if one knows that the angles of all -^
triangles are equal to two right angles, one knows in a sense
potentially that the isosceles angles also are equal to two
right angles, even if one does not know that the isosceles is
a triangle ; but to grasp this posterior proposition is by no
means to know the commensurate universal either potentially
or actually. Moreover, commensurately universal demon
stration is through and through intelligible ; particular
demonstration issues in sense-perception. 3 o

25 The preceding arguments constitute our defence of the
superiority of commensurately universal to particular de
monstration. That affirmative demonstration excels nega
tive may be shown as follows.

(i) We may assume the superiority cctcris paribus of the
demonstration which derives from fewer postulates or hypo
theses in short from fewer premisses ; for, given that all 35
these are equally well known, where they are fewer knowledge
will be more speedily acquired, and that is a desideratum.
The argument implied in our contention that demonstration
from fewer assumptions is superior may be set out in uni
versal form as follows. 1 Assuming that in both cases alike
the middle terms are known, and that middles which are
prior are better known than such as are posterior, we may
suppose two demonstrations of the inherence of A in E, the
one proving it through the middles B, C and D, the other 86 b

1 Reading xa66\ov o>5e with Waitz ; D Kad6\ov 65e.
F 2

ANALYTICA POSTERIORA

through F and G. Then l A-D is known to the same
degree as A-E (in the second proof), but A-D is better
known than and prior to A-E (in the first proof) ; since
A-E is proved through A-D, and the ground is more
certain than the conclusion. 2

5 Hence demonstration by fewer premisses is cctcris
paribus superior. Now both affirmative and negative
demonstration operate through three terms and two pre
misses, but whereas the former assumes only that something
is, the latter assumes both that something is and that some
thing else is not, and thus operating through more kinds of
premiss 3 is inferior.

i (2) It has been proved 4 that no conclusion follows if both
premisses are negative, but that one must be negative, the
other affirmative. So we are compelled to lay down the
following additional rule : as the demonstration expands,
the affirmative premisses must increase in number, but there

l s cannot be more than one negative premiss in each complete
proof. 5 Thus, suppose no B is A, and all C is B. Then,
if both the premisses are to be again expanded, a middle
must be interposed. Let us interpose D between A and B,
and E between B and C. Then clearly E is affirmatively

20 related to B and C, while D is affirmatively related to B but
negatively to A ; for all B is D, but there must be no D
which is A. Thus there proves to be a single negative
premiss, A-D. In the further prosyllogisms too it is the
same, because in the terms of an affirmative syllogism the
middle is always related affirmatively to both extremes ; in

25 a negative syllogism it must be negatively related only to
one of them, and so, this negation comes to be a single
negative premiss, the other premisses being affirmative. If,

1 Reading 6/zouo? 817 with Boethius and vet. Interp. So Waitz.

2 The two proofs are (l) AB (2) AF

BC FG

. . A C . . AG

C-D G-E

.-. AD :. AE

DE

:. AE

3 Specie non numero plura , Zabarella. 4 An. Pr. i, ch. 7.

5 i.e. in one syllogism and two prosyllogisms proving its premisses.

BOOK I. 25 86 b

then, that through which u truth is proved is a better known
and more certain truth, and if the negative proposition is
proved through the affirmative and not vice versa, affirma
tive demonstration, being prior and better known and more
certain, will be superior.

(3) The basic truth of demonstrative syllogism is the 30
universal immediate premiss, and the universal premiss
asserts in affirmative demonstration and in negative denies :
and the affirmative proposition is prior to and better known
than the negative (since affirmation explains denial and is
prior to denial, just as being is prior to not-being). It follows 35
that the basic premiss of affirmative demonstration is
superior to that of negative demonstration, and the demon
stration which uses superior basic premisses is superior.

(4) Affirmative demonstration is more of the nature of a
basic form of proof, because it is a sine qua non of negative
demonstration.

26 Since affirmative demonstration is superior to negative, it 87
is clearly superior also to reductio ad imp os sib He. We must
first make certain what is the difference between negative
demonstration and reductio ad impossibile. Let us suppose
that no B is A, and that all C is B : the conclusion neces
sarily follows that no CisA. If these premisses are assumed, 5
therefore, the negative demonstration that no C\s A is direct.
Reductio ad impossibile, on the other hand, proceeds as follows
Supposing we are to prove that A does not inhere in /?, we
have to assume that it does inhere, and further that B
inheres in C, with the resulting inference that A inheres in
C. This we have to suppose a known and admitted im
possibility ; and we then infer that A cannot inhere in B. TO
Thus if the inherence of B in C is not questioned, A s in
herence in B is impossible.

The order of the terms is the same in both proofs : they
differ according to which of the negative propositions is the
better known, the one denying A of B or the one denying
A of C. When the falsity of the conclusion a is the better

1 i. e. the impossibility of A-C, the conclusion of the hypothetical
syllogism.

87 a ANALYTICA POSTERIORA

15 known, we use rediictio ad impossibile\ when the major
premiss of the syllogism is the more obvious, we use direct
demonstration. All the same the proposition denying A of
B is, in the order of being, prior to that denying A of C\ for
premisses are prior to the conclusion which follows from
them, and no C is A is the conclusion, no B is A one of

20 its premisses. For the destructive result of rednctio ad
impossibile is not a proper conclusion, nor are its antecedents
proper premisses. On the contrary : the constituents of
syllogism are premisses related to one another as whole to
part or part to whole, 1 whereas the premisses A-C and A-B

25 are not thus related to one another. Now the superior
demonstration is that which proceeds from better known
and prior premisses, and while both these forms depend for
credence on the not- being of something, yet the source of
the one is prior to that of the other. Therefore negative
demonstration will have an unqualified superiority to rednctio
ad impossibile, and affirmative demonstration, being superior
to negative, will consequently be superior also to rednctio ad

30 impossibile.

The science which is knowledge at once of the fact and 27
of the reasoned fact, not of the fact by itself without the
reasoned fact, is the more exact and the prior science.

A science such as arithmetic, which is not a science of
properties qua inhering in a substratum, is more exact than
and prior to a science like harmonics, which is a science of
properties inhering in a substratum ; and similarly a science
like arithmetic, which is constituted of fewer basic elements,
is more exact than and prior to geometry, which requires
35 additional elements. What I mean by additional elements
is this : a unit is substance without position, while a point is
substance with position ; the latter contains an additional
element.

1 Deleting commas after ov and ta-nv in a 22. In An. Pr. 25 b 32~5
Aristotle defines the first figure as that in which the middle term is
contained in the major as in a whole and the minor is contained in
the middle as in a whole. Hence major premiss is related to minor
as whole to part. The first figure is perfect because it displays the
natural organic movement of thought from minor through middle to
major. Rednctio ad impossibile perverts this natural movement and its
premisses do not stand in this organic relation.

BOOK I. 28 8y

28 A single science is one whose domain is a single genus,
viz. all the subjects constituted out of the primary entities
of the genus i. e. the parts of this total subject and their
essential properties.

One science differs from another when their basic truths
have neither a common source nor are derived those of the
one science l from those of the other. This is verified when 87
we reach the indemonstrable premisses of a science, for they
must be within one genus with its conclusions : and this
again is verified if the conclusions proved by means of them
fall within one genus i. e. are homogeneous.

29 One can have several demonstrations of the same 5
connexion not only by taking from the same series of
predication middles which are other than the immediately
cohering term 2 e.g. by taking C, D, and F severally
to prove A-B but also by taking a middle from another
series. Thus let A be change, D alteration of a property, B
feeling pleasure, and G relaxation. We can then without
falsehood predicate D of B and A ofD, for he who is pleased 10
suffers alteration of a property, and that which alters a
property changes. Again, we can predicate A of G without
falsehood, and G of B ; for to feel pleasure is to relax, and
to relax is to change. So the conclusion can be drawn
through middles which are different, i. e. not in the same
series yet not so that neither of these middles is predicable
of the other, for they must both be attributable to some one 15
subject.

A further point worth investigating is how many ways of
proving the same conclusion can be obtained by varying the
figure.

30 There is no knowledge by demonstration of chance
conjunctions ; for chance conjunctions exist neither by
necessity nor as general connexions but comprise what 20
comes to be as something distinct from these. Now
demonstration is concerned only with one or other of these
two ; for all reasoning proceeds from necessary or general
premisses, the conclusion being necessary if the premisses

1 Reading TV/J<H. * Cf. note on 95 b 3 and 4.

87 b ANALYTICA POSTERIORA

35 are necessary and general if the premisses are general.
Consequently, if chance conjunctions are neither general nor
necessary, they are not demonstrable.

Scientific knowledge is not possible through the act of 3 1
perception. Even if perception as a faculty is of the such
and not merely of a this somewhat 7 yet one must at any
rate actually perceive a ( this somewhat , and at a definite

30 present place and time : but that which is commensurately
universal and true in all cases one cannot perceive, since it
is not this and it is not now ; if it were, it would not be
commensurately universal the term we apply to what is
always and everywhere. Seeing, therefore, that demonstra
tions are commensurately universal and universals imper
ceptible, we clearly cannot obtain scientific knowledge by

35 the act of perception : nay, it is obvious that even if it were
possible to perceive that a triangle has its angles equal to
two right angles, we should still be looking for a demonstra
tion we should not (as some 2 say) possess knowledge of it ;
for perception must be of a particular, whereas scientific
knowledge involves the recognition of the commensurate
universal. So if we were on the moon, and saw the earth

40 shutting out the sun s light, we should not know the cause
88 a of the eclipse : we should perceive the present fact of the
eclipse, but not the reasoned fact at all, since the act of
perception is not of the commensurate universal. I do not,
of course, deny that by watching the frequent recurrence
of this event we might, after tracking the commensurate
universal, possess a demonstration, for the commensurate
universal is elicited from the several groups of singulars.
5 The commensurate universal is precious because it makes
clear the cause ; so that in the case of facts like these which
have a cause other than themselves universal knowledge 3 is
more precious than sense-perceptions and than intuition.
(As regards primary truths there is of course a different
account to be given. 4 ) Hence it is clear that knowledge of

1 Cf. note on 73 b 7.

2 Protagoras is perhaps referred to.

3 i. e. demonstration through the commensurate universal.

4 Cf. e.g. ioo b 12.

BOOK I. 31 88 E

things demonstrable 1 cannot be acquired by perception,
unless the term perception is applied to the possession of 10
scientific knowledge through demonstration. Nevertheless
certain points do arise with regard to connexions to be
proved which are referred for their explanation to a failure
in sense-perception : there are cases when an act of vision
would terminate our inquiry, not because in seeing we
should be knowing, but because we should have elicited the
universal from seeing ; if, for example, we saw the pores in
the glass and the light passing through, the reason of the 15
kindling would be clear to us 2 because we should at the
same time see it in each instance and intuit that it must be
so in all instances.

32 All syllogisms cannot have the same basic truths. This
may be shown first of all by the following dialectical
considerations, (i) Some syllogisms are true and some
false : for though a true inference is possible from false 20
premisses, yet this occurs once only I mean if A, for
instance, is truly predicable of C, but B, the middle, is false,
both A-B and B-C being false ; nevertheless, it middles are
taken to prove these premisses, they will be false because
every conclusion which is a falsehood has false premisses, 25
while true conclusions have true premisses, and false and true
differ in kind. Then again, (2) falsehoods are not all derived
from a single identical set of principles : there are falsehoods
which are the contraries of one another and cannot coexist,
e. g. justice is injustice , and justice is cowardice ; man is
horse , and man is ox ; the equal is greater , and the equal
is less. From our established principles we may argue the 30
case as follows, confining ourselves therefore to true conclu
sions. Not even all these are inferred from the same basic
truths ; many of them in fact have basic truths which differ
generically and are not transferable ; units, for instance,
which are without position, cannot take the place of points,
which have position. The transferred terms could only fit

1 Reading iinodfiKruv with Waitz ; cf. 9o b 10 and note.
* A theory of the concentration of rays through a burning-glass
which was not Aristotle s.

88 a ANALYTICA POSTERIORA

35 in as middle terms or as major or minor terms, or else have

some of the other terms between them, others outside them. 1

Nor can any of the common axioms such, I mean, as

the law of excluded middle serve as premisses for the

88 b proof of all conclusions. For the kinds of being are different,

and some attributes attach to quanta and some to qnalia

only; and proof is achieved by means of 2 the common

axioms taken in conjunction with these several kinds and

their attributes.

Again," it is not true that the basic truths are much fewer
5 than the conclusions, for the basic truths are the premisses,
and the premisses are formed by the apposition of a fresh
extreme term or the interposition of a fresh middle.
Moreover, the number of conclusions is indefinite, though the
number of middle terms is finite ; and lastly some of the
basic truths are necessary, others variable.

1 i. e. the transference of a/j^ u from one science to another must
mean that the terms of which they consist will appear in the second
science either always as middles or always as majors or always as
minors, or else now as middles between terms native to the second
science, now as extreme terms linked by middles native to the second
science : therefore the second science would contain a demonstration
the terms of which were not within one genus, and therefore not
predicable xad nvro of one another as Aristotle has shown passim,
cf. e.g. 75 b lo-i2. The usually assumed reference to the figures of
syllogism seems irrevelant.

2 N.B. dia, not t K : i.e. if demonstration is to be possible, you
require premisses containing the genus and its properties, as well as
the Koii a o^tto/iOTo as regulative canons.

3 The argument from Vi al iipxni 88 b 3 to eY&x ( V fI m in b 8 ap
pears to be as follows : (Actually, the conclusions are many ; but
if the iipx^i of all demonstration were the same, there would only be a
few conclusions.) But it is not true that the px are much fewer
than the conclusions, for the apxni are the premisses, and the premisses
are formed either (i) by the apposition of fresh extreme terms, or (2) by
the interpolation of fresh middies (and therefore in (i) you get a fresh
upx>) for every fresh conclusion, the other premiss being a previous
conclusion (cf. note on 7& a i4); while in (2) the premisses become
each in turn a conclusion). Moreover the number of conclusions is
indefinite (. . once again that of the apxni cannot be small) though
of course (if you are proceeding by iruKi><a<ns of a Swar^i requiring
mediation) the middle terms (required before you reach immediate
premisses) are not indefinite in number. Finally there are variable
as well as necessary dpxni (and therefore once more the number cannot
be small).

The last sentence is a final argument that the iip\m are not few in
number, and is admissible because the whole treatment is dialectical,
cf. 8S a i.

BOOK I. 32 88*

Looking at it in this way we see that, since the number of
conclusions is indefinite, the basic truths cannot be identical
or 1 limited in number. If, on the other hand, identity is used 10
in another sense, and it is said, e. g , these and no other are
the fundamental truths of geometry, these the fundamentals
of calculation, these again of medicine ; would the statement
mean anything except that the sciences have basic truths?
To call them identical because they are self-identical is
absurd, since everything can be identified with everything
in that sense of identity. Nor again can the contention 15
that all conclusions have the same basic truths mean that
from the mass of all possible premisses any conclusion may
be drawn. That would be exceedingly naive, for it is not
the case in the clearly evident mathematical sciences, nor is
it possible in analysis, since it is the immediate premisses
which are the basic truths, and a fresh conclusion is only formed
by the addition of a new immediate premiss 2 : but if it be 2 o
admitted that it is these primary immediate premisses which
are basic truths, each subject-genus will provide one basic
truth/ 1 If, however, it is not argued that from the mass of all
possible premisses any conclusion may be proved, nor yet
admitted that basic truths differ so as to be generically
different for each science, it remains to consider the
possibility that, while the basic truths of all knowledge are
within one genus, special premisses are required to prove
special conclusions. But that this cannot be the case has 25
been shown by our proof that the basic truths of things
generically different themselves differ generically. For
fundamental truths are of two kinds, those which are
premisses of demonstration 4 and the subject-genus ; and
though the former are common, the latter number, for
instance, and magnitude are peculiar.

1 Reading /} ircrvfpncr^fviiy with D.

2 Such a suggestion would be stupid (i) because you can see at
once so clear are they that the demonstrations which build up the
mathematical sciences by synthesis from their basic elements do not all
start from the same n/JX fl ; and (2) because in analysis of a con
clusion into its ultimate premisses (= from the complementary point
of view wwcrawtc of a Stdcmj^n) different <ip,v ni/ are reached in different
sciences.

8 sc. at least one its own definition . 4 Cf. note on 75 b 2.

88 b ANALYTICA POSTERIORA

30 Scientific knowledge and its object differ from opinion 33
and the object of opinion in that scientific knowledge is
commensurately universal and proceeds by necessary con
nexions, and that which is necessary cannot be otherwise.
So though there are things which are true and real and yet
can be otherwise, scientific knowledge clearly does not con
cern them : if it did, things which can be otherwise would

35 be incapable of being otherwise. Nor are they any concern
of rational intuition by rational intuition I mean an
originative source of scientific knowledge nor of in
demonstrable knowledge, 1 which is the grasping of the
8g a immediate premiss. Since then rational intuition, science,
and opinion, and what is revealed by these terms, are the
only things that can be true , it follows that it is opinion
that is concerned with that which may be true or false, and
can be otherwise : opinion in fact is the grasp of a premiss
which is immediate but not necessary. This view also fits
5 the observed facts, for opinion is unstable, and so is the kind
of being we have described as its object. Besides, when
a man thinks a truth incapable of being otherwise he always
thinks that he knows it, never that he opines it. He thinks
that he opines when he thinks that a connexion, though
actually so, may quite easily be otherwise ; for he believes

10 that such is the proper object of opinion, while the necessary
is the object of knowledge.

In what sense, then, can the same thing be the object
of both opinion and knowledge ? And if any one chooses
to maintain that all that he knows he can also opine, why
should not 2 opinion be knowledge ? For he that knows and
he that opines will follow the same train of thought through
the same middle terms until the immediate premisses are

15 reached; because it is possible to opine not only the fact
but also the reasoned fact, and the reason is the middle
term ; so that, since the former knows, he that opines also
has knowledge.

The truth perhaps is that if a man grasp truths that

1 vovs (cf. notes on 85*1 and 77 a 4) grasps the individual nature,
TO TI r)v dual or the definition, as a unity ; e raoT/;^; dvanodeiKTos gives
this as a premiss.

2 Reading form for tanv with A, B, C, and Waitz.

BOOK I. 33 8g a

cannot be other than they are, in the way in which he
grasps l the definitions through which demonstrations take
place, he will have not opinion but knowledge : if on the
other hand he apprehends these attributes as inhering in
their subjects, but not in virtue of the subjects substance
and essential nature, he possesses opinion and not genuine 20
knowledge ; and his opinion, if obtained through immediate
premisses, will be both of the fact and of the reasoned fact;
if not so obtained, of the fact alone. The object of opinion
and knowledge is not quite identical ; it is only in a sense
identical, just as the object of true and false opinion is in a
sense identical. The sense in which some maintain that 25
true and false opinion can have the same object leads them to
embrace many strange doctrines, particularly the doctrine
that what a man opines falsely he does not opine at all.
There are really many senses of identical , and in one
sense the object of true and false opinion can be the same,
in another it cannot. Thus, to have a true opinion that the
diagonal is commensurate with the side would be absurd : 30
but because the diagonal with which they are both con
cerned is the same, the two opinions have objects so far
the same : on the other hand, as regards their essential
definable nature these objects differ. The identity of the
objects of knowledge and opinion is similar. Knowledge is
the apprehension of, e. g., the attribute animal as incapable
of being otherwise, opinion the apprehension of animal as
capable of being otherwise e. g. the apprehension that 35
animal is an element in the essential nature of man is know
ledge ; the apprehension of animal as predicable of man but
not as an element in man s essential nature is opinion : man
is the subject in both judgments, but the mode of inherence
differs.

This also shows that one cannot opine and know the
same thing simultaneously ; for then one would apprehend
the same thing as both capable and incapable of being
otherwise an impossibility. Knowledge and opinion of8Q b
the same thing can coexist in two different people in the
sense we have explained, but not simultaneously in the
1 Reading e^a with MSS.

8g b ANALYTICA POSTERIORA

same person. That would involve a man s simultaneously
apprehending, e. g.. (i) that man is essentially animal i. e.
cannot be other than animal and (2) that man is not
5 essentially animal, that is, we may assume, 1 may be other
than animal.

Further consideration of modes of thinking and their
distribution under the heads of discursive thought, intuition,
science, art, practical wisdom, and metaphysical thinking,
belongs rather partly to natural science, partly to moral
philosophy.

10 Quick wit is a faculty of hitting upon the middle term 34
instantaneously. It would be exemplified by a man who
saw that the moon has her bright side always turned
towards the sun, and quickly grasped the cause of this,
namely that she borrows her light from him ; or observed
somebody in conversation with a man of wealth and divined
that he was borrowing money, or that the friendship of these
people sprang from a common enmity. In all these in
stances he has seen the major and minor terms and then

j. grasped the causes, the middle terms.

Let A represent bright side turned sunward , B lighted
from the sun , C the moon. Then B, lighted from the
sun , is predicable of C, the moon, and A, having her bright
side towards the source of her light , is predicable of B.

20 So A is predicable of C through B.

1 Reading eorw with B, C, and Waitz.

BOOK II

1 THE kinds of question we ask are as many as the kinds
of things which we know. They are in fact four: (i)
whether the connexion of an attribute with a thing is a fact,
(2) what is the reason of the connexion, (3) whether a thing
exists, (4) what is the nature of the thing. Thus, when our 25
question concerns a complex of thing and attribute 1 and we
ask whether the thing is thus or otherwise qualified whether,
e.g., the sun suffers eclipse or not then we are asking as to
the fact of a connexion. That our inquiry ceases with the
discovery that the sun does suffer eclipse is an indication of
this ; and if we know from the start that the sun suffers
eclipse, we do not inquire whether it does so or not. On the
other hand, when we know the fact we ask the reason ; as,
for example, when we know that the- sun is being eclipsed
and that an earthquake is in progress, it is the reason of 3
eclipse or earthquake into which we inquire.

Where a complex is concerned, then, those are the two
questions we ask ; but for some objects of inquiry we have
a different kind of question to ask, such as whether there is
or is not a centaur or a God. (By is or is not* I mean is
or is not, without further qualification ; as opposed to is
or is not (e. g.) white .) On the other hand, when we have
ascertained the thing s existence, we inquire as to its nature,
asking, for instance, what, then, is God ? or what is
man? . 35

2 These, then, are the four kinds of question we ask, and it
is in the answers to these questions that our knowledge
consists. 2

1 So Zabarella and Pacius explain eij apidnov Qivrfs. Waitz takes
it as meaning enumerating the alternative possibilities .

2 In ch. I Aristotle has distinguished four forms of inquiry, and the
enumeration is taken to be exhaustive. These were: (i) TO on., Is
S P? (-2) TO Start, Why is S P? (3) el eon, Does 6" exist?
(4) TI f cm, What is 6"? . (i) answered affirmatively provokes (2),
and (3) answered affirmatively provokes (4). In ch. 2 we learn that
all four questions are questions as to the cause ; that Is S /*? means
Has P-S a cause? , and that Does S exist? means Has S a

8g b ANALYTICA POSTERIORA

Now when we ask whether a connexion is a fact, or
whether a thing without qualification is, we are really asking
whether the connexion or the thing has a middle ; l and
when we have ascertained either that the connexion is a fact
or that the thing is i.e. ascertained either the partial or the
go a unqualified being of the thing and are proceeding to ask
the reason of the connexion or the nature of the thing, then
we are asking what the middle is.

(By distinguishing the fact of the connexion and the

cause ? ; and again that Why is S P ? means What is the cause of
P-S ? , and What is 5 ? means What causes S ?

This is obscurely worked out because Aristotle is hampered by his
theory of predication. On the one hand (A) all four questions ask
the cause of the being of S, which is a substance; (i) and (2) ask
respectively Is there a cause and What is the cause of S having
being as the subject of an attribute i. e. they seek a cause of part of6"s
being, .5"s being in so far as S is P; while (3) and (4) ask respectively Is
there a cause and What is the cause of S having being as a substance
i. e. they inquire as to a cause of the complete unqualified (on-Awy)
being of S. On the other hand, (B) (i) and (2) in asking the cause of
5" being P, are really asking What is the cause of P ? , for /"s being
consists in its inherence in 6", This seems to distinguish (i) and (2)
as concerning the cause of attributes from (3) and (4) as concerning
the cause of substances. But you can also ask (3) and (4) of an
attribute S need not be a substance e.g. vv in 9O a 5, given as an
instance of a arr\ms of, is an attribute, and in a 15 ff. (where r( etrriv
tK\(i\l/is ; is shown to be equivalent to 8ia ri fa-nv tK\(L\l/is ; and to have
the same pta-ov) 8th ri cVXeiVfi rj af\f]t>t] ; is given as the equivalent of
8ta TI f<TTiv ex\(i\lfis ;

In 1. 31 to the end of the chapter it seems doubtful whether, as I have
taken the passage, Aristotle is saying that to know what a thing is is
to know what causes it, equally as regards S qua S and S qua P (i. e.
equally as regards the complete and the partial being of a substance) ;
or equally as regards the being of S and the being of P.

The source of this obscurity is Aristotle s struggle necessitated by
his view of predication to distinguish grammatical subject and pre
dicate as substance and attribute, which consequently tend to become
two kinds of thing. The same struggle is seen in the fluctuation of
the meaning of i>noKeip.fvoi>, which means now the complete substance,
(a) as a totality of the elements constituting its definition and of its
essential properties, (b) as a totality of its defining attributes only ;
now (c) a mere substratum which alone remains when you remove all
its attributes from a substance.

1 Middle : p.fo-ov in this chapter is extended to mean proximate
cause ; it is wider than the middle term of a syllogism. It is, or
rather is reflected by, the middle term of a syllogism in the case of the
definition of an attribute, because the definition of an attribute is a
Xdyoy of it as inhering in the subject, and the middle term which
proves, also causes, or reflects the cause of, this inherence ; but the
cause of a substance possessing unqualified being is not something
other than itself, but its Xciyoy, its definition by genus and differentia;
and this cannot be the middle term of a syllogism, because such
definition is not demonstrable (cf. ii, ch. 4).

BOOK II. 2 go

existence of the thing as respectively the partial and the
unqualified being of the thing, I mean that if we ask does
the moon suffer eclipse ? , or does the moon wax ? , the
question concerns a part of the thing s being ; for what we
are asking in such questions is whether a thing is this or that,
i.e. has or has not this or that attribute : whereas, if we ask
whether the moon or night exists, the question concerns the
unqualified being of a thing.)

We conclude that in all our inquiries we are asking either 5
whether there is a middle or what the middle is : for the
middle here is precisely the cause, and it is the cause that
we seek in all our inquiries. Thus, Does the moon suffer
eclipse? means Is there or is there not a cause producing
eclipse of the moon ? , and when we have learnt that there
is, our next question is, What, then, is this cause ? ; for the
cause through which a thing is not is this or that, i. e. has
this or that attribute, but without qualification is and the 10
cause through which 1 it is not is without qualification, but
is this or that as having some essential attribute or some
accident are both alike the middle . By that which
is without qualification I mean the subject, e. g. moon or
earth or sun or triangle ; by that which a subject is (in the
partial sense) I mean a property, e. g. eclipse, equality or
inequality, interposition or non-interposition. For in all
these examples it is clear that the nature of the thing and
the reason of the fact are identical: the question What is 15
eclipse ? and its answer The privation of the moon s light
by the interposition of the earth are identical with the
question What is the reason of eclipse ? or Why does the
moon suffer eclipse? and the reply Because of the failure
of light through the earth s shutting it out . Again, for
What is a concord ? A commensurate numerical ratio of
a high and 2 a low note , we may substitute What reason
makes a high and a low note concordant ? Their relation 20
according to a commensurate numerical ratio. Are the
high and the low note concordant ? is equivalent to Is

1 Reading rov elvai for TO e?i/at with Bonitz in go a g.

2 Reading KU\ for r) with D in 90* 19.

go a ANALYTICA POSTERIORA

their ratio commensurate? ; and when we find that it is
commensurate, we ask What, then, is their ratio ? .

Cases in which the middle is sensible show that the

25 object of our inquiry is always the middle : we inquire,
because we have not perceived it, whether there is or is not
a middle causing e.g. an eclipse. On the other hand, if
we were on the moon we should not be inquiring either as
to the fact or the reason, but both fact and reason would be
obvious simultaneously. For the act of perception would
have enabled us to know the universal too ; since, the
present fact of an eclipse being evident, perception would
then at the same time give us the present fact of the earth s

;;o screening the sun s light, and from this would arise the
universal.

Thus, as we maintain, to know a thing s nature is to know
the reason why it is ; and this is equally true of things in so
far as they are said without qualification to be as opposed
to being possessed of some attribute, and in so far as they
are said to be possessed of some attribute such as equal to
two right angles, or greater or less.

35 It is clear, then, that all questions are a search for .a 3
middle . Let us now state how essential nature is revealed,
and in what way it can be reduced to demonstration ; l what
definition is, and what things are definable. And let us
first discuss certain difficulties which these questions raise,
9O b beginning what we have to say with a point most intimately
connected with our immediately preceding remarks, namely
the doubt that might be felt as to whether or not it is
possible to know the same thing in the same relation, both
by definition and by demonstration. It might, I mean, be
urged that definition is held to concern essential nature and
is in every case universal and affirmative ; whereas, on the
; other, hand, some conclusions are negative and some arc not
universal ; e. g. all in the second figure are negative, none in
the third are universal. And again, not even all affirmative
conclusions in the first figure are definable, e. g. every tri
angle has its angles equal to two right angles . An argument

1 Cf. 94 a ii-i4.

BOOK II. 3 90

proving this difference between demonstration and definition
is that to have scientific knowledge of the demonstrable l is
identical with possessing a demonstration of it: hence if 10
demonstration of such conclusions as these is possible, there
clearly cannot also be definition of them. If there could,
one mi^ht know such a conclusion also in virtue of its
definition without possessing the demonstration of it ; for
there is nothing to stop our having the one without the
other.

Induction too will sufficiently convince us of this difference;
for never yet by defining anything essential attribute or ,-
accident did we get knowledge of it. Again, if to define
is to acquire knowledge of a substance, at any rate such
attributes are not substances.

It is evident, then, that not everything demonstrable can
be defined. What then? Can everything definable be
demonstrated, or not ? There is one of our previous
arguments which covers this too. Of a single thing qua 2 o
single there is a single scientific knowledge. Hence, since
to know the demonstrable scientifically is to possess the
demonstration of it, an impossible consequence will follow :
possession of its definition without its demonstration will
give knowledge of the demonstrable.

Moreover, the basic premisses of demonstrations are
definitions, and it has already been shown 2 that these will be
found indemonstrable ; either the basic premisses will be 25
demonstrable and will depend on prior premisses, and the
regress will be endless ; or the primary truths will be
indemonstrable definitions.

But if the definable and the demonstrable are not wholly
the same, may they yet be partially the same ? Or is that
impossible, because there can be no demonstration of the
definable? There can be none, because definition is of the 30
essential nature or being of something, and all demon-

o o -

strations evidently posit and assume the essential nature
mathematical demonstrations, for example, the nature of

1 Reading aTruSeiKTw with Waitz, who is confirmed by aTrodeiKTov (A,
B, and C) in a 21. A reads dirafciKTiKoi , 13, D, M, n, u an-oSfuriKwy.

2 Cf. 72 b 18-25 ancl ?4 a 3- b 2 -

go b ANALYTICA POSTERIORA

unity and the odd, and all the other sciences likewise.
Moreover, every demonstration proves a predicate of a
subject as attaching or as not attaching to it, but in defini-

35 tion one thing is not predicated of another ; we do not,
e. g., predicate animal of biped nor biped of animal, nor
yet figure of plane plane not being figure nor figure plane. 1
Again, to prove essential nature is not the same as to
gi a prove the fact of a connexion. Now definition reveals
essential nature, demonstration reveals that a given attribute
attaches or does not attach to a given subject ; but different
things require different demonstrations 2 unless the one
demonstration is related to the other as part to whole.
I add this because if all triangles have been proved to possess
angles equal to two right angles, then this attribute has
been proved to attach to isosceles ; for isosceles is a part of
5 which all triangles constitute the whole. But in the case
before us the fact and the essential nature are not so related
to one another, since the one is not a part of the other.

So it emerges that not all the definable is demonstrable
nor all the demonstrable definable ; and we may draw the
general conclusion that there is no identical object of which
it is possible to possess both a definition and a demonstration.

10 It follows obviously that definition and demonstration are
neither identical nor contained either within the other : if
they were, their objects would be related either as identical
or as whole and part.

So much, then, for the first stage of our problem. The 4
next step is to raise the question whether syllogism i. e.
demonstration of the definable nature is possible or, as our
recent argument assumed, 3 impossible.

1 sc. within the definitory Xd-yor. In the definition of avdpuiTcos, wnv-
blrrow-XoyiKw, the three moments are severally and collectively
predicable of avdpairo?, but they are not, when considered as moments
constituting the definition of (IvdpcajrHs, predicable of each other.

2 Aristotle argues that what definition reveals and what ordinary
demonstration reveals are different. Therefore if definition is a kind
of demonstration it is at any rate not the ordinary kind, and the
definable has not been shown to be the demonstrable in the sense
required.

8 Aristotle has been assuming that nTrofctgis is only of TO on. Cf.
e.g. 9o b 3i-9i a 2.

ROOK II. 4 9i

We might argue it impossible on the following grounds :
(a) syllogism proves an attribute of a subject through the
middle term; on the other hand (b) its definable nature is both 15
peculiar l to a subject and predicated of it as belonging to
its essence. But in that case (i) the subject, its definition, and
the middle term connecting them must be reciprocally predi-
cable of one another; for if A is peculiar to C, obviously A is
peculiar to B and B to C in fact all three terms are
peculiar to one another : and further (2) if A inheres in
the essence of all B and B is predicated universally of all C
as belonging to C s essence, A also must be predicated of C 20
as belonging to its essence.

If one does not take this relation as thus duplicated if,
that is, A is predicated as being of the essence of B, but B
is not of the essence of the subjects of which it is predi
cated A will not necessarily be predicated of C as belong
ing to its essence. So both premisses tW// predicate essence,
and consequently B also will be predicated of C as its
essence. Since, therefore, both premisses do predicate 2=,
essence i. e. definable form C s definable form will appear
in the middle term before the conclusion is drawn.

We may generalize by supposing that it is possible to
prove the essential nature of man. Let 7 be man, A man s
essential nature two-footed animal, or aught else it may
be. Then, if we are to syllogize, A must be predicated
of all B. But this premiss will be mediated by a fresh
definition, which consequently will also be the essential 3
nature of man. 2 Therefore the argument assumes what it
has to prove, since B too is the essential nature of man. It
is. however, the case in Which there are only the two
premisses i. e. in which the premisses are primary and
immediate which we ought to investigate, because it best
illustrates the point under discussion.

Thus they who prove the essential nature of soul or man 35

1 t<5ior, cf. note on 73 a 7.

2 sc. and an indefinite regress occurs . This argument is a corollary
of the proof in 91*15-26 that if the proposition predicating A its
definition of C can be a conclusion, there must be a middle term, B,
and since A, B, and C are reciprocally predicable, B too, as well as A,
will be a definition of C.

9i a ANALYTICA POSTERIORA

or anything else through reciprocating terms beg the
question. It would be begging the question, for example,
to contend that the soul is that which causes its own life,
and that what causes its own life is a self-moving number ;
for one would have to postulate that the soul is a self-
9l b moving number in the sense of being identical with it. 1 For
if A is predicable as a mere consequent of B and B of C, A
will not on that account be the definable form of C : A
will merely be what 2 it was true to say of C. Even if A is
predicated of all B inasmuch as B is identical with a species
of A, still it will not follow: being an animal is predicated
5 of being a man since it is true that in all instances to be
human is to be animal, just as it is also true that every man
is an animal but not as identical with being man. 3

We conclude, then, that unless one takes both the pre
misses as predicating essence, one cannot infer that A is
the definable form and essence of C . but if one does so take
them, in assuming B one will have assumed, before drawing
the conclusion, what the definable form of C is ; 4 so that
10 there has been no inference, for one has begged the
question.

Nor, as was said in my formal logic, 5 is the method of 5
division a process of inference at all, since at no point does
the characterization of the subject follow necessarily from
the premising of certain other facts c : division demonstrates
15 as little as does induction. For in a genuine demonstration
the conclusion must not be put as a question nor depend on
a concession, but must follow necessarily from its premisses,
even if the respondent deny it. The clefiner asks Is man
animal cr inanimate? and then" assumes he has not

1 oTtfp apidfjLov eli ai avrov airov KIVO^VTU alone would mean to be of
the genus self-moving number ; as qualified by on- TO avro ot> it means
fully identical with and completely definable as self-moving number .

2 Reading nXX (o) d\r]6( s.

3 Treating <l\t]6fs yap gi b 5 ... fwor b 7 as a parenthesis.

4 Bywater s ort e ovl TO -n rjv tlvai is easier.

6 Cf. An. Pr. i, ch. 31. iv 77; ava\vcrti rfj irtfn ra a^^ora means
literally in that part of the logicalj resolution of conclusions into
their premisses which concerns the figures .

A reminder of the definition of o-vXXoyurpo?, An, Pr. i, 24 18-20.

7 i.e. when the respondent has replied animal .

BOOK II. 5 91

inferred that man is animal. Next, when presented with
an exhaustive division of animal into terrestrial and aquatic,
he assumes that man is terrestrial. Moreover, that man is 20
the complete formula, terrestrial-animal, does not follow
necessarily from the premisses : this too is an assumption,
and equally an assumption whether the division comprises
many differentiae or few. (Indeed as this method of division
is used by those who proceed by it, even truths that can be
inferred actually fail to appear as such.) l For why should
not the whole of this formula be true of man, and yet not 25
exhibit his essential nature or definable form ? Again,
what guarantee is there against an unessential addition, or
against the omission of the final or of an intermediate
determinant of the substantial being ?

The champion of division might here urge that though
these lapses do occur, yet we can solve that difficulty if all
the attribute s we assume are constituents of the definable
form, and if, postulating the genus, we produce by division
the requisite uninterrupted sequence of terms, 2 and omit
nothing ; and that indeed we cannot fail to fulfil these 30
conditions if what is to be divided falls whole into the
division at each stage, and none of it is omitted ; and that
this the dividendum must without further question be
(ultimately) incapable of fresh specific division. 3 Never-

1 Treating uo-uXAo-yioror (rv\\oyiad?irai in b 23 and 24 as a paren
thesis.

2 The terms of a series are (4>erjs when nothing of the same kind as
they intervenes between them, cf. Phys. vi. 23i b 23 and note on 95 b 4.
The completed dialptais of a yeios must present a set of terms such
that between any two terms which are next to one another, either
horizontally or vertically, no term of the same genus intervenes.
Thus, if a yews A is divided into B and C, and C must be ( q>ei]s :
if B and C are divided respectively into B 1 B 2 and C 1 C 2 , each of these
pairs must be e $fi5? and also the pairs AB, BB^, BB 2 , and^4C, CC 1 ,
L C 2 , must each be efafrjs.

s Omitting yap and 8el in b 32 with A. TOVTO in b 32 refers to the
subject of f^niirrei in b 3i. The divider is supposed to argue that if
the process of division fulfils certain conditions which, if at each stage
it exhausts the dividendum, it cannot fail to do then its final result
must be an aropov tlSos the essentially definable. In the next
sentence Aristotle does not dispute that dtalpems may reach an aro^ov
dSos but denies that it does so by a process of inference. fjStj in b 32
seems to mean without more ado , without having any further con
dition to fulfil : B el Sj/, \Yaitz ddti.

b

gi b ANALYTICA POSTERIORA

theless, we reply, division does not involve inference ;
if it gives knowledge, it gives it in another way. Nor is
there any absurdity in this : induction, perhaps, is not
demonstration any more than is division, yet it does make
35 evident some truth. Yet to state a definition reached by
division is not to state a conclusion : as, when conclusions
are drawn without their appropriate middles, the alleged
necessity by which the inference follows from the premisses
is open to a question as to the reason for it, so definitions
reached by division invite the same question. Thus to the
g2 a question What is the essential nature of man ? the divider
replies Animal, mortal, footed, biped, wingless ; and when
at each step he is asked Why ? , he will say, and, as he
thinks, prove by division, that all animal is mortal or
immortal : but such a formula taken in its entirety is not
definition; so that even if division docs demonstrate its
formula, definition at any rate does not turn out to be a
5 conclusion of inference.

Can we nevertheless actually demonstrate what a thing 5
essentially and substantially is, but hypothetically, i. e. by
premising (i) that its definable form is constituted by the
peculiar l attributes of its essential nature ; (2) that such
and such are the only attributes of its essential nature, and
that the complete synthesis of them is peculiar to the
thing ; and thus since in this synthesis consists the being
of the thing obtaining our conclusion ? Or is the truth

10 that, since proof must be through the middle term, the
definable form is once more assumed in this minor premiss
too?

Further, just as in syllogizing we do not premise what
syllogistic inference is (since the premisses from which we
conclude must be related as whole and part), 2 so the
definable form must not fall within the syllogism but remain
outside the premisses posited. It is only against a doubt

15 as to its having been a syllogistic inference at all that we

1 Cf. note on 73 a 7.

2 A reminder of a necessary condition of syllogism. If the definition
of syllogism is premised the conclusion would have to affirm some
subject to be of the nature of syllogism.

BOOK II. 6 92

have to defend our argument as conforming to the defini
tion of syllogism. It is only when some one doubts whether
the conclusion proved is the definable form that we have
to defend it as conforming to the definition of definable
form which we assumed. Hence syllogistic inference must
be possible even without the express statement of what
syllogism is or what definable form is. 1

The following type of hypothetical proof also begs the 20
question. If evil is definable as the divisible, and the defini
tion of a thing s contrary if it has one is the contrary of
the thing s definition ; 2 then, if good is the contrary of evil
and the indivisible of the divisible, we conclude that to be
good is essentially to be indivisible. The question is begged
because definable form is assumed as a premiss, and as a
premiss which is to prove definable form. But not the
same definable form , you may object. 3 That I admit, for 25
in demonstrations also we premise that this is predicable
of that ; 4 but in this premiss the term we assert of the
minor is neither the major itself nor a term identical in
definition, or convertible, with the major.

Again, both proof by division and the syllogism just
described are open to the question why man should be
animal-biped-terrestrial and not merely animal and terres
trial, since what they premise does not ensure that the 30
predicates shall constitute a genuine unity and not merely
belong to a single subject as do musical and grammatical
when predicated of the same man.

7 How then by definition shall we prove substance or
essential nature ? We cannot show it as a fresh fact ?,5
necessarily following from the assumption of premisses
admitted to be facts the method of demonstration : we
may not proceed as by induction to establish a universal on
the evidence of groups of particulars which offer no excep-

1 Reading t) TO ri ?)v flvm with A.

* The full Greek would be ei TU KUK<^ TO tlvai e ori TO StatperoJ tiVoi, TW
6" ivavrUf TO tlvai fan TO TW eV.im w tlvni. . . It would however be easier
to read TO (so B and YVaitz) KUKO> (sc. dvai) eoVi TO ftiaipntp ttvai y TO
fi tvavriu (sc. fivni) TO TO> e vavTtai (ivat.

3 Placing a colon after /xeWm.

4 ToSe KOTII Toi"Se = minor premiss.

92 a ANALYTICA POSTERIORA

tion, because induction proves not what the essential nature
Q2 b of a thing is but that it has or has not some attribute.
Therefore, since presumably one cannot prove essential
nature by an appeal to sense perception l or by pointing
with the finger, what other method remains ?

To put it another way: how shall we by definition prove
essential nature ? He who knows what human or any other
5 nature is, must know also that man exists ; for no one
knows the nature of what does not exist one can know
the meaning of the phrase or name goat-stag but not
what the essential nature of a goat-stag is. But further, if
definition can prove what is the essential nature of a thing,
can it also prove that it exists? And how will it prove
them both by the same process, 2 since definition exhibits one

10 single thing and demonstration another single thing, and
what human nature is and the fact that man exists are not
the same thing ? Then too we hold that it is by demon
stration that the being of everything must be proved
unless indeed to be were its essence ; and, since being is not
a genus, 3 it is not the essence of anything. Hence the being
of anything as fact is matter for demonstration ; and this

15 is the actual procedure of the sciences, for the geometer
assumes the meaning of the word triangle, but that it is
possessed of some attribute 4 he proves. What is it, then,
that we shall prove in defining essential nature ? Triangle ?
In that case a man will know by definition what a thing s
nature is without knowing whether it exists. But that is
impossible.

Moreover it is clear, if we consider the methods of de
fining actually in use, that definition does not prove that

20 the thing defined exists : since even if there does actually

1 Cf. for this use of modern e.g. Met. iO25 b II, io64 a 8, Rhet. 1386*
32 (best MSS.).

2 Placing a comma after TI tan and a note of interrogation after ort
(irr(, and reading Km Trias ro5 mm5 Aoyo> with A and B. So Waitz.

3 Cf. Met. 998 b 22 ff. and io45 b 6.

4 Triangle is for the geometer most naturally a subject and not an
attribute : and in that case on d eort should mean not that it exists ,
but that it has some attribute , e. g. equality to two right angles. It
is tempting to read rr! W.

Cf., however, note on 71* 15, and it is possible that Aristotle is
speaking loosely in this dialectical passage.

BOOK II. 7 92 b

exist something 1 which is equidistant from a centre, 2 yet
why should the thing named in the definition exist ? :! Why,
in other words, should this be the formula defining circle ?
One might equally well call it the definition of mountain
copper. For definitions do not carry a further guarantee
that the thing defined can exist or that it is what they
claim to define : one can always ask why. 25

Since, therefore, to define is to prove either a thing s
essential nature or the meaning of its name, we may con
clude that definition, if it in no sense proves essential nature,
is a set of words signifying precisely what a name signifies.
But that were a strange consequence ; for (i) both what is
not substance and what does not exist at all would be
definable, since even non-existents can be signified by
a name: (2) all sets of words or sentences would be defini- 3
tions, since any kind of sentence could be given a name ; so
that we should all be talking in definitions, and even the
Iliad would be a definition : (3) no demonstration 4 can
prove that any particular name means any particular thing: 5
neither, therefore, do definitions, in addition to revealing the
meaning of a name, also reveal that the name has tJiis
meaning. It appears then from these considerations that 35
neither definition and syllogism nor their objects are iden
tical, and further that definition neither demonstrates nor
proves anything, and that knowledge of essential nature is
not to be obtained either by definition or by demonstra
tion.

8 We must now start afresh and consider which of these 93*
conclusions are sound and which are not, and what is the
nature of definition, and whether essential nature is in any
sense demonstrable and definable or in none.

Now to know its essential nature is, as we said, 6 the same
as to know the cause of a thing s existence, and the proof

1 Reading n luov for TO to-or, with A and D.

- An abbreviated definition of circle, cf. Euclid, El em. i, Defs. xv
and xvi.

3 Accenting tori.

4 Omitting {VicTr/}^ with A, B, D, and supposing a7rciSi(y to be
understood.

6 sc. as on this assumption it would have to do .

6 ii, ch. 2. In 93 a 4 read TOV fan with A, C, and B corn

93 a ANALYTICA POSTERIORA

5 of this depends on the fact that a thing must have a cause.
Moreover, this cause is either identical with the essential
nature of the thing or distinct from it ; and if its cause is
distinct from it, the essential nature of the thing is either
demonstrable or indemonstrable. Consequently, if the
cause is distinct from the thing s essential nature and
demonstration is possible, the cause must be the middle
term, and, the conclusion proved being universal and affirm
ative, the proof is in the first figure. So the method just
examined of proving it through another essential nature

10 would be one way of proving essential nature, because
a conclusion containing essential nature must be inferred
through a middle which is an essential nature just as
a peculiar 2 property must be inferred through a middle
which is a peculiar property ; so that of the two definable
natures of a single thing this method will prove one and
not the other. 3

Now it was said before 4 that this method could not
amount to demonstration of essential nature it is actually

15 a dialectical proof of it so let us begin again and explain
by what method it can be demonstrated. When we are
aware of a fact we seek its reason, and though sometimes
the fact and the reason dawn on us simultaneously, yet we
cannot apprehend the reason a moment sooner than the
fact ; and clearly in just the same way we cannot apprehend
a thing s definable form without apprehending that it exists,

20 since while we are ignorant whether it exists we cannot
know its essential nature. Moreover we are aware whether
a thing exists or not sometimes through apprehending an
element in its character, and sometimes accidentally, as,

1 distinct from it ; i.e. in the case si properties, with the definition
of which Aristotle is alone concerned in this chapter. The being of a
property consists in its inherence in a substance through a middle
which defines it. Cf. the following chapter.

2 Cf. note on 73* 7.

3 a 12 rtov ri TIP cti iu : Aristotle speaks of two moments of the
definable form as two essential natures. His argument amounts to
this : that if the conclusion contains the whole definition, the question
has been begged in the premisses (cf. ii, ch. 4). Hence syllogism and
even so merely dialectical syllogism is only possible if premisses and
conclusion each contain a part of the definition. 4 ii, ch. 2.

" The distinction is that between genuine knowledge of a connexion

BOOK II. 8 93*

for example, when we are aware of thunder as a noise in
the clouds, of eclipse as a privation of light, or of man as
some species of animal, or of the soul as a self-moving
thing. As often as we have accidental knowledge that
the thing exists, we must be in a wholly negative state 25
as regards awareness of its essential nature ; for we have
not got genuine knowledge even of its existence, and to
search for a thing s essential nature when we are unaware
that it exists is to search for nothing. On the other hand,
whenever we apprehend an element in the thing s character
there is less difficulty. Thus it follows that the degree
of our knowledge of a thing s essential nature is determined
by the sense in which we are aware that it exists. Let us
then take the following as our first instance of being aware
of an element in the essential nature. Let A be eclipse, C 30
the moon, B the earth s acting as a screen. Now to ask
whether the moon is eclipsed or not is to ask whether
or not B has occurred. But that is precisely the same as
asking whether A has a defining condition ; 1 and if this
condition actually exists, we assert that A also actually
exists. Or again we may ask which side of a contradiction
the defining condition necessitates : does it make the angles
of a triangle equal or not equal to two right angles ? When
we have found the answer, if the premisses are immediate, 2
we know fact and reason together ; if they are not im- 35
mediate, we know the fact without the reason, as in the
following example : let C be the moon, A eclipse, B the
fact that the moon fails to produce shadows 3 though she is
full and though no visible body intervenes between us and

through its cause and accidental knowledge of it through a middle not
the cause.

1 \6yos varies in meaning from mere statement to the formula
giving TO ri rfv (Ivat of a substance , but always the underlying unity
of its meanings is the rationality, the intelligible connexion, which dis
courseverbal or held by the soul with herself exhibits in varying
degrees. Here it is equivalent to proximate cause . The fact that
Xoyo? also means definition assists Aristotle to identify cause and
definition. Defining condition perhaps to some degree covers the
two senses.

2 Reading St a^.fa-u>v with Waitz.

3 i. e. that there is no moonlight casting shadows on the earth on
a clear night at full moon.

93 a ANALYTICA POSTERIORA

her. Then if B, failure to produce shadows in spite of the
93 b absence of an intervening body, is attributable to C, and A,
eclipse, is attributable to />, it is clear that the moon is
eclipsed, but the reason why is not yet clear, and we know
that eclipse exists, but \ve do not know what its essential
nature is. But when it is clear that A is attributable to
C and we proceed to ask the reason of this fact, we are
5 inquiring what is the nature of B : is it the earth s acting
as a screen, or the moon s rotation or her extinction? But
B is the definition of the other term, viz., in these examples,
of the major term A ; for eclipse is constituted by the earth
acting as a screen. Thus, (i) What is thunder? The
quenching of fire in cloud , and (a) Why does it thunder?
Because fire is quenched in the cloud , are equivalent.

10 Let Cbe cloud, A thunder, B the quenching of fire. Then
B is attributable to C, cloud, since fire is quenched in it ;
and A, noise, is attributable to B ; and B is assuredly the
definition of the major term A. If there be a further
mediating cause of B, it will be one of the remaining
partial definitions of A.

15 We have stated then how essential nature is discovered
and becomes known, and we see that, while there is no
syllogism i. e. no demonstrative syllogism of essential
nature, yet it is through syllogism, viz. demonstrative syl
logism, that essential nature is exhibited. So we conclude
that neither can the essential nature of anything which has
a cause distinct from itself be known without demonstra
tion, nor can it be demonstrated ; and tin s is what we

20 contended in our preliminary discussions. 1

Now while some things have a cause distinct from them- 9
selves, others have not. Hence it is evident that there are
essential natures which are immediate, that is are basic
premisses ; and of these not only that they are but also
ivhat they are must be assumed or revealed in some other
way. This too is the actual procedure of the arithmetician,
25 who assumes both the nature and the existence of unit. On
the other hand, it is possible (in the manner explained) to

1 ii, ch. 3.

BOOK II. 9 93 b

exhibit through demonstration the essential nature of things
which have a middle V i. e. a cause of their substantial
being other than that being itself; but we do not thereby
demonstrate it.

10 Since definition is said to be the statement of a thing s
nature, obviously one kind of definition will be a statement
of the meaning of the name, or of an equivalent nominal 30
formula. A definition in this sense tells you, c. g., the
meaning of the phrase triangular character . 2 When we
are aware that triangle exists, we inquire the reason why it
exists. But it is difficult thus to learn the definition of
things the existence of which we do not genuinely know
the cause of this difficulty being, as we said before, 3 that
we only know accidentally whether or not the thing exists. 35
Moreover, a statement may be a unity in cither of two ways,
by conjunction, like the Iliad, or because it exhibits a single
predicate as inhering not accidentally in a single subject. 4

That then is one way of defining definition. Another kind
of definition is a formula exhibiting the cause of a thing s
existence. Thus the former signifies without proving, but 94*
the latter will clearly be a (///^/-demonstration of essential
nature, differing from demonstration in the arrangement
of its terms. For there is a difference between stating why
it thunders, and stating what is the essential nature of
thunder : since the first statement will be Because fire
is quenched in the clouds , while the statement of what the
nature of thunder is will be The noise of fire being
quenched in the clouds . Thus the same statement takes 5
a different form : in one form it is continuous 5 demonstra
tion, in the other definition. Again, thunder can be defined

1 Cf., however, ii, ch. 2, and note on 89 * 38. Aristotle here uses neaov
in the more restricted sense.

2 i. e. as treated by geometry ; that is, as abstracted a mater ia and
treated as a subject. Cf. 8l b 25

3 Cf. 93 a 16-27.

4 Presumably a reason for there being a kind of definition other than
nominal. The reference is obviously to 92 b 32.

s Demonstration, like a line, is continuous because its premisses are
parts which are conterminous (as linked by middle terms), and there
is a movement from premisses to conclusion. Definition resembles
rather the indivisible simplicity of a point.

94 a ANALYTICA POSTERIORA

as noise in the clouds, which is the conclusion of the
demonstration embodying essential nature. On the other
hand the definition of immediates is an indemonstrable
10 positing of essential nature.

We conclude then that definition is (a) an indemonstrable
statement of essential nature, or (b] a syllogism of essential
nature differing from demonstration in grammatical form,
or (c) the conclusion of a demonstration giving essential
nature.

Our discussion has therefore made plain (i) in what
sense and of what things the essential nature is demon-
is strable, and in what sense and of what things it is not;

(2) what are the various meanings of the term definition, and
in what sense and of what things it proves the essential
nature, and in what sense and of what things it does not ;

(3) what is the relation of definition to demonstration, and
how far the same thing is both definable and demonstrable
and how far it is not.

20 We think we have scientific knowledge when we know II
the cause, and there are four causes : (i) the definable form,
(2) an antecedent which necessitates a consequent, 1 (3) the

1 By this Aristotle appears to mean the material cause ; cf. Physics
ii, I95 a 18, 19, where the premisses of a syllogism are said to be the
material cause of the conclusion. In this chapter Aristotle gives no
separate example of formal cause as the middle term of demonstration,
and seems rather, in virtue of a different classification of cause, to
regard the middle of demonstration as always a formal cause because it
defines the major term, and as generically embracing material, efficient,
and final causes. But as the transition is neither explicit nor complete,
this is confusing. In the Metaphysics Aristotle teaches that formal,
final, and efficient causes coalesce (cf. e.g. Met. io44 b i, io7o b 26),
while the material cause remains distinct. The treatment of causation
here is presumably earlier than the teaching of the Metaphysics, though
in the last part of the chapter Aristotle is moving towards the position
he there adopts. Possibly he felt that if the middle of arrodfigis must
reflect the full proximate cause of a connexion, then the four causes
could not remain wholly distinct from one another, and hence his
attempt here to unite them under the formal cause. He may sub
sequently have been induced to omit the material cause from this
unification from a consideration of the unknowable and merely potential
nature of v\rj. Even here the example he gives of a material cause is
not what one expects, i.e. not one such as, e.g., bricks taken as the
material cause of a house. Aristotle s difficulty is due to the fact that
he is trying to equate scientific conceptions of causation, which he
should have recognized as niKflm apxai, or at least as axioms not trans
ferable without modification from spheres which they were formulated

BOOK II. ii 94

efficient cause, 1 (4) the final cause. Hence each of these
can be the middle term of a proof, for 2 (a) though the
inference from antecedent to necessary consequent does not
hold if only one premiss is assumed two is the minimum 25
still when there are two it holds on condition that they
have a single common middle term. So it is from the
assumption of this single middle term that the conclusion
follows necessarily. The following example will also show
this. 3 Why is the angle in a semicircle a right angle ? or
from what assumption does it follow that it is a right angle ?
Thus, let A be right angle, B the half of two right angles,
C the angle in a semicircle. Then B is the cause in virtue 3
of which A, right angle, is attributable to C, the angle in a
semicircle, since B = A and the other, viz. C, B, for C is
half of two right angles. Therefore it is the assumption of
B, the half of two right angles, from which it follows that A
is attributable to C, i. e. that the angle in a semicircle is a
right angle. Moreover, B is identical with (b] the defining
form of A, since it is what A s definition 4 signifies. More- 35
over, the formal cause has already been shown to be the
middle. 5 (c) Why did the Athenians become involved in
the Persian war ? means What cause originated the
waging of war against the Athenians ? and the answer
is, Because they raided Sardis with the Eretrians , since Q4 b
this originated the war. Let A be war, B unprovoked
raiding, C the Athenians. Then B, unprovoked raiding, is
true of C, the Athenians, and A is true of B, since men
make war on the unjust aggressor. So A, having war 5
waged upon them, is true of B, the initial aggressors, and

to explain, with the logical category of ground and consequent, which
for him takes the narrowly specialized form of inherence of attribute in
subject. Two thousand years later Leibniz was still making the same
attempt.

1 17 TI Trplror should be thus accented.

2 sc. lest you should suppose that (2) could not be a middle .

3 sc. that (2) can appear as a middle .

4 Cf. Euclid, Elem. i, Uef. x, but Aristotle may be referring to some
earlier definition. The proof here given that the angle in a semicircle
is a right angle is not that of Euclid iii. 31 ; cf. Heath, Greek
Mathematics, i. pp. 339, 340.

5 The reference is to 93 a 3ff., and other passages such as 94 a 5 ff.,
where the middle is shown to define the major.

646-24-4 JJ

94 b ANALYTICA POSTERIORA

B is true of 6", the Athenians, who were the aggressors.
Hence here too the cause in this case the efficient cause
is the middle term, (d) This is no less true where the cause
is the final cause. E. g. why does one take a walk after
supper? For the sake of one s health. Why does a house

10 exist ? For the preservation of one s goods. The end in
view is in the one case health, in the other preservation. To
ask the reason why one must walk after supper is precisely
to ask to what end one must do it. Let C be walking after
supper, B the non-regurgitation of food, A health. Then
let walking after supper possess the property of preventing

*5 food from rising to the orifice of the stomach, and let this
condition be healthy ; since it seems that B, the non-regurgi
tation of food, is attributable to C, taking a walk, and that
A, health, is attributable to B. What, then, is the cause
through which A, the final cause, inheres in C? It is B,
the non-regurgitation of food ; but B is a kind of definition

20 of A, for A will be explained by it. Why is B the cause
of A s belonging to C? Because to be in a condition such
as B is to be in health. The definitions must be transposed,
and then the detail will become clearer. 1 Incidentally, here
the order of coming to be is the reverse of what it is in
proof through the efficient cause : in the efficient order the
middle term must come to be first, whereas in the teleo-

25 logical order the minor, C, must first take place, and the
end in view comes last in time. 2

1 The argument from 94 b 8 is roughly as follows :

Health A, digestion Z>, walking (. .

The final cause A inheres in C through the efficient cause B. (A-B,
B-C, . . A-C.)

{But the final cause naturally appears as the effect of the efficient
cause ; which means that) B, the efficient cause, is a kind of definition
of A, the final cause.

(Since A is It s final cause, just as much as B is A s efficient cause,
A is also a kind of definition of B. Hence) we can transpose A and B,
and prove the inherence of B in C through A. (B-A, A-C, . . B-C.)

This seems to foreshadow the doctrine of the ultimate identity of
final, efficient, and formal cause, cf. note on 94* 22.

2 The actual yeveais or order of events is walking digestion
health. The terms of the syllogism through the efficient cause reflect

C B A

these stages as follows : minor middle major. In the syllogism through

C B A

final cause they appear as minor major middle. Aristotle should,

BOOK II. ii 94 b

The same thing may exist for an end and be necessi
tated as well. For example, light shines through a lantern
(j) because that which consists of relatively small particles
necessarily passes through pores larger than those particles
assuming that light does issue by penetration and (2) for 30
an end, namely to save us from stumbling. If, then, a
thing can exist through two causes, can it come to be
through two causes as for instance if thunder be a hiss and
a roar necessarily produced by the quenching of fire, and
also designed, as the Pythagoreans say, for a threat to
terrify those that lie in Tartarus ? l Indeed, there are very
many such cases, mostly among the processes and products 35
of the natural world ; 2 for nature, in different senses of the
term nature , produces now for an end, now by neces
sity.

Necessity too is of two kinds. It may work in accordance
with a thing s natural tendency, or by constraint and in 95 a
opposition to it ; as, for instance, by necessity a stone is
borne both upwards and downwards, but not by the same
necessity.

Of the products of man s intelligence some are never due
to chance or necessity but always to an end, as for example
a house or a statue ; others, such as health or safety, may 5
result from chance as well.

It is mostly in cases where the issue is indeterminate
(though only where the production does not originate in

however, have said of the middle in the efficient order not 8e I yemr$<u
Trpwrov, but that it must come to be before the major.

But possibly eVel in b 24 = in the ideological order , evravOa, ^25,
in the efficient order , and Aristotle is comparing the order of steps in
a 8ov\fv(ns (an dvdXvcris of an end into its means, cf. e.g. E.N. ni2 b
1 1-24) with the actual order of events reflected by the syllogism through
the efficient cause. In this case he naturally says that in the teleo-
logical order the middle health, the end in view is conceived first
(cf. E. N. loc. cit.)- The objection to this second view is that Aristotle
is unlikely to speak of awiXucm as a ycVeo-ir : in the passage quoted from
E.N. he contrasts dvd\va-is and yeWo-ir.

1 Placing a comma after eV&r xmu in b 32 and a note of interrogation
after (f)o$nvT<u in ^34.

* (Tvvio-Ta(j.tvois : probably the natural processes by which e.g. o^oio/ifpf)
are formed from oroixela. This is an instance of dual causation in
yiyveaOat, cf. 94 b 31. crvvtaruxriv : probably natural products qua main
taining themselves in being (e.g. plants and animals) an instance of
dual causation in tlvai, cf. ibid.

II 2

95 a ANALYTICA POSTERIORA

chance, and the end is consequently good), 1 that a result is
due to an end, and this is true alike in nature or in art. By
chance, on the other hand, nothing comes to be for an end.

10 The effect may be still coming to be, or its occurrence 12
may be past or future, yet the cause will be the same as
when it is actually existent for it is the middle which is
the cause 2 except that if the effect actually exists the cause
is actually existent, if it is coming to be so is the cause, if
its occurrence is past the cause is past, if future the cause is
future. For example, the moon was eclipsed because the
earth intervened, is becoming eclipsed because the earth is

15 in process of intervening, will be eclipsed because the earth
will intervene, is eclipsed because the earth intervenes.

To take a second example : assuming that the definition
of ice is solidified water, let C be water, A solidified, B the
middle, which is the cause, namely total failure of heat.
Then B is attributed to C, and A, solidification, to B : ice

20 forms when B is occurring, has formed when B has occurred,
and will form when B shall occur.

This sort of cause, then, and its effect come to be simul
taneously when they are in process of becoming, and exist
simultaneously when they actually exist ; and the same holds
good when they are past and when they are future. But
what of cases where they are not simultaneous ? Can causes
and effects different from one another form, as they seem

25 to us to form, a continuous succession, a past effect resulting
from a past cause different from itself, a future effect from a
future cause different from it, and an effect which is coming-
to-be from a cause different from and prior to it ? Now on
this theory it is from the posterior event that we reason (and
this though these later events actually have their source of
origin in previous events a fact which shows that also
when the effect is coming-to-be we still reason from the
posterior event), and from the prior event we cannot reason

1 Bracketing 95 a 7 orav . . . a 8 ayaQov and reading a comma after ?J
in a y. The end is consequently good i.e. a genuine end.

2 Bracketing TO yap pta-ov alnov and following it with a colon.
Aristotle means that he is here only dealing with causes which can
be middle terms of demonstration, i.e. which reciprocate with their
effects.

BOOK II. 12 95 a

(we cannot argue that because an event A has occurred, 30
therefore an event /> has occurred subsequently to A but
still in the past and the same holds good if the occurrence
is future) l cannot reason because, be the time interval
definite or indefinite, it will never be possible to infer that
because it is true to say that A occurred, therefore it is true
to say that B, the subsequent event, occurred ; for in the
interval between the events, though A has already occurred,
the latter statement will be false. And the same argument 35
applies also to future events ; 2 i.e. one cannot infer from an
event which occurred in the past that a future event will
occur. The reason of this is that the middle must be
homogeneous, past when the extremes are past, future when
they are future, coming to be when they are coming-to-be,
actually existent when they are actually existent ; and there
cannot be a middle term homogeneous with extremes
respectively past and future. And it is a further difficulty
in this theory that the time interval can be neither indefinite 40
nor definite, since during it the inference will be false. 5 We 95 b
have also to inquire what it is that holds events together so
that the coming-to-be now occurring in actual things follows
upon a past event. It is evident, we may suggest, that a
past event and a present process cannot be contiguous , 4
^ Treating as parentheses a 28 apx i S<= . . . a 2g ucravTus and a 3o

mov . . . a 31 u>cravT(t>s.

2 Placing a comma after fVo/ieVov in a 36.

3 i. e. a further difficulty created by taking cause and effect as
punctual events is that, since time is continuous and not composed
of atomic nows , there must be a time interval between any two such
punctual events. Rut during this interval the inference must be
false, because the causal nexus cannot leap the gap nor, ex hyfothesi,
persist through it. In fact such an account of cause and effect does
not correspond to the real connexions in things. Cf. e. g. Physics vi.

4 Terms are * <!}?, successive , if they are next one another and
nothing of the same kind intervenes. Terms are c x<jp(i>a, contiguous ,
if they are f $eiji- and also in contact; e.g. boats at the start of
a bumping race are ifagijs ; houses in a row of houses any and every
pair of which share a party-wall are e^ M 61 "- If the members of any
series are conterminous i.e. if any point at which you divide the
series is a term of the series they are <rwfxn or continuous . Cf.
Met. io68 b 3off.

Aristotle asks whether it is possible, while regarding time as con
tinuous, yet to suppose that within any duration, past or future, two
disjunct or punctual events can be connected as cause and effect ; and
further whether an event now occurring, not itself punctual but a
specious present, can have as its cause a punctual past event.

95 b ANALYTICA POSTERIORA

for not even two past events can be contiguous . For past
5 events are limits and atomic ; so just as points are not
contiguous neither are past events, since both are indi
visible. For the same reason a past event and a present
process cannot be contiguous , for the process is divisible.
the event indivisible. Thus the relation of present process
to past event is analogous to that of line to point, since a

10 process contains an infinity of past events. These questions,
however, must receive a more explicit treatment in our
general theory of change. 1

The following must suffice as an account of the manner
in which the middle would be identical with the cause on
the supposition that coming-to-be is a series of consecutive
events: for 2 in the terms of such a series too the middle

15 and major terms must form an immediate premiss; e.g.
we argue that, since C has occurred, therefore A occurred :
and C s occurrence was posterior, A s prior; but C is the
source of the inference because it is nearer to the present
moment, and the starting-point of time is the present. We
next argue that, since/) has occurred, therefore C occurred.
Then we conclude that, since D has occurred, therefore A

20 must have occurred ; and the cause is C, for since D has
occurred C must have occurred, and since 7 has occurred A
must previously have occurred.

If we get our middle term in this way, will the series
terminate in an immediate premiss, or since, as we said, no
two events are contiguous , will a fresh middle term always
intervene because there is an infinity of middles? No:
though no two events are contiguous , yet we must start
from a premiss consisting of a middle and the present event

25 as major. 3 The like is true of future events too, since if it

1 Cf. Physics vi.

2 i.e. Aristotle has had in this chapter to explain (i) how syllogisms
concerning a process of events can be brought into line with other
demonstrations equally derivable from immediate primary premisses,
and (2) in what sense the middle term contains the cause. He has in
fact had (i) to show that in these syllogisms inference must find its
primary premiss in the effect, and (2) to imply that the cause which
appears as middle when cause and effect are not simultaneous is a
causa cognoscendi and not essendi.

3 Waitz reads im aufaov in b 25 for UTTO /ut o-ov (D UTTO TOU neaov) : ( from

BOOK II. 12 95 b

is true to say that D will exist, it must be a prior truth to
say that A will exist, and the cause of this conclusion is C ;
for if D will exist, C will exist prior to /?, and if C will
exist, A will exist prior to it. And here too the same
infinite divisibility might be urged, since future events are ?o
not contiguous . But here too an immediate basic premiss
must be assumed. And in the world of fact this is so: if a
house has been built, then blocks must have been quarried
and shaped. The reason is that a house having been built
necessitates a foundation having been laid, and if a founda
tion has been laid blocks must have been shaped beforehand. 35
Again, if a house will be built, blocks will similarly be
shaped beforehand ; and proof is through the middle in the
same way, for the foundation will exist before the house.

Now we observe in Nature a certain kind of circular
process of coming-to-be; and this is possible only if the
middle and extreme terms l are reciprocal, since conversion 40
is conditioned by reciprocity in the terms of the proof.
This the convertibility of conclusions and premisses has g6 a
been proved in our early chapters, 2 and the circular process
is an instance of this. In actual fact it is exemplified thus:
when the earth had been moistened an exhalation was
bound to rise, and when an exhalation had risen cloud was
bound to form, and from the formation of cloud rain neces
sarily resulted, and by the fall of rain the earth was
necessarily moistened: but this was the starting-point, so 5
that a circle is completed ; for posit any one of the terms
and another follows from it, and from that another, and
from that again the first.

Some occurrences are universal (for they are, or come-to-
be what they are, always and In every case) ; others again
are not always what they are but only as a general rule : I0
for instance, not every man can grow a beard, but it is the
general rule. In the case of such connexions the middle
term too must be a general rule. For if A is predicated

an immediate premiss, i. e. the primary " now " ; but irpunov is used in
b 1 5 as = major term .

1 We should perhaps read opot with A and Waitz; but the sense
is the same.

2 i, ch. 3 and An. Pr. ii, cc. 3-5, 8-10.

g6 a ANALYTICA POSTERIORA

universally of B and B of C, A too must be predicated
always and in every instance of C, since to hold in every
15 instance and always is of the nature of the universal. But
we have assumed a connexion which is a general rule ;
consequently the middle term B must also be a general rule.
So connexions which embody a general rule i. e. which
exist or come to be as a general rule will also derive from
immediate basic premisses.

20 We have already explained how essential nature is set I3 1
out in the terms of a demonstration, and the sense in which
it is or is not demonstrable or definable ; so let us now
discuss the method to be adopted in tracing the elements
predicated as constituting the definable form.

Now of the attributes which inhere always in each several
thing there are some which arc wider in extent than it but

25 not wider than its genus (by attributes of wider extent
I mean all such as are universal attributes of each several
subject, but in their application are not confined to that
subject). 2 I. e. while an attribute may inhere in every triad,
yet also in a subject not a triad as being inheres in triad
but also in subjects not numbers at all odd on the other
hand is an attribute inhering in every triad and of wider

30 application (inhering as it does also in pentad), 3 but which
does not extend beyond the genus of triad ; for pentad is a
number, but nothing outside number is odd. It is such
attributes which we have to select, up to the exact point at
which they are severally of wider extent than the subject
but collectively coextensive with it ; for this synthesis
must be the substance of the thing. For example every

35 triad possesses the attributes number, odd, and prime in both
senses, i.e. not only as possessing no divisors, but also as not
being a sum of numbers. This, then, is precisely what triad
is, viz. a number, odd, and prime in the former and also the
latter sense of the term : for these attributes taken severally

1 This chapter treats only the definition of substances.

2 Bracketing \ey<a 1. 25 ... XXw 1. 27, and following the bracket
with a comma.

3 Bracketing Ka] . . . vnupxfi 1. 30, and following the bracket with a
comma.

BOOK II. 13 g6 b

apply, the first two to all odd numbers, the last to the dyad g6 b
also as well as to the triad, but, taken collectively, to no other
subject. Now since we have shown above l that attributes
predicated as belonging to the essential nature are necessary
and that universals are necessary, and since the attributes
which we select as inhering in triad, or in any other subject
whose attributes we select in this way, are predicated as be
longing to its essential nature, triad will thus possess these 5
attributes necessarily. Further, that the synthesis of them
constitutes the substance of triad is shown by the following
argument. If it is not identical with the being of triad, it must
be related to triad as a genus named or nameless. It will then
be of wider extent than triad assuming that wider potential
extent is the character of a genus. If on the other hand 10
this synthesis is applicable to no subject other than the
individual triads, it will be identical with the being of triad,
because we make the further assumption that the substance
of each subject is the predication of elements in its essential
nature down to the last differentia characterizing the in
dividuals. It follows that any other synthesis thus exhibited
will likewise be identical with the being of the subject.

The author of a hand-book 2 on a subject that is a generic 15
whole should divide the genus into its first infimae species
number e.g. into triad and dyad and then endeavour to
seize their definitions by the method we have described
the definition, for example, of straight line or circle or right
angle. After that, having established what the category is
to which the subaltern genus belongs quantity or quality,
for instance he should examine the properties peculiar 3 20
to the species, working through the proximate 4 common
differentiae. He should proceed thus because the attributes
of the genera compounded of the infimae species will be
clearly given by the definitions of the species ; since the
basic element of them all 5 is the definition, i. e. the simple

1 i, ch. 4.

2 \\ ith the remainder of the chapter compare An. Pr. i, ch. 25,
where the treatment covers all syllogism.

3 vide note on 73* 7.

4 TrpwTwf appears to mean first in a scale ascending towards the
genus . B sc, genera and species.

g6 b ANALYTICA POSTERIORA

infima species, 1 and the attributes inhere essentially in
the simple injimae species, in the genera only in virtue of
these.

25 Divisions according to differentiae are a useful accessory
to this method. What force they have as proofs we did,
indeed, explain above, 2 but that merely towards collecting
the essential nature they may be of use we will proceed to
show. They might, indeed, seem to be of no use at all, but
rather to assume everything at the start and to be no better

30 than an initial assumption made without division. But, in
fact, the order in which the attributes are predicated does make
a difference it matters whether we say animal tame-
biped, or biped- animal tame. For if every definable thing
consists of two elements and animal-tame forms a unity,
and again out of this and the further differentia man (or
whatever else is the unity under construction) is constituted,
then the elements we assume have necessarily been reached

35 by division. Again, division is the only possible method
of avoiding the omission of any element of the essential
nature. Thus, if the primary genus is assumed and we then
take one of the lower divisions, the dividendum will not fall
whole into this division : e. g. it is not all animal which is
either whole-winged or split-winged but all winged animal,
97 a for it is winged animal to which this differentiation ?> belongs.
The primary differentiation of animal is that within which
all animal falls. The like is true of every other genus,
whether outside animal or a subaltern genus of animal ; e. g.
the primary differentiation of bird is that within which
falls every bird, of fish that within which falls every fish.
So, if we proceed in this way, we can be sure that nothing
5 has been omitted : by any other method one is bound to
omit something without knowing it.

1 TW opicrnov Km TO <i7rXoCi : i. e. the infima species, which is
simple because below it are only uSutyopa, and which is the essen
tially definable.

2 ii, ch. 5 and An. Pr. \, ch. 31, where 8iaipTis is shown not to be
inference.

3 Aristotle tends to use Sicxpopa and 8iaipf<ris indifferently in this
chapter. This is natural, since a subject which obtains its &ia(popd by
falling on one side of a Biaipecns is ipso facto qualified by its distinction
from the other side.

BOOK II. 13 97

To define and divide one need not know the whole of
existence. Yet some hold it impossible to know the
differentiae distinguishing each thing from every single other
thing without knowing every single other thing ; and one
cannot, they say, know each thing without knowing its
differentiae, since everything is identical with that from 10
which it does not differ, and other than that from which it
differs. Now first of all this is a fallacy : not every differentia
precludes identity, since many differentiae inhere in things
specifically identical, though not in the substance of these
nor essentially. Secondly, when one has taken one s
differing pair of opposites and assumed that the two sides
exhaust the genus, and that the subject one seeks to define 15
is present in one or other of them, and one has further
verified its presence in one of them ; then it does not matter
whether or not one knows all the other subjects of which
the differentiae are also predicated. For it is obvious that
when by this process one reaches subjects incapable of further
differentiation one will possess the formula defining the sub
stance. Moreover, to postulate that the division exhausts
the genus is not illegitimate if the opposites exclude a middle ; 20
since if it is the differentia of that genus, anything contained
in the genus must lie on one of the two sides.

In establishing a definition by division one should keep
three objects in view : (i) the admission only of elements in
the definable form, (2) the arrangement of these in the right
order, (3) the omission of no such elements. The first is 25
feasible because one can establish genus and differentia
through the topic of the genus, 1 just as one can conclude the
inherence of an accident through the topic of the accident. 2
The right order will be achieved if the right term is assumed
as primary, and this will be ensured if the term selected is
predicable of all the others but not all they of it ; since 30
there must be one such term. Having assumed this we at
once proceed in the same way with the lower terms ; for our
second term will be the first of the remainder, our third the
first of those which follow the second in a contiguous :>>
series, since when the higher term is excluded, that term of

1 Cf. Topics iv. 2 Cf. Topics ii. 3 Cf. note on95 1j 4.

97 a ANALYTICA POSTERIORA

the remainder which is contiguous to it will be primary,
and so on. Our procedure makes it clear that no elements
35 in the definable form have been omitted : we have taken the
differentia that comes first in the order of division, pointing
out that animal, e.g., is divisible exhaustively into A and B,
and that the subject accepts one of the two as its predicate.
Next we have taken the differentia of the whole thus reached,
and shown that the whole we finally reach is not further
divisible i.e. that as soon as we have taken the last
differentia to form the concrete totality, this totality admits
97 of no division into species. For it is clear that there is no
superfluous addition, since all these terms we have selected
are elements in the definable form ; and nothing lacking,
since any omission would have to be a genus or a differentia.
Now the primary term is a genus, and this term taken in
conjunction with its differentiae is a genus: moreover the
differentiae are all included, because there is now no further
5 differentia ; if there were, the final concrete would admit
of division into species, which, we said, is not the case.

To resume our account of the right method of investigation: 1
We must start by observing a set of similar i. e. specifically
identical individuals, and consider what element they have
in common. We must then apply the same process to
another set of individuals which belong to one species 2 and
are generically but not specifically identical with the former
10 set. When we have established what ;! the common element
is in all members of this second species, and likewise in
members of further species, we should again consider whether
the results established possess any identity, and persevere until
we reach a single formula, since this will be the definition
of the thing. But if we reach not one formula but two or
more, evidently the definicndum cannot be one thing but
J? must be more than one. I may illustrate my meaning as
follows. If we were inquiring what the essential nature of
pride is, we should examine instances of proud men we
know of to see what, as such, they have in common ; e. g.

1 Aristotle resumes the discussion broken in 96 b 25 by the digression
on 8<m peo-ir and deals with the question of defining a yeVor.

2 Reading avrolt with A (?). 3 Reading ri mivTa.

b

BOOK II. 13 97

if Alcibiades was proud, or Achilles and Ajax were proud,
we should find, on inquiring what they all had in common,
that it was intolerance of insult ; it was this which drove
Alcibiades to war, Achilles to wrath, and Ajax to suicide. 20
We should next examine other cases, Lysander, for example,
or Socrates, and then if these have in common indifference
alike to good and ill fortune, I take these two results and
inquire what common element have equanimity amid the
vicissitudes of life and impatience of dishonour. If they
have none, there will be two genera 1 of pride. Besides, every 25
definition is always universal and commensurate : 2 the
physician does not prescribe what is healthy for a single eye,
but for all eyes or for a determinate species of eye. It is
also easier by this method to define the single species than
the universal, and that is why our procedure should be
from the several species to the universal genera this for
the further reason too that equivocation is less readily 30
detected in genera than in infimae species. Indeed, per
spicuity is essential in definitions, just as inferential move
ment 3 is the minimum required in demonstrations; and we
shall attain perspicuity if we can collect separately the
definition of each species 4 through the group of singulars
which we have established 5 e. g. the definition of similarity
not unqualified but restricted to colours and to figures ; 35
the definition of acuteness,but only of sound and so proceed
to the common universal with a careful avoidance of equivo
cation. We may add that if dialectical disputation must
not employ metaphors, clearly metaphors and metaphorical
expressions are precluded in definition : otherwise dialectic
would involve metaphors. 6

14 In order to formulate the connexions we wish to prove g8

1 tidy here must mean yivrj, an apparent reversion to Plato s in
discriminate use of the terms, and contrary to Aristotle s general
usage elsewhere.

2 This sentence explains why the absence of a common element
means that there are two genera : a definition, being commensurate,
cannot embrace subjects with nothing in common.

8 Reading o-vXXeXoyur$m, with B and Waitz.

4 yii here must be equivalent to *i8ei, cf. note on 97 l>2 5 t

5 Reading tl\rinp,iv<ov for ilpriiuvwi ; cf. 97 b 12.

6 sc. as sometimes involving definition.

g8 a ANALYTICA POSTERIORA

we have to select our analyses and divisions. 1 The method
of selection consists in laying down the common genus of
all our subjects of investigation if e.g. they are animals,
we lay down what the properties are which inhere in every
animal. These established, we next lay down the properties
5 essentially connected with the first of the remaining classes 2
e.g. if this first subgenus is bird, the essential properties
of every bird and so on, always characterizing the
proximate subgenus. 3 This will clearly at once enable us
to say in virtue of what character 4 the subgenera man,
e. g., or horse possess their properties. Let A be animal,
10 B the properties of every animal, C D E various species of
animal. Then it is clear in virtue of what character />
inheres in D namely A and that it inheres in C and E
for the same reason: and throughout the remaining subgenera
always the same rule applies.

We are now taking our examples from the traditional
class-names, but we must not confine ourselves to considering
these. We must collect any other common character which
1 5 we observe, and then consider with what species it is
connected and what properties belong to it. For example,
as the common properties of horned animals we collect the
possession of a third stomach and only one row of teeth.
Then since it is clear in virtue of what character they possess
these attributes namely their horned character the next
question is, to what species does the possession of horns
attach ?

20 Yet a further method of selection is by analogy : for we
cannot find a single identical name to give to a squid s
pounce, a fish s spine, and an animal s bone, although these

1 avaTonri seems to mean that analysis of a subject, for the purpose of
eliciting its properties, which would precede the process of division
exhibiting the true generic character in virtue of which the subject
possesses those properties. Bonitz, however, takes it as equivalent to
8iaipfa-is (Index s. v.).

2 i. e. the subgenera. Cf. the previous chapter.

3 Placing commas after Spvidt a 6 and eyyvrnra a 7.

4 Aristotle in this chapter is explaining how to select the true
primary subject cf. i, 4 ad fin. of a property ; not how to find the
middle term with which he deals, e.g., in cc. I 5-18 and Sia ri here
means quatenus^ not propter quod.

BOOK II. 14 9 a

too possess common properties as if there were a single
osseous nature.

Some connexions that require proof are identical in that
they possess an identical middle 1 e. g. a whole group
might be proved through reciprocal replacement and of 25
these one class are identical in genus, namely all those whose
difference consists in their concerning different subjects or
in their mode of manifestation. This latter class may be
exemplified by the questions as to the causes respectively of
echo, of reflection, and of the rainbow : the connexions to
be proved which these questions embody are identical gene-
rically, because all three are forms of repercussion ; but
specifically they are different.

Other connexions that require proof only differ in that
the middle of the one is subordinate to the middle of 3
the other. For example : Why does the Nile rise towards
the end of the month ? Because towards its close the
month is more stormy. Why is the month more stormy
towards its close ? Because the moon is waning. Here the
one cause is subordinate to the other.

The question might be raised with regard to cause and 35
effect whether when the effect is present the cause also is
present ; whether, for instance, if a plant sheds its leaves or
the moon is eclipsed, there is present also the cause of the
eclipse or of the fall of the leaves the possession of broad
leaves, let us say, in the latter case, in the former the Q8 b
earth s interposition. 3 For, one might argue, if this cause is
not present, these phenomena will have some other cause :
if it is present, its effect will be at once implied by it the
eclipse by the earth s interposition, the fall of the leaves by
the possession of broad leaves ; 4 but if so, they will be
logically coincident and each capable of proof through the
other. Let me illustrate : Let A be deciduous character, 5

1 vide note on S9 b 38.

2 Cf. Waitz ad loc.

3 Placing a dash instead of a full stop after f<rtai in a 38.

4 Placing a colon instead of a full stop after <pv\\oppo{l in b 4.

g8 b ANALYTICA POSTERIORA

B the possession of broad leaves, C vine. Now if A inheres
in B (for every broad-leaved plant is deciduous), and B in C
(every vine possessing broad leaves) ; then A inheres in C
(every vine is deciduous), and the middle term B is the

10 cause. But we can also demonstrate that the vine has
broad leaves because it is deciduous. Thus, let D be broad-
leaved, E deciduous, F vine. Then E inheres in F (since
every vine is deciduous), and D in E (for every deciduous

15 plant has broad leaves) : therefore every vine has broad
leaves, and the cause is its deciduous character. If, 1 how
ever, they cannot each be the cause of the other (for cause
is prior to effect, and the earth s interposition is the cause of
the moon s eclipse and not the eclipse of the interposition) 2
if, then, demonstration through the cause is of the

20 reasoned fact and demonstration not through the cause is
of the bare fact, one who knows it through the eclipse
knows the fact of the earth s interposition but not the
reasoned fact. Moreover, that the eclipse is not the cause
of the interposition, but the interposition of the eclipse, is
obvious because the interposition is an element in the
definition of eclipse, which shows that the eclipse is known
through the interposition and not vice versa.

2 5 On the other hand, can a single effect have more than
one cause ? One might argue as follows : if the same
attribute is predicable of more than one thing as its primary
subject, let B be a primary subject in which A inheres, and
C another primary subject of A, and D and E primary
subjects of B and C respectively. A will then inhere in D
and E, and B will be the cause of A s inherence in D, C
of A s inherence in E. The presence of the cause thus

30 necessitates that of the effect, but the presence of the effect
necessitates the presence not of all that may cause it but
only of a cause which yet need not be the whole cause.

1 Here begins Aristotle s answer.

2 The parenthesis should evidently continue to tK\(intiv in b 19 and
be followed by a dash. The construction is an anacoluthon : Aristotle
instead of continuing Km . . . breaks off and starts again, and ends
with an apodosis which is the consequent of the second clause ;
though his real conclusion that such demonstration is not circular
because demonstration through the effect is only of the bare fact is
wider, and follows from both clauses.

BOOK II. 16 g8 l

We may, however, suggest 1 that if 2 the connexion to be
proved is always universal and commensurate, not only
will the cause be a whole but also the effect will be universal
and commensurate. For instance, deciduous character will
belong exclusively to a subject which is a whole, and, if this
whole has species, universally and commensurately to those
species i. e. cither to all species of plant or to a single
species. So in these universal and commensurate con- 35
nexions the middle and its effect must reciprocate, i. e. be
convertible. Supposing, for example, that the reason why
trees are deciduous is the coagulation of sap, then if a tree
is deciduous, coagulation must be present, and if coagulation
is present not in any subject but in a tree then that tree
must be deciduous.

17 Can the cause of an identical effect be not identical in gg s
every instance of the effect but different? Or is that
impossible ? Perhaps it is impossible if the effect is
demonstrated as essential and not as inhering in virtue
of a symptom or an accident because the middle is then
the definition of the major term though possible if
the demonstration is not essential. Now it is possible
to consider the effect and its subject as an accidental con- 5
junction, though such conjunctions would not be regarded
as connexions demanding scientific proof. But if they are
accepted as such, 3 the middle will correspond to the extremes,
and be equivocal if they are equivocal, generically one if
they are generically one. 4 Take the question why pro
portionals alternate. The cause when they are lines, and
when they are numbers, 5 is both different and identical ;
different in so far as lines arc lines and not numbers,
identical as involving a given determinate increment. In 10
all proportionals this is so. Again, the cause of likeness
between colour and colour is other than that between figure
and figure; for likeness here is equivocal, meaning perhaps

1 Here begins Aristotle s answer.

2 Really equivalent to emi, but is more consonant with the tentative
form in which Aristotle offers his solution.

3 i.e. if an accidental connexion is accepted as a T

4 We should perhaps read Zv for V in a 7.
6 Placing a comma after apiOpms in a 9.

eis-i4-4 I

99 ANALYTICA POSTERIORA

in the latter case equality of the ratios of the sides and
equality of the angles, in the case of colours identity of the

15 act of perceiving them, or something else of the sort.
Again, connexions requiring proof which are identical by
analogy have middles also analogous.

The truth is that cause, effect, and subject are reciprocally
predicable in the following way. If the species are taken
severally, the effect is wider than the subject (e. g. the
possession of external angles equal to four right angles is
an attribute wider than triangle or square), but it is co-

20 extensive with the species taken collectively (in this instance
with all figures whose external angles are equal to four right
angles). And the middle likewise reciprocates, for the
middle is a definition of the major ; which is incidentally
the reason why all the sciences are built up through defini
tion.

We may illustrate as follows. Deciduous is a universal
attribute of vine, and is at the same time of wider extent
than vine ; and of fig, and is of wider extent than fig : but
it is not wider than but coextensive with the totality of the

a? species. Then if you take the middle which is proximate, 1
it is a definition of deciduous. I say that, because you will
first reach a middle 2 next the subject, 3 and a premiss assert
ing it 4 of the whole subject, and after that a middle the
coagulation of sap or something of the sort proving the
connexion of the first middle with the major : 5 but it is the
coagulation of sap at the junction of leaf-stalk and stem
which defines deciduous. 6

1 sc. to TO $>v\\oppo(~iv, the major. 2 sc. broad-leaved.

3 Vine, fig, &c. 4 One should perhaps read o n.

5 Broad-leaved with deciduous.

6 Aristotle contemplates four terms: (i) deciduous, (2) coagulation,
(3) broad-leaved, (4) vine, fig, &c.

If we get the middle proximate to (i) it is a definition of (i).
But in investigating vines, figs, &c. according to the method of
chapter 13, we shall first find a common character of them in broad-
leaved, and, taking this as a middle, we shall prove that vine, fig,
c., qua broad-leaved, are deciduous. But this proof is not demonstra
tion, because broad-leaved is not a definition of deciduous. So our
next step will be to find a middle coagulation mediating the major
premiss of this proof, and demonstrate that broad-leaved plants, qua
liable to coagulation, are deciduous. This is strict demonstration,
because coagulation defines deciduous.

BOOK II. 17 99*

If an explanation in formal terms of the inter-relation of 30
cause and effect is demanded, we shall offer the following.
Let A be an attribute of all />, and B of every species of D,
but so that both A and B are wider than their respective
subjects. Then B will be a universal attribute of each
species of D (since I call such an attribute universal even
if it is not commensurate, and I call an attribute primary
universal if it is commensurate, 1 not with each species
severally but with their totality), 2 and it extends .beyond
each of them taken separately. Thus, B is the cause of A s 35
inherence in the species of D : consequently A must be of
wider extent than B ; otherwise why should B be the cause
of A s inherence in D any more than A the cause of fi s
inherence in D ? Now if A is an attribute of all the species
of E, all the species of E will be united by possessing some
common cause other than B : otherwise how shall we be
able to say that A is predicable of all of which E is
predicable, while E is not predicable of all of which A can 99 b
be predicated ? I mean how can there fail to be some
special cause of A s inherence in E, as there was of A s
inherence in all the species of D ? 3 Then are the species
of E, too, united by possessing some common cause ? This
cause we must look for. Let us call it C,^

We conclude, then, that the same effect may have more
than one cause, but not in subjects specifically identical.
For instance, the cause of longevity in quadrupeds is lack of 5
bile, in birds a dry constitution or certainly something
different.

18 If immediate premisses are not reached at once, and there

1 But cf. i, ch. 4, 73 b 2i-74 a 3.

2 The parenthesis should clearly terminate at avucrrptfai a 35.

3 Reading rov TO A inrdp^eiv in h 2.

* The schema of Aristotle s argument in this paragraph is :

A

C

5 It seems best to begin this chapter at d 8( els . . . b 7, and place a
comma after n\ti<a in b 8. The Se after nnrtpov in b 9 will then be
roughly parallel to e. g. Pol. iii. 16, I287 b 13 (cf. Bonitz, Ind. s. v.),
though the apodosis is not here an antithesis.

I 2

gg b ANALYTICA POSTERIORA

is not merely one middle but several middles, i. e. several
causes ; is the cause of the property s inherence in the
several species the middle which is proximate to the primary
:o universal, 1 or the middle which is proximate to the species ? 2
Clearly the cause is that nearest to each species severally
in which it is manifested, for that is the cause of the subject s
falling under the universal. To illustrate formally : C is
the cause of s inherence in D ; hence C is the cause of
A s inherence in D, B of A s inherence in C, while the cause
of A s inherence in B is B itself.

15 As regards syllogism and demonstration, the definition 19
of, and the conditions required to produce each of them, are
now clear, and with that also the definition of, and the
conditions required to produce, demonstrative knowledge,
since it is the same as demonstration. As to the basic
premisses, how they become known and what is the developed
state of knowledge of them is made clear by raising some
preliminary problems.

20 We have already said 3 that scientific knowledge through
demonstration is impossible unless a man knows the primary
immediate premisses. But there are questions which might
be raised in respect of the apprehension of these immediate
premisses: one might not only ask whether it is of the
same kind as the apprehension of the conclusions, but also
whether there is or is not scientific knowledge of both ;
or scientific knowledge of the latter, and of the former a
different kind of knowledge ; and, further, whether the

25 developed states of knowledge are not innate but come to
be in us, or are innate but at first unnoticed. Now
it is strange if we possess them from birth ; for it means
that we possess apprehensions more accurate than de
monstration and fail to notice them. If on the other
hand we acquire them and do not previously possess them,
how could we apprehend and learn without a basis of pre-
existent knowledge? For that is impossible, as we used

30 to find 4 in the case of demonstration. So it emerges that
. neither can we possess them from birth, nor can they come

1 i.e. the property. 2 the subject. " i, ch. 2. 4 i, ch. I.

BOOK II. 19 99 b

lo be in us if we arc without knowledge of them to the extent
of having no such developed state at all. Therefore we must
possess a capacity of some sort, but not such as to rank
higher in accuracy than these developed states. And this
at least is an obvious characteristic of all animals, for they
possess a congenital discriminative capacity which is called 35
sense-perception. But though sense-perception is innate in
all animals, in some the sense-impression comes to persist,
in others it does not. So animals in which this persistence
does not come to be have either no knowledge at all outside
the act of perceiving, or no knowledge of objects of which
no impression persists ; animals in which it does come into
being have perception and can continue to retain the sense-
impression in the soul : and when such persistence is ioo a
frequently repeated 1 a further distinction at once arises
between those which out of the persistence of such sense-
impressions develop a power of systematizing them and
those which do not. So out of sense-perception comes to
be what we call memory, and out of frequently repeated
memories of the same thing develops experience ; for a 5
number of memories constitute a single experience. 2 From
experience again i.e. from the universal now stabilized in
its entirety within the soul, the one beside the many which
is a single identity within them all originate the skill of
the craftsman and the knowledge of the man of science,
skill in the sphere of coming to be and science in the sphere
of being.

We conclude that these states of knowledge are neither
innate in a determinate form, nor developed from other 10
higher states of knowledge, but from sense-perception. It
is like a rout in battle stopped by first one man making a
stand and then another, until the original formation has
been restored. The soul is so constituted as to be capable
of this process.

Let us now restate the account given already, though
with insufficient clearness. When one of a number of 15
logically indiscriminable particulars has made a stand, the

1 Reading ytvoptvuv with D in loo a i.

1 Cf. Met. A 980"* 28. Met. A i should be compared with this chapter.

ioo a ANALYTICA POSTERIORA

earliest universal is present in the soul : for though the act
of sense-perception is of the particular, its content is uni-
ioo b versal is man, for example, not the man Callias. 1 A fresh
stand is made among these rudimentary universals. and the
process does not cease until the indivisible concepts, the
true universals, 2 are established : e. g. such and such a species
of animal is a step towards the genus animal, ;; which by the
same process is a step towards a further generalization.

Thus it is clear that we must get to know the primary
premisses by induction ; for the method by which even sense-
5 perception implants the universal is inductive. Now of the
thinking states by which we grasp truth, some are unfailingly
true, others admit of error opinion, for instance, and calcu
lation, whereas scientific knowing and intuition 4 are always
true : further, no other kind of thought except intuition is
more accurate than scientific knowledge, whereas primary
premisses are more knowable than demonstrations, and all
10 scientific knowledge is discursive. From these considerations
it follows that there will be no scientific knowledge of the
primary premisses, and since except intuition nothing can
be truer than scientific knowledge, it will be intuition that
apprehends the primary premisses a result which also follows
from the fact that demonstration cannot be the originative
source of demonstration, nor, consequently, scientific know
ledge of scientific knowledge. If, therefore, it is the only
other kind of true thinking except scientific knowing, intuition
15 will be the originative source of scientific knowledge. And
the originative source of science grasps the original basic
premiss, while science as a whole is similarly related as
originative source to the whole body of fact. 5

1 Removing the brackets, reading a colon after Ka6u\ov a 16 and
a full stop after KaXXiou uvBpa-nov in *> I.

2 i.e. the categories, which are par excellence universal and are
indivisible because not constituted .of genus and differentia, cf. Met.
io84 b 14 and 1023 24. For this sense ofcififptj cf. the use of royna in
Met. 994 b 21.

3 Following fcos- (war with a comma.

4 Cf. note on 85* I. 6 i.e. the conclusions.

INDEX

i a I I5 b 33 = Categoriae.

l6 a I 24 b 9 = De Interpretation,
24 a 10 ;o b 38 = Analytica Priora.
71 a I loo 1 17 = Analy tica Posteriora.

Accident, v. Attribute.

Achilles 97 b i8.

Action 2 a 4, i i b 1-7.

Affection i b 27, 2 a 4, 9 a 28-io a 10,

ii b i-7; of the soul o, b 34 ;

a. as distinct from qualities ib.

29

Affective qualities 9*28.

Affirmation ) negation 2 a 5, li h
19, I2 b 6, i3 a 37- b 35, i/ a S,
I9 b i2, 72 a 13, def. 17" 25.

Alcibiades 97 h i8.

All, meanings of 74 a 30-2.

Alteration, distinct from other
forms of motion I5 a i4.

Alternation 74 a 16-25, 99*8-10.

Anacharsis 78 b 30.

Analogy 76 a 38, 98 a 20-3, 99 a 15.

Analysis (dvaXvtw, afaXvo-ts) of rea
soning into the three figures of
syllogism 4/ a 4, 5O a 8 ; hypo
thetical arguments not reso
luble into the figures 5o a 30,
b 3 ; of syllogisms in one figure
into another ib. 30, 33, 5i a 2,

1 8 ; of premisses into terms 49 a

19 ; analytic ) dialectical proof
(ava\VTiKuis ) Ao-yiKws) 84 a "J , b 2 ;
analysis (cmiro/ir/) 98 a 2.

Appropriate, premisses appropri
ate to (homogeneous with) con
clusion 7i b 23, 72 a 6, 74 b 26, 75 b
38, 76 a 6, and An. Post, passim.

Aristomenes 47 b 22.

Aristotle, references to Cat. 49*
7(?); An.Pr. I9 b 3i,73 a 8, 14,
77 a 3S, 8o a 7, 86 b io, 9i b 13,
96 a i ; An. Post. 24 b 14, 25 b 27,
32 b 23, 43 a 36 ; Top. 2o b 26, 24 b
12, 46 a 30, 47 a I7,64 a 37; Soph. \
El. 2o b 26, 6s b i6; Phys. 95
ii ; De An. i6 a 8 ; Met. 6
26 (?).

Arithmetic, assumptions of 76 b 8,
93 b 24 ; more accurate than
Geometry v more abstract 87*
33 ; differs generically from
Geometry 75 a 39, b 3. Cf.
Science,

Art (reV?) 89 b S, IOO a 8.

Article, definite 49 b io.

Assumptions of a science, (a) fact,
(b) meaning, (c) meaning and
fact 71* 12-16, 76 b 3i-6, go b 24;
not expressly assumed 76 b 15-

20, 7 7 a 1 0-25. Cf. Axioms,
Demonsh ation, Mai hematics.

Astronomy 76 b 1 1 ; relation of
science to experience 46 a i9;
mathematical Y nautical 78 b
40.

Athenians 69 a I, 94 a 37.

Atomic disconnexion 79 a 33~ b 22.

Attribute 2 a 34, 43 b 3, 41 ; predic-
able of a subject l a 20, 2 a 19 ;
present in a subject 1*23, 2 a
27; true in every instance
(<aru irnvTos) 73* 28-34 ; essen
tial, defined as (i) = element in
definition of subject, (ii) contain
ing its subject in its definition
(cf. 75 b i), in some cases as pair
of disjunctive opposites, (iii)
in respect of singular sub
stance, (iv) consequentially con
nected 73 a 34- b 24; type (ii)
limited in number 82 b 39, 84*

21, commensurate with subject
84 a 24; (ii) and (iii) 74 b 7-10, 84 a
12-17 : commensurate and uni
versal (Kado\ov) 73 b 26 74 a 3,
elicited from singulars 7i a 2o,
8i a 4, makes clear the cause
88 a 5 : accident or coincident
(<rvp.p(p,]K6s) 73 b 4, 75 a 18-21 ;
X essentia type (ii) 83"* 25-32,

INDEX

b 20 ; never a subject ({nroKeifj.f-
rov) 83 b 22, but designated as
qualifying a subject 83 23. Cf.
Assumptions.

Axioms, defined 72*16-18; ;.
hypotheses 76^ 23 ; community
of sciences through 77*26-31;
as Laws of Thought , not
universal premisses 88 a 36- b 3 ;
excluded middle 7i a 14, 72 b 23,
express assumption of 7 7 a 22-5 ;
law of contradiction, express as
sumption of 77 a 10-21 ; quan
titative axioms, function in
demonstration 75 a 39, b 3~5
76*42, b io, 14, 77*27- 3 t,S8 b
28. Cf. Assumptions, Demon
stration.

Basic truth (ap%i)), in wide sense
76 a 3i ; common X peculiar 76 a
37~ b 5, 88 b 27 ; individual s
knowledge of 99 1 15 ioo b 17.
Cf. Premiss.

Being, in unqualified sense
possessing an attribute 89 b 33,
90*9-14, 32; (essence v not
a genus 92 b i4: non-existents
nameable 92 b 30.

Better known, two senses of 7i b
33 72*5.

Bryson 75 b 4o.

Caeneus 77*41.

Callias43 a 27, 77* 17, 83 b 4, ioo b i.

Callippus l6 a 21.

Capacity, indicated by qualitative
terms 9 a 15.

Case 6 b 33, i6 b I ; terms to be
stated in nominative, but pre
misses to be understood with
reference to cases of terms
48 b 40.

Categories io h 2i, 49 a 7, 83*21,
83 b i 4-1 7; enumerated and illus
trated I b 25 2 a 4.

Cause, premisses cause of conclu
sion 7i b 22; reasoned know
ledge of conclusion is through
cause passim ; higher knowledge
through higher cause 76*18;
proximate cause 78 b 4, 15, 99
9-14; (a) identical with, (b)
distinct from essential nature
93*5, b 2i-8; ) chance 95*
3-9 ; as middle term, formal

93 a I ff., 94*5, material 94*
24-35, efficient 94 a 36- b 8, final
94 b 8-26 ; final and material
may mediate one connexion
94 b 27-37; cause and effect as
reciprocal 78 a 27, 98*35 99 b S,
non-reciprocal 78^12, 98*35
99 h 8, simultaneous 95*10-24,
98*35- b 24, successive 95*24-
b 37, circular 95 b 38 96 a 7 ;
plurality of causes g8 b 25-38,
of effects 99* i- b 8. Cf. Middle
term.

Chance conjunctions not demon
strable 87 b 19-27 ; ( necessity
and final cause 95*4.

Circular proof 57 b 18 59* 41 ;
denned 57 b i8, 58*33.

Cleon 43*26.

Close-packing (TTVKVUMTIS) 79* 30,

82 b 7, 84*34-9, 8 4 b 35-

Coincident, v. Attribute.

Combination of predicates 2O b 3i.

Conclusion 32*6-14, 42 b 4; of
demonstration necessary 73 b
13-18 ; reveals attribute as in
hering as such 75 b 38, as essen
tial, as eternal 75 b 22; homo
geneous with basic premisses
76* 30 ; reciprocal with pre
misses 78* 10. Cf. Attribute,
Cause, Demonstration, Premiss,
&c.

Concrete and abstract terms 47 b
4048*28.

Connexion for proof (Trpo/SX^a)
88* 12, (87 b 5); how to select
98* 1-23 ; community of middle
in ib. 24-34.

Consequential connexion 75*37.
Cf. Attribute.

Contiguous (e ^ojufj/of) 82 a I, 95 b

3-25-

Contingency 32* i6- b 37 ; contra
dictory of propositions express
ing 21 b 10.

Continuous 4 b 2O.

Contradiction 17*33, 1>2 6, 72 a 12-
14, 73 b 2i, 93 a 34-

Contradictory propositions I7 b 17,
20*30,21*30; contradictories
of contrary propositions 20*
16.

Contrary of a proposition I7 b 45
is it a denial or a contrary
affirmation? 23* 27 24 b g; con
traries 4* 10, 6 a i, 17, Ii b 34

INDEX

12*25, I3 1> 36 14* 25 ; con
traries, existing in case of
qualities lo b 12, of relations 6 b
15, of actions n b I, not of sub
stances 3 b 24, nor of quantities
3 b 29, 5 b li ; with and without
intermediates I2 a I.

Conversion, of propositions, asser-
toric 2j a 5, apodictic ib. 27,
problematic ib. 37, 32 a 3o, 3o b
35; of syllogisms 59 b I 6i a 16;
defined 59 b i, 6i a 5 ; reductio
ad impossible 6l a 21 ; of terms
of syllogism 67 b 27 68*25.

Conviction, degree required by
science 72 a 37~ b 4. Cf. Opinion.

Copula 24 b 17, 25 b 22, 32 b I.

Coriscus S 5 a 24.

Correlation 6 b 6, 28, 7*20, 8 a 35 ;
coining names to express 7 a 5 ;
importance of correct termino
logy 6 b 36.

Conelatives ll b 17-33 5 appre
hension of one of pair involves
that of the other 8*35.

Definition 43 b 2, 5o a II ; nominal
7i a l3, 93 b 29~3i : real (a) of
substance, (b) of attribute 75 b
31, 93 b 32 94 a 13 : def. of sub
stance is premiss of demonstra
tion 75 b 3i; = commensurate
synthesis of attributes 96 a 24-
b 14 ; not demonstrable 90*6
9i a n, 9i a i2- b ii, 92 b 4-38,
even hypothetically 91*6-33 ;
not inferred by division 9i b
12 92 a 5 ; method of obtain
ing 96 b i5-24, 97 b 7~34; aid
lent by division 96 b 25 97 b 6:
def. of attribute, how revealed
by demonstration 93 a 3- b 2O, 94"
1-9, dialectically 93 a l5~ b 2o:
def. (as a unity) does not assert
76 b 30, is neither universal nor
particular 77 a 4; (as predicated)
commensurate and universal
97 b 26 ; only possible if ele
ments of definiendum are
limited 82 b 38, 84* 26 ; need of
perspicuity in 9/ b 32 ; hypo
thesis 73*21-4, 76 b 35-77* 4 ; ;.
induction 92* 37-** I ; growth
of science through 99* 22. Cf.
Assumption, Attribute, Cause,
Middle term, Species.

Degree, variation of, in substance
3 h 33, in quantity 6 a 19, in
quality io J 26.

Demonstration 24*11, 25 b 27, 32 b
18, 4o b 23; demonstrative pre
miss ( dialectical 24 a 22 ; de
fined as syllogism giving scien
tific knowledge 7i b i8, as pro
ceeding from necessary pre
misses 74 b 16-18, as involving
necessary middle term 75* 13,
76 a 5, as necessarily involv
ing natural predication 83* 20 ;
unit of 84 b 6 85*1 ; elements
of 75 a 39- b 2, 76 b ii-22; con
fined to one genus 75 b 3-u,
84 b 17 ; transference possible
only in case of subalternate
sciences 75 b 14, 76* 22-5 ;
vicious transference of 75
4076*3, 8S a 3i-6; as (
definition is continuous 94 a 6;
commensurate and universal
73 b 32 74 a 3, 74* 32- b 4,
wrongly supposed commen
surate and universal 74* 4-32 ;
universal particular 85 a 13,
20 86 a 3o; affirmative ) nega
tive 86* 32- b 39 ; circular and
reciprocal 72 b 17, 72 b 25 73*
20, 9i a 35- b n; possibility of
several demonstrations of one
connexion 87 b 5-18 ; no demon
stration of accidents 75 a 18-21,
31-3, nor of chance conjunc
tions 87 b 19-27. Cf. Definition,
Knowledge, Predication, Re
ductio ad impossible,

Denial, def. 17" 25.

Derivatives i a 12, io a 27.

Desirable 68*25- b 7.

Dialectic 24 a 22, 46*30, 65*37,
71*5, 22-7; its method inter
rogative X demonstration 77*
31-4; dialectic X strict proof
8 i b 18-23, 84*7, 84 2, 86*21,
88*19, 30; dialectical ques
tion 2O b 22-30. Cf. Proposition,
Syllogism.

Dictum de otuni et nullo 25 b 32.

Differentia i b 17, 3 a 22, 74 a 37- b 3,
83 b i, 96 b 12, 20, 25 97 b 6.

Disjunction 73 b 2i-4, 78 b 17-20.

Disposition b b 27, 35, 11*22.

Distinctive mark of substance 4*
10, of quantity 6* 26, of quality
11* 18.

INDEX

Distributed subject I7 b 14.

Division 46 a 3i- b 37; proper use
of 9i b 29-32 ; not inference 9i b
12, 36, 96 b 25 -97 b 6. Cf. De
finition.

Eclipse 7 5 a 34, 88 a 1 , 89 b 30, 90* 3,

3, 93 a 23, 3. 37, 9& b i8.
Enthymeme 7o a 3~ b 38, 7i a io;

defined 7o a 10.
Enunciation 72 a li.
Equality 6 a 26.
Equivocal i a i,7/ a 9, b 24, 8$ b II,

1 6, 97 b 36, 99 a 7-

Eretria 94 b I.

Error 66 b 18 67 b 26, 77 b 18-33 ;
positive ). nescience as direct
belief 79 b 26-8 : as inferential,
in atomic connexion or discon
nexion, affirmative 79 b 23 8o a
7, negative 8o a 7~ b 16 ; in me
diate conn, or disconn., nega
tive 8o b 16 8l a 14, affirmative
8i a 16-34 ; as formal fallacy 77 b
20-33 > rare m Maths. 77 b 27-
33 ; due to taking mere attribute
as middle 77 b 40 78 a i3; as
material fallacy 77 b 2l.

Essential nature, v. Definition.

Event, atomic 96 a 1-7.

Example (TrapaSfiy^n) 68 b 38
69 a 19, 7i a lo; ) induction
69" 1 6.

Excess, contrary of defect 14* 2.

Excluded middle i8 a 28 I9 b 4.

Existence, v. Being.

Experience (ffjurcipia) 46 a 18, ico a

5-9-

Exposition 28*23, 3 a 9- 3 1 ? 49
33-

Fact X reasoned fact 75 a 16, 76 a
11-13, 87 a 31 ; within one
science 78 a 22- b 3i; as be
longing to different sciences
78 b 32 79 a 16 ; in relation to
perception / knowledge 88 a I ;
both as object of opinion 89 a
15 ; when both are obvious to
perception 89 b 23-35, c,o a 25-
30, 93 a l7-20. Cf. Cause, De
monstration, Middle term.

Fallacy, v. Error.

False cause 65* 38 66 a 15.

Falsehood, falsity i6 a i2, 8S a 25-
30. Cf. Error.

P atality iS b 26 I9 b 4.

Features, inference of character
from 7o b 7.

Figure, first 25 b 26 26 b 33, def.
25 b 32, 26 b 33; second 26 b 34
28 a 9, def. 26 b 34; third 28*
10 29 a 1 8, def. 28 a lo; fourth
2 9 ftl 9> 53 a 3; common proper
ties of the three figures 29 a 19-
b 28 ; all syllogisms reducible
to universal moods of first figure
29 b I, 4o b i7-4i b 5; uses of
the figures 42 b 27 43* 19 ;
analysis of syllogisms in one
figure into another 5o b 5 ji b
2 ; three figures only 4i a 14.

Forms 79 a 7 ; Platonic 77 a 5, 83 a
33, 8s b 19.

Fortuitous, def. i8 b 8.

Genus, relative, individual not ii a
20; X species 96 b 2i~5; prior
to species I5 a 4; genera, co
ordinate i b 16, subordinate ib.
21. Cf. Subject, Demonstra
tion, elements of.

Geometry 75 b 12-14, I 7~ I 9> 77 a
4O- b 27 ; use of diagrams in
49 b 35 i its assumptions 76 b 9,
are not false 76 b 39 77 a 2 ;
differs generically from Arith
metic 75 a 39, b 3- Cf. Science.

Good ) the good 49 10.

Habit X disposition 8 h 27, 35, 9 a
4, Ii a 22.

Harmonics 75 b 16, 76 a 10, 76 a 24,
7& b 38 ; mathematical \ acous
tical 79 a I.

Have, uses of word I5 b 17-33.

Hypothesis 72*20-4; X axiom
y6 b 23-34; X definition 76 b 35
77 a 4 > X illegitimate postu
late 76 b 30-4 ; hypothetical rea
soning 4o b 25, 4i a 22, 50* 16,
72 b 13-15, 92*6-33; rule of
hypothetical reasoning 53 b i2,
57 b I. Cf. Rednctio ad impos
sible.

Ignorance, v. Error.
Iliad, the 92 b 32, 93 b 36.
Immediate propositions 48* 33,
68 b 30 ; immediately cohering
87 b 6.

INDEX

Impossibility, contradictory of pro
positions expressing 22 a 6.

Indefinite noun 16*32, I9 b 8, verb
l6 b 14, I9 b 10, premiss 24*19,
26 a 28 ; proof from indef. nature
of particular statement 26 b 14,
2/ b 2o, 28, 28 b 28,35 b ii ; =pos-
sible 32 b lo, 19. Cf. Infinite.

Individual i b 4, 3 a 35, I7 a 37, 40,

Induction 28 b 2i, 42 a 3, 67 a 23. 68 b
8-37, 69*16, 7i a 6, 10, 72 b 30,
77 b 35, 78*35, 8i b 3, 9o b 14 ;
gives grasp of universal 8i b 2,
loo b 4; conn, with sense-per
ception 8i a 38- b 9 ;

stration 91 35;

demon
definition

Infinite proposition, an affirma
tion 25 b 22, 5i b 31, 52 a 24. Cf.
Indefinite.

Instances, proof by taking 26* 8,
30* 28, 3i b 4. 33 b 3, 49 b 33.

Intuition (i/oOs) 85 a I, 88 a 7, 16,

35,

ioo b s-i7. Cf.

Knowledge, Demonstration.
Inversion of subject and predicate

20 b I.

Isosceles triangle, proof of equality
of angles at base 4i b 14.

Knowledge 67^ 4 ; of universal (
particular 67 a 17 ; kn. pre-exis-
tent, dependence of instruction
on 7i a i-n, two kinds of a 11-
b 8 ; discursive (SiaVom) 89 b 7 ;
scientific kn. (tifurriiiui), its ob
ject immutable 7l b 15, its truth
necessary 73 a 21, based on ap
propriate premisses 76 a 27,
accidental kn. = kn. through
cause 7i b 9-i2, 74 b 23, 26-39,
76 a 4-6, = kn. of definition 93 a
20-6, 94 a 20, suggested impos
sibility of 72 b 5-i5 ; ) intuition
99 b 5 I0 b !7 i X sense-per
ception 87 b 28 88 a 17, 99 b 15
loo b 17 ; ; opinion 88 b 30 89
6; unqualified ; universal 7 i u
28, } hypothetical 83 b 38 ; as
state (is) 99 b 18 loo b 17 ;
growth of in individual soul ib. ;
? innate ib. ; ? all kn. demon
strable 72 b 6, 15-18, 84*31 ; kn.
of basic premisses (vovs) 72 b 24,
is prior and superior to kn. of
conclusion 72"* 26, indemon

strable and source of demon
stration 72 b i8-24, 84 a 3i, 9o b 25
and passim. Cf. also Demon
stration, Intuition.

Limit as genus of figure /4 b I.

Line, a quantity 5 a 17.

Love 68 a 39.

Lunules, squaring of circle by

means of 69 a 33.
Lysander 97 b 21.

Major term 26^22, b 37, 2S a i3;
wider than middle 77 a 18. Cf.
Middle term.

Mathematics, nature of 79 a 7-9,
8i b 4, 93 b 24; its teaching de
pends on previous knowledge
7i a 3, on induction 8i b 3; for
mal fallacy rare in 77 b 27-33;
) dialectic 78 a 12. Cf. Arith
metic, Geometry, Stereometry,
Science.

Mechanics 76 a 24, /8 b 39.

Medicine 77 a 4i, 79 a 14.

Memory, developed from sense-
perception 99 b 36, into experi
ence ioo a 3-6.

Metaphor 97 b 37-

Metaphysics (<ro(/>i a) 8g b 8.

Miccalus 47 b 30.

Middle term 4i a 3, 47 a 38 b l4;
homogeneous with extremes
( appropriate ) 75 b lo, 8o b 18-
21, 8i a i7, 84 b i5, 93 a lo; in
causal inference 95* 36-9;
necessary ; contingent 74 b 26
a i2, 75 a i7, 76 a s; as cause
7S b 4, 89 b 36 9o a ^passim, 93*
3-8; defines major term 93 b 6,

defines minor tetm 72 b 24 ; de
fined by major term 94 b 2i.
Cf. Cause, Close-packing, De
monstration, Fact, Predication,
Quick wit.

Minor term 26 a 2^ b 38, 28 a 14.
Cf. Middle term.

Modality 2i a 34 23*26, 25 a 1, 29
29, 32 a 15, 34 a 5 ; modal syllo
gisms 29 b 29 40 b i6, 45 b 2S-

Movement, kinds of 15*13-33;
contrary of 1 5 b I .

Natural 32 b 5, 16, 7o b S.

Necessary, v. Attribute, Demon
stration, Premiss, &c.

Necessity, contradictory of pro
positions expressing 2i b 26, 22 a
3; in inference 24 19, 26 a 3,
47 a 33, 53 b i8, 57 a 4o, 62 a u ; j
in conversion 25 a 5 ; two kinds !
of 94 b 37 ; necessary ; possible I
32 !l i8, 28; nothing n. follows ;
from single statement 34 a i7, j
4 b 35> 53 bj 6; conversion of [
n. propositions 25 b 2/; syllo- [
gisms with two n. premisses |
29 29 3c a 14 ; with one pure
and one n. premiss 30* 15 32 a
5 ; with one contingent and one
n. premiss 35 b 23 36 25, 38"
13 39 a 3, 4o a 4- b i6; conclu
sion n. though only one premiss
n. 3o a 15, b 9, 32*7.

Negation ,( affirmation I3 a 37~
b 35. I7 a 9, 25, 72*14.

Negative term 5i 5 52 b 34.

Nile 98*31.

Noun def. i6 a i9; composite ib.
23 ; indefinite ib. 30 ; cases of
i6 b i.

Number 4 b 23.

Objection (eWrncrir) 69*37 7o a 2,
73 a 33, 74 b 19-21, 76 b 26, 77 b !

34-9-
Opinion 4 a 23, 66 b i9; defined !

8g a 4 ; X knowledge 88 b 30

8g b 6 ; true false 89 a 24-32.

Cf. Fact.
Opposite, four uses of term n b

16 I3 b 35 ; o. propositions, six

pairs of I9 b 24 2o a 3.
Opposition 27 * 29, 59 b 6, 63 b 24;

of propositions ig b 5 2o b 10 ;

of problematic and apodictic

propositions 32 a 22, 37 a 9.
Optics 75 b -*6, 76 a 24, 77 a 2, 78 b 37.
Ostensive proof 4O b 3O; ;( red^tc-

tio ad impossibile 29" 31, 45 a

26, 36, 62 b 29 63 b 22.

Particulars ioo a i5 b i; objects
of sense-perception X science
8i b 1-9. Cf. Universal, Sense-
perception.

Peculiar (iSio?), v. Property; ap
plied to elements in essential
nature 9l a 15, 92 a 8.

Perception, v. Sense-perception.

Persian war 94" 36.

Petitio principii 4i b 8, 64 28

65*37.
Phocians 69 a 2.

Pittacus 70* 1 6. 26.

Place 2 a i, ii b ii.

Plato, reference to Aleno 67 a 2i,
7l a 29, (Euthydemus) 74 b 23,
(J heaetetus] /6 b 25; method
of division 46 a 31. Cf. Forms.

Position 2 a 2, Ii b 9.

Positive privative I2 a 26 I3 a
36.

Possibility 2i a 35, b i2, 23 a 7, 32 a
i6- b 37, 36 b 2637" 18 ; def.
32 a 1 8, cf. 33 b 30, 34 b 27 ; mean
ings of 22 a i5, 25 a 37, b i5, 3i ! >
*> 32 b 4, 33 a 3 37 a IS! conver
sion in mode of 25 a 37, 32 a 29,
33 a 8, 35 b 35 ; syllogisms with
two contingent premisses 32 b

4- b 6 ; with one contingent
and one pure premiss 33 b 25
35 b 22, 37 b 19-38* 12, 39"7
4o a 3 ; with one contingent and
one necessary premiss 35 b 23
36 b 25, 38 a 13 39 a 3, 4o a 4-
b i6.

Postulate, illegitimate hypothesis
76 b 23, 30-4.

Potentiality, various senses of 22 b
36 23 a i8.

Practical wisdom (fywvr/a-ts) 89 8.

Predetermination of future events
19*7-22.

Predication 24 17, 26, 25 b 20, 26 a
17, 32 b 25, 4i a iS, 43 a 25, b i?>
48 ;1 4O, 49 a i6; natural i, ac
cidental Si b 24-9, 82 a 2o, 83*
1-20 ; possibility of infinite
series of 8i b 3O 84 b 2 ; implies
single subject and single attri
bute 83 a 22, b i7: series of
(arva-Toixia) 79 7, 8l a 21, 87 b
6, 14.

Premiss (n-pdrao-ts), def. 24 a i6;
species of ib. 17, 25 a I ; demon
strative K dialectical 24 a 22;
number of 42 a 32 ; rules for
selecting 43 a 2046* 30 ; pro
per form of 7i b 4; at least two
required for inference 73*10;
as elements of conclusion (cf.
also Resolution} 84 2 1 ; related
as whole and part 92 a l2; as
reciprocating with conclusion

INDEX

78*10; necessary general
X chance 87 19-27 ; false pre
misses may give true conclusion
75 a 4, 78 a 7, 8S a 2O ; non-neces
sary premisses may give neces
sary conclusion 75 a 3 : as basic
truth MPA-I?), = in immediate
proposition (npoTna-is) 72 a 7 ;
must be true, primary (and . .
indemonstrable 76*16), better
known than, cause of, conclu
sion 7i b 2i-3, necessary 73* 24,
. . essential 74 b 5-i2, 75 a 3o,
homogeneous with conclusion
87 b i-4; equal in number to
middle terms84 b 2l ; not much
fewer than conclusions SS b 3-7 ;
none common to all sciences 6 a
17, 8S a i8- b 29; as definitions
75 b 3) 9 o1) 2 4 ! as "n t f demon
stration 84 36 85 a I ; negative
84 29-31 : how the individual
comes to know them 99 b 15
ioo b i7. Cf. Demonstration,
Basic truth, Knowledge, Intui
tion.

Prime, two meanings of 96 a 35-

Prior, five senses of 14*26 - 23 ;
two senses of 7i b 33 72 a 5.

Privation 73 b 21.

Privative ( positive terms I2 a
26 I3 a 36, 52* 1 5.

Probability (eiYo r) 7O a 3.

Property 43 b 3; peculiar ( i8tov)
73 a 7, 9i a I5 92 a 8, and An.
Post, passim. Cf. Attribute.

Proportion, geometrical 78 a I.
Cf. Alternation.

Proposition, simple I7 a 8, 20, i8 a
8-17; composite I7 a o, 21;
contrary I7 b 20 i8 a 12 ; con
tradictory 1 7*25-37, b 17 ; uni
versal, particular, indefinite I7 a
38- b 16, 24 a 17; universal
affirmative 24 26; negative
ib. 30; particular affirmative
25 a 10, neg. ib. 12, 22, 26 b l4;
singular universal 43 a 25; =
either part of an enunciation
72 a 8 ; immediate ib. ; dialec
tical 72 a 9 ; demonstrative 72 a
10. Cf. Premiss.

Prosyllogism 42 b 5, 53 a 4o, 66 a 25,
82 b 26, 86 b 23.

Pythagoreans 94 b 33.

Quality i b 26, 29, 8 b 25 11*38;

(n-oidn/r) not predicable of a

quality 82 a 36.

Quantification of predicate 43 b 17.
Quantity I b 26, 28, 4 b 2c 6*35;

discrete > continuous 4 b 20 ; of

premisses 47 b 1 5-40.
Question, dialectical 2o b 22.
Questions, four which cover the

whole sphere of knowledge 8g b

21-36; these all concern cause

and middle term 89 b 37 9o a 35.
Quick wit (tryxtVota) 89 b io-2o.

Reason, cannot be established
from false premisses 53 b 9, 57 a
40.

Reciprocity of correlatives 6 1 28
7 b 14; reciprocal proof 57 b 18,
59 a 3 2.

Reductio ad impossibile 2S b i5,
29 a 35, "6, 34 a 3, 36*22, 3 7 a 9 ,
4i a 2i, 45 a 23 46 a 2, 50*29-
38, 6i a i7-63 b 2l, 77*22; (
conversion 6i a 21 ; \ ostensive
proof 62 b 29 63 * 22 ; X an ^ r -
mative demonstration 87 a 28-
30; X negative demonstration
ib. 1-28.

Reduction 4O b i7~4i b 5, 50 5
5i b 2, 69 a 20-36 ; byconversion
27 a 6, 28 a 19, 29 a 3o, undAn. Pr.
passim ; per impossibile 27 a 38,
28 b 1 7, and An. Pr. passim ; all
syllogisms reducible to univer
sal moods of fig. I 29 i, 41 b
3 ; reduction of arguments to
figures and moods of syllogism
46 b 40 50 b 4.

Refutation 66 b 4-1 7; ) proof 42 b
27 -43 b 38.

Relation I b 26.

Relative 5" 16, 6 a 36-8 24.

Relatives, such in virtue of refer
ence to something external 6 a

37-
Resolution 78 a 7 ; of composite

predicates 2i a 18.
Rhetoric 71" 9.

Sardis 94 b I.

Science 32 1 8, 46 a 3 ; the more
abstract the more accurate 87 a
31-7; expansion b.y apposition
78 a 14-21, 86 b 5, by interposi
tion 88 b 6 (cf. Close-packing) \
one science one genus 87 a 38-

INDEX

b 4 : subalternate sciences 75 b
14-16, 76 a 9-i5, 78 b 3" 79 a 16.
Cf. Demonstration, Knowledge.

Scythians 78 b 3o.

Self-evident 64 36, 65 a 9.

Sense, loss of a 8i a 38- 9.

Sense-perception 7 b 35, S a i-i2,
5o a i, 78* 35 ; defined gg b 35 ;
X knowledge 8i b 6, S6 a 3o, 87 b
2888* 17 ; conn, with induc
tion 8i a 38- 9, loo b 5 ; its
development into memory Q6 b
36 100*3; content of 87 29,
ioo b 17.

Sentence i6 b 26 I7 a 7; def. i6 b
26.

Sequence of being 14*30, 35, b 12,
I5 a 6, in propositions express
ing contingency, necessity, im
possibility, &c. 22 a 14 23 a 26.

Sign 7o a 3 ; proof through 75 a 33,

99 a 3-

Simultaneity; kinds of I4 b 24 I5 a [
12 ; s. of most correlatives
7 b i5; simultaneous by nature
!5 a S.

Sophistic argument 7i a 3O. Cf.
Knowledge.

Soul, discourse within 76 25 ;
growth of knowledge in 99 b
15 ioo b i7.

Space, a quantity 5 a 6.

Species, secondary substance 2 a
14, b 7, 29; how related to
genus 2 b 7, 19 ; simultaneous
I4 b 33 ; univocally predicated of
individual 3* 33- 9 ; infima
96 b 20 ; as definable form ib. 23
and g6 a 20 97 b 39 passim. Cf.
Genus, Definition, Subject.

Speech, a quantity 4 b 32.

State i b 27.

Stereometry 78 b 38.

Subject I a 2o, 2 a l2, 3 a 8; primary
s. of demonstration 73 b 39 74 a
3 ; as reciprocating with predi
cate 82 a 15-20; as infima species
passim ; as element in defini
tion of a substance 83 b 26 ; as
substratum (vnoKeifjifvov) 79 a 9,
8i b 28, 83 a 6, 13, 12, 22; sub
ject-genus 75*39- !, 76 a 12.

Substance (oixria) l ]) 2J, 2 a II
4 b 19; primary 2 a n, 35, h 5, 3 b
25, 8 a 15, 23* 24 ; secondary 2 a
14, b 7; basis of all predication
2 a 34> bl 5! as a this some

what (ro Sf T() 3 b 10, 73 b 7, 87 b
29 ; as infima species 73 a 32
and An. Post, passim ; essen
tially definable 83 b 5. Cf. De
finition, &c.

Substratum, v. Subject.

Syllogism def. 24 b 18 ; V. demon
stration 24*27, 25 b 27, 7l b 22,
8i b 18-23 ; perfect V imperfect
24 22, 25 b 35, 26 b 29, 27 a 16,
28 a 4, 29 a 15, 30, 33 a 2o, 34 a i,
42 a 33 ; valid 27* 2, 28 a 16, 4i b
33 ; indirect 29 a 19, 53 a 3 ; os-
tensive hypothetical 40 * 27 ;
hypothetical 4i a 38, 45 b 15, 5o a
i6- b 4; inductive 68 b 15 ; alls,
reducible to universal moods of
fig. I 29 b i, 40 19 ; depends on
universal without temporal limi
tation 34 7 ; every s. requires
three terms 40 30, 4l b 36, two
premisses 42 a 32 ; one premiss
must be affirmative 4i b 6, and
one universal ib. 7 ; fundamen
tals of 8i b 10-15 dialectical
71* 5 : figures of, 1st 79 a 17^32,
8o a 27 8i a 5, 85 a 8; 2nd 78 b
24, 79 a 25, 8i a 5, 82 13-20, 85*
4-8, 90 b 6 ; 3rd 7g a 27, 82 21-
8, 85 a 10, 90 7 : syllogistic
questions 77 a 36- b 33.

Term, def. 24 b 16 ; major, minor,
middle in fig. I 25 b 35, 26 a 2i,
in fig. II 26^36, in fig. Ill 28 a
12; middle 4o b 30, 4i4> 4 2b
6, 46 a 40, 47 a 38 ; importance
of setting out terms well 47 lj
40 48 a 28 ; terms may be re
lated in various ways indicated
by oblique cases 48 a 40 49 a 5 ;
should be stated in nominative,
but premisses must be under
stood with reference to cases
of terms 48 b 4o ; rules for set
ting out t. in which some quali
fication or condition is intro
duced 49 a ii- b 2.

Thebans 69 a I.

Thesis 72 a 14-24.

This somewhat , cf. Substance.

Thunder 93 a 22, 94* 5, b 32.

Time 2*2, n b lo; a quantity 5 a
6.

Triangle, as subject passim ; as
property (?) 7i a 14, 76 a 35, cf.
93 b 3i-

INDEX

Truth and falsity of propositions
i6 a 9-iS, I8 a 26, 24 b 6; refer
ring to future 18*33; always
self-consistent 4/ a 8 ; from true
premisses what is false cannot
be inferred 53 7 ; from what is
false a true conclusion may be
drawn 53 b 4 57 b i7, but it is
not necessitated 57 a 4o.

Unity, numerical I b 6 ; of mean
ing 20 b 15 ; conjunct ( immedi
ate 93 b 35.

Universal 17* 38 ; u. proposition
24 a 18, u 27 ; X individual as
subject of proposition 43* 25 ;
in syllogism one premiss must
be u. 4i b 6, 47 h 26; u. conclu
sions most difficult to estab
lish, easiest to overthrow 43 a I ;

knowledge of u. ( particular
67 a i7; implicit in particular
7i a 7 ; explicit in particular
71*18; ( particular 79 a 5 ;
grasped by induction 8i b 2.
Cf. Attribute, Demonstration,
Knowledge, Premiss, &.C.
Univocal terms i a 6, 3 a 34, h 7.

Verb I9 b i2; def. i6 b 6; indefi
nite ib. 14, I9 b 10 ; terms of ib.
16; verbal nouns and adjec
tives ib. 19.

Whole, inclusion in a 24 b 26, 25 b

32, 53 a 2i.
Words, spoken l6 a 3 ; written ib. 4.

Zeno 6s b i8.

TOPICA

AND

DE SOPHISTICIS ELENCHIS

BY

W. A. PICKARD-CAMBRIDGE

PREFACE

THE following translation of the Topics and Sophistici
Elenchi was begun upon the basis of Bekker s text, and
though Strache s recension (edited by Wallies) certainly
improves upon it at many points, I have not found reason
to abandon the earlier text as a whole. A different reading
from Bekker, where adopted, is indicated in a foot-note. In
addition to the Greek commentaries and the anonymous
paraphrase of Sophistici Elenc/ii, I have used the Latin
translation and commentary of Pacius, and the editions of
Buhle and Waitz. Of modern translations of the whole work,
the most useful have been those of Kirchmann, St. Hilaire,
and Rolfes. For the Sophistici Elenchi I have further had
the advantage of Poste s edition and of the free paraphrase
which serves for translation therein ; also of some notes of
the late Professor Cook Wilson (kindly lent me by Lt.-Col.
A. S. L. Farquharson), principally on some points of
mathematical theory. I am very much indebted to Mr.
W. D. Ross for many useful criticisms and suggestions,
and to my wife and Miss D. M. Hall for much tedious but
invaluable labour in typing the translation and in the con
struction of the index.

TOPICA
CONTENTS

INTRODUCTORY (Book I, ch. 1-3)
BOOK I.
ch. I. Programme of treatise.

2. Uses of treatise.

3. Ideal aimed at.

A. SUBJECTS AND MATERIALS OF DIS
CUSSIONS (Book I, ch. 4-12)

4. Subjects (Problems) and materials (Propositions) classified into

four groups according to nature of Predicable concerned.

5. The four Predicables.

6. How far to be treated separately.

7. Different kinds of sameness.

8. Twofold proof of division of Predicables.

9. The ten Categories and their relation to the Predicables.

10. Dialectical Propositions.

11. Dialectical Problems : Theses.

12. Dialectical Reasoning )( Induction.

B. THE SUPPLY OF ARGUMENTS
(Book I, ch. 13-Book VII)

13. Four sources of arguments :

14. (i) How to secure propositions.

15. (2) ,, distinguish ambiguous meanings.

16. (3) ,, note differences.

17. (4) ,, ,, resemblances.

1 8. The special uses of the last three processes.

COMMONPLACE RULES RESPECTING PREDICATIONS

(a) OF ACCIDENT, (i) Universal Predications (Books II-III, ch. 5)

Part I Simple predications of Accidents generally (Book II)

BOOK II.

ch. i. Proposed plan of treatment.

2. Various rules.

3. Rules for dealing with Ambiguity.

4. Various rules.

5. Rules for diverting the argument.

6. Various rules.

7. Rules drawn from contraries.

vi TOPICA

BOOK II.

ch. 8. Rules drawn from different modes of opposition, or kinds of
opposite.

9. Rules drawn from co-ordinates and inflexions, from contraries,
and from processes or agents whereby things come to be or
are destroyed.

10. Rules drawn from likeness between things or their relations,

and from variations in degree.

11. Rules for arguing (a) from the results of adding things together

to the character of the things ; (b) from qualified to simple
or absolute predications.

Part II Comparative predications of Value-predicates of A or B

(Book III, ch. 1-3)
BOOK III.
ch. I. Various rules; including rules drawn from nature of subjects

to which A or B belong (ii6 b 12-22) ; or from consideration

of ends and means (n6 b 22-36).

2. Various rules ; including rules drawn from consideration of

antecedents and consequences (H7 a 5-iS); of numbers
(117*16-25); of times and seasons (117*26-37); of self-
sufficiency (Il7 a 37- b 2) ; of destructions, losses, contraries,
production, and acquisition (li7 b 3-9) ; of some ideal pattern
(H7 b 10-27).

3. Various rules ; including rules drawn from comparison with

some common standard (ll8 b i-4); from result of adding
A and B to, or subtracting them from, some other thing of
known value (ll8 b 10-19) > from comparison of grounds for
desiring A or B (ii8 b 20-36).

Part 111 Simple predications of Value-predicates
(Book III, ch. 4)

How to adapt previous rules.

Part IV Comparative predications of Accidents generally

(Book III, ch. 5)
5. Various rules.

(ii) Particular Predications (Book III, ch. 6)

6. How to adapt the previous rules (H9 a 32-i2O a 5).

Proof and disproof, how affected by definiteness or indefinite-
ness of thesis (120*6-31).
How to adapt the previous rules, continued (120* 32-** 7).

CONTENTS vii

(b) OF GENUS (Book IV)
BOOK IV.
ch. 1-2. Various rules.

3. Various rules ; including rules from contraries, usefulfor dis

proof (I23 b i-i24 a 2), and for proof (I24 a 3-lo); from in
flexions and co-ordinates (124* 10-14).

4. Various rules ; including rules from likeness of relations (124*

15-19) ; from processes or agents of generation and destruc
tion (124*20-30); from capacities and uses of things (124*
31-34); from opposition between states and their privations
(I24 a 35~ b 6); from contradictory oppositions (I2^ b 7-i4);
from relative oppositions (i24 b 15-34) ; from inflexions (i24 b
35~I25 :1 4): also special rules applying where genus and
species are relative terms (125* 5-*" 14).

5. Various rules ; including special rules applying where genus

or species is a state, or a capacity or an affection.

6. Various rules ; including rules from variations in degree, useful

for disproof (i27 b 18-36) and for proof (I2; b 37-I28 a 12) ;
also rules for distinguishing genus from differentia (i28 a 2o-
30).

(c) OF PROPERTY (Book V)
BOOK V.

ch. i. Different kinds of property (i2S b 16-129* 16).
Suitability of each for discussion (i29 a 17-31).
Lines of argument upon each (129*32-35).

2-3. Rules for testing whether a property is rendered correctly.
4-end. Rules for testing whether a term belongs as a property at
all:

4. Various rules ; including note on certain sophistical difficulties

arising from ambiguity of the terms same and different .

5. Various rules ; including notes on difficulties arising from

failure to say explicitly hou> the alleged property belongs
(I34 a 5~17, 18-25, 26-135*9); and a special rule applying
to a whole consisting of like parts (I35*2o- b 6).

6. Rules drawn from different modes of opposition contrary

opposition (I35 b 7-i6), relative opposition d35 b 17-26),
that of a state and its privation (l35 b 27-136* 4), contradic
tory opposition, applied to predicates only (136*6-13), to
both predicates and subjects (136 14-28), and to subjects
only (!36*29- b 2); from co-ordinate members of a division
(I36 b 3-l4).

7. Rules drawn from inflexions (i36 b 15-32) ; from relations like

the relation alleged to be a property (I36 b 33-137*7) ; from
identity of relations between the alleged property and two
subjects (137*8-20); from processes of becoming and
destruction (I37*2i- b 2); from reference of the alleged
property to the idea of its subject (l37 b 3-13).

8. Rules drawn from variations in degree (I37 b 14-138*29) ;

from comparison of an attribute-relation that is like the
alleged property-relation, between a different attribute and
a different subject (I38*3o- b 5), between the subject of the
alleged property and a different attribute ( 1 38 b 6-15), between
the alleged property and a different subject (i38 b 16-22).

9. Two rules (I38 b 27-l39* 8, 139*9-20).

viii TOPICA

(d) OF DEFINITION (Book VI)
BOOK VI.

ch. I. General division of problems relating to definition (139*24-35).
Distinction of problems treated and problems yet to be treated

(i39 3 6- b u).

Rules for testing whether definition is rendered correctly :
obscurity and redundancy to be avoided (I39 b 12-18).

2. Obscurity, how avoided.

3. Redundancy, how avoided.

4-end. Rules for testing whether the formula rendered is a definition
at all.

4. Rules to secure that terms of definition shall be prior and

more intelligible ; how to detect failure in latter respect
(l4i b 3-142*21) ; in former (i42 a 22- b 19).

5 . Rules as to genus.

6. ,, differentia.

7. Various rules, including rules for testing the definition of

terms admitting variations in degree (146*3-20).

8. Rules for testing the definition of a relative term.

9. Rules for testing the definition of a state (i47 a 12-22) ; of a

relative term (147*23-31); of contraries (i47 a 32- b 25) ; of
a privation (I47 b 26-148*2) or what is confused with one

(148*3-9).

10. Rules drawn from like inflexions (148* 10-13) j from reference

of the definition to the idea of the term defined (148* 14-
22);
Rules for testing the definition of an ambiguous term (148* 23-

b 22).

11. Rules for testing the definition of a complex term.

12. Various rules, including rules for testing the definition of any

thing real (i49*38- b 3); of a relative term (I49 b 4~23); of
any term intrinsically valuable (i49 b 31-39).

13. Definitions of the forms

(1) X is A and B (150*1-21).

(2) X is the product of A and B (150* 22- 1 26).

(3) X is A + B (I5o b 27-I5i*i9).

14. Various rules ; including rules how to test the definition of

compound whole (151*20-31); and how to examine an
unclear defini ion (i5i b 3-17).

(e) OF SAMENESS (Book VII, ch. 1-2)
BOOK VII.
ch. I. Various rules.

2. Bearing of these rules on problem of definition.

(/) OF DEFINITION continued (Book VII, ch. 3)
3. Rules for establishing a. definition.

4. Note on the comparative usefulness of the different kinds of

commonplace-rules.

5. Note on the comparative difficulty of proving or disproving

the various kinds of Predicable.

CONTENTS ix

C. CONCERNING THE PRACTICE OF, AND PRACTICE
IN, DIALECTICS (Book VIII)

(a) How to arrange and put questions (Book VIII, ch. 1-3)
BOOK VIII.
ch. I. Introductory (l55 b 3-17).

( I ) Of necessary and other premisses.

Premisses other than necessary premisses, and their four aims

(I55 b 18-28).

Use of necessary premisses (i55 b 29-156 2).
Use of premisses other than necessary

(1) for inductions (156*3-7).

(2) concealment of intended conclusion (156*7-157* 5).

(3) ornament (157*6-13).

(4) ,, clearness (157*14-17).

2. (2) Of inductions (157*18-33).

(3) Of objections (157* 34- b 33).

(4) Of argument per impossible (l57 b 34-158* 2).

(5) Miscellaneous hints (l5<5*3-3o).

3. On the comparative difficulty or ease of certain dialectical

arguments.

(b) How to answer (Book VIII, ch. 4-10)

4. Answerer s role )( questioner s role.

5. Introductory note on lack of tradition respecting discussions

held for training and examination (159*25-37).
The answerer s procedure as determined by the character
(i) of his own thesis (159* 38-^3$) ;

6-8. (2) of the particular question put its general acceptability
and relevance (ch. 6), its clearness (ch. 7), and its importance
for the argument (ch. 8).

9. Rules respecting the answerer s original thesis.

10. On the solution of fallacious arguments (i6o b 23~39).
Four types of objection distinguished (161* 1-15).

(c) Supplementary discussions (Book VIII, ch. 11-14)

1 1. On faults of argument and faults of questioner.

12. On clearness in argument : its three kinds distinguished

(i62*35- b 2).

On fallacy in argument: its four kinds distinguished (i62 b 3-
15) ; how far censurable (i62 b 16-24) : test questions for its
detection (i62 b 24-30).

13. On begging the question, and on the begging of contraries :

five types of each distinguished.

14. Hints upon training and practice in dialectical arguments.

DE SOPHISTICIS ELENCHIS

INTRODUCTORY (ch. 1-2)

ch. i. General distinction of genuine )( merely apparent reasonings
and refutations.

2. Four classes of arguments in dialogue form : Didactic argu

ments, Dialectical arguments, Examination arguments, and
Contentious arguments (the subject of the present book).

PERPETRATION OF FALLACIES (ch. 3-15)

3. Aims of contentious reasoning fivefold :

4. A. REFUTATION

(a) by fallacies dependent on diction : proof that these are

six in number (i65 b 24-30) : due respectively to

(1) Ambiguity (i65 b 30- i66 a 6) ;

(2) Amphiboly (166*6-23) ;

(3) Ambiguous combination of words (l66 a 23-32) ;

(4) Ambiguous division of words (i66 a 33-8) ;

(5) Wrong accent (i66 b 1-9) ;

(6) The form of expression used (l66 b 10-21).

(b] by fallacies not dependent on diction : seven in number

(l66 b 21-7) : depending respectively upon

5. (i) Accident (i66 b 28-36) ;

(2) The use of words without or with qualification (l66 b 37-

167*20) ;

(3) Ignoratio elenchi (i67 a 2l~35) ;

(4) Petitio principii (i67 a 36-g);

(5) The consequent (i67 b 1-20) ;

(6) False cause (i67 b 21-38) ;

(7) Many questions (i67 b 38-i68 a 16).

6. Proof that all the above can be exhibited as forms of a single

fallacy, viz. ignoratio elenchi.

7. Proof that all the above arise from confusion and failure to

draw proper distinctions.

8. (c) by arguments (or refutations] which, though valid, are

only apparently appropriate to the subject-matter )(
Examination-arguments, which expose ignorance of the
subject by arguments really appropriate to it (l69 b 1 8-
29).
These sophistical refutations can all be analysed by the same

method as the forms of apparent proof ( 1 69" 30- 170* n).
Sophistical refutation never refutes absolutely, but always
relatively (to the answerer) (i7o a 12-19).

9. Refutations being infinite in number, an exhaustive study of

all is impossible (170* 20-34).

Our concern is not with those that rest on principles peculiar
to any particular science (l7O a 34-8).

The object of dialectic is to grasp how to construct and to
solve refutations that depend on dialectic, i. e. on common
principles (i. e. such refutations as are either really dialectical
or apparently dialectical, or suited to an examination) (170*
38- b n).

CONTENTS xi

ch. 10. The distinction of arguments directed against the expression
)( arguments directed against the thought expressed, exposed
as unreal.
Didactic )( dialectical argument d7i a 3i- b 2 : cf. 172* 15-21).

11. Examination-argument and dialectical (171 3-6, I72 a 2i- b i).
Contentious (sophistical) reasoning )( dialectical (i7i b 6-7, 34-

172*15).
Two types of contentious reasoning (i7i b 8-io, u ff.).

12. /> . FALLACY: how to show d72 b 10-28).

C. PARADOX: ho\v to entrap into (I72 b 10-24, 29-173* 30).

13. D. BABBLING: how to produce.

14. E. SOLECISM: how to produce.

15. How to arrange arguments most effectively.

SOLUTION OF FALLACIES (ch. 16-32).

1 6. General remarks: uses of studying solutions: need of

practice.

17. Of apparent solutions.

18. Of genuine solutions.

19. A. Solution of REFUTATIONS

(a) dependent on diction (ch. 19-23)

(1) Ambiguity, and

(2) Amphiboly.

20. (3) Ambiguous division, and

(4) Ambiguous combination, of words.

21. (5) Wrong accent.

22. (6) Like expressions for different things.

23. General rule for solution of fallacies depending on diction

(/>) not dependent on diction (ch. 24-30).

24. (i) Accident.

25. (2) The use of words with or without qualification.
20 - (3) Ignoratio elenchi.

27. (4) Petitio principii.

28. (5) The consequent.

29. (6) Inserrion of irrelevant matter (False cause).

30. (7) Many questions.

31. B. Solution of arguments tending to BABBLING.

32. C. ,, SOLECISM.

33. Varying degrees of difficulty in respect of fallacies.

EPILOGUE

34. (i) Our programme and its performance (183* 27~ b 15).

(2) History of dialectical theory compared with that of rhetoric
(i83 b i5-end).

BOOK I

ioo a

i OUR treatise proposes to find a line of inquiry where- 18
by we shall be able to reason from opinions that are gen
erally accepted about every problem propounded to us, 20
and also shall ourselves, when standing up to an argument,
avoid saying anything that will obstruct us. First, then, we
must say what reasoning is, and what its varieties are, in
order to grasp dialectical reasoning: for this is the object
of our search in the treatise before us.

Now reasoning is an argument in which, certain things 25
being laid down, something other than these necessarily
comes about through them, (a) It is a demonstration ,
when the premisses from which the reasoning starts are
true and primary, or are such that our knowledge of them
has originally come through premisses which are primary
and true : (b] reasoning, on the other hand, is dialectical , 3
if it reasons from opin ions that are generally accepted. Things
are true and primary which are believed on the strength ioo b
not of anything else but of themselves : for in regard to the l8
first principles of science it is improper to ask any further
for the why and wherefore of them ; each of the first prin- ao
ciples should command belief in and by itself. On the other
hand, those opinions are generally accepted which are
accepted by every one or by the majority or by the philoso
phers i. e. by all, or by the majority, or by the most notable
and illustrious of them. Again (c), reasoning is contentious
if it starts from opinions that seem to be generally accepted,
but are not really such, or again if it merely seems to reason 25
from opinions that are or seem to be generally accepted.
For not every opinion that seems to be generally accepted
actually is generally accepted. For in none of the opinions
which we call generally accepted is the illusion entirely on
the surface, as happens in the case of the principles of con
tentious arguments ; for the nature of the fallacy in these is

ioo b TOPICA

3 obvious immediately, and as a rule even to persons with
ioi a little power of comprehension. So then, of the contentious
reasonings mentioned, the former really deserves to be called
reasoning as well, but the other should be called conten
tious reasoning , but not reasoning , since it appears to
reason, but does not really do so.

5 Further (d), besides all the reasonings we have mentioned
there are the mis-reasonings that start from the premisses
peculiar to the special sciences, as happens (for example) in
the case of geometry and her sister sciences. For this form
of reasoning appears to differ from the reasonings mentioned
above ; the man who draws a false figure reasons from things

10 that are neither true and primary, nor yet generally accepted.
For he does not fall within the definition ; he does not assume
opinions that are received either by every one or by the
majority or by philosophers that is to say, by all, or by
most, or by the most illustrious of them but he conducts
his reasoning upon assumptions which, though appropriate

15 to the science in question, are not true; for he effects his
mis-reasoning either by describing the semicircles wrongly
or by drawing certain lines in a way in which they could
not be drawn.

The foregoing must stand for an outline survey of the
species of reasoning. In general, in regard both to all that

20 we have already discussed and to those which we shall
discuss later, we may remark that that amount of distinction
between them may serve, because it is not our purpose to
give the exact definition of any of them ; we merely want
to describe them in outline; we consider it quite enough
from the point of view of the line of inquiry before us to be
able to recognize each of them in some sort of way.

25 Next in order after the foregoing, we must say for how 2
many and for what purposes the treatise is useful. They
are three intellectual training, casual encounters, and the
philosophical sciences. That it is useful as a training is
obvious on the face of it. The possession of a plan of inquiry

30 will enable us more easily to argue about the subject pro
posed. For purposes of casual encounters, it is useful because

BOOK I. 2 ioi a

when we have counted up the opinions held by most people,
we shall meet them on the ground not of other people s
convictions but of their own, while we shift the ground of
any argument that they appear to us to state unsoundly.
For the study of the philosophical sciences it is useful,
because the ability to raise searching difficulties on both 35
sides of a subject will make us detect more easily the truth
and error about the several points that arise. It has a further
use in relation to the ultimate bases of the principles used
in the several sciences. 1 For it is impossible to discuss them
at all from the principles proper to the particular science in
hand, seeing that the principles are the prius of everything
else : it is through the opinions generally held on the par- ioi b
ticular points that these have to be discussed, and this task
belongs properly, or most appropriately, to dialectic : for
dialectic is a process of criticism wherein lies the path to
the principles of all inquiries.

3 We shall be in perfect possession of the way to proceed 5
when we are in a position like that which we occupy in
regard to rhetoric and medicine and faculties of that kind :
this means the doing of that which we choose with the
materials that are available. For it is not every method
that the rhetorician will employ to persuade, or the doctor
to heal : still, if he omits none of the available means, we
shall say that his grasp of the science is adequate. 10

4 First, then, we must see of what parts our inquiry con
sists. Now if we were to grasp (a) with reference to how
many, and what kind of, things arguments take place, and
with what materials they start, and (b) how we are to
become well supplied with these, we should have sufficiently
won our goal. Now the materials with which arguments
start are equal in number, and are identical, with the sub
jects on which reasonings take place. For arguments start 15
with propositions , while the subjects on which reasonings
take place are problems . Now every proposition and

1 Or (omitting a PX S)v in 1. 37 with B corr. and C) in relation to the
ultimate bases of the several sciences .

B 2

ioi b TOPICA

every problem indicates either a genus or a peculiarity or
an accident for the differentia too, applying as it does to
a class (or genus), should be ranked together with the genus.
Since, however, of what is peculiar to anything part signifies

20 its essence, while part does not, let us divide the peculiar
into both the aforesaid parts, and call that part which
indicates the essence a definition , while of the remainder
let us adopt the terminology which is generally current
about these things, and speak of it as a : property . What
we have said, then, makes it clear that according to our
present division, the elements turn out to be four, all told,

35 namely either property or definition or genus or accident.
Do not let any one suppose us to mean that each of these
enunciated by itself constitutes a proposition or problem,
but only that it is from these that both problems and
propositions are formed. The difference between a problem
and a proposition is a difference in the turn of the phrase.

30 For if it be put in this way, " An animal that walks on two
feet " is the definition of man, is it not ? or " Animal " is
the genus of man, is it not ? the result is a proposition :
but if thus, Is " an animal that walks on two feet " a defini
tion of man or no ? [or Is " animal " his genus or no ? ] l the
result is a problem. Similarly too in other cases. Naturally,

35 then, problems and propositions are equal in number : for
out of every proposition you will make a problem if you
change the turn of the phrase.

We must now say what are definition , property , 5
genus , and accident . A definition is a phrase signi
fying a thing s essence. It is rendered in the form either of
ioa a a phrase in lieu of a term, or of a phrase in lieu of another
phrase ; for it is sometimes possible to define the meaning
of a phrase as well. People whose rendering consists of
a term only, try it as they may, clearly do not render the
definition of the thing in question, because a definition is
5 always a phrase of a certain kind. One may, however, use
the word definitory also of such a remark as The " be
coming " is " beautiful " , and likewise also of the question,

1 ioi b 33. The words KOI . . . cvriv do not occur in the best MSS.

BOOK I. 5 102

Are sensation and knowledge the same or different ? , for
argument about definitions is mostly concerned with ques
tions of sameness and difference. In a word we may call
definitory everything that falls under the same branch of
inquiry as definitions; and that all the above-mentioned 10
examples are of this character is clear on the face of them.
For if we are able to argue that two things are the same or
are different, we shall be well supplied by the same turn of
argument with lines of attack upon their definitions as well :
for when we have shown that they are not the same we shall
have demolished the definition. Observe, please, that the
converse of this last statement does not hold : for to show 15
that they are the same is not enough to establish a definition.
To show, however, that they are not the same is enough
of itself to overthrow it.

A property is a predicate which does not indicate the
essence of a thing, but yet belongs to that thing alone, and
is predicated convertibly of it. Thus it is a property of man
to be capable of learning grammar: for if A be a man, then 20
he is capable of learning grammar, and if he be capable of
learning grammar, he is a man. For no one calls anything
a property which may possibly belong to something else,
e. g. sleep in the case of man, even though at a certain
time it may happen to belong to him alone. That is to say,
if any such thing were actually to be called a property, it 25
will be called not a property absolutely, but a tem
porary or a relative property : for being on the right
hand side is a temporary property, while two-footed is
in point of fact ascribed as a property in certain relations ;
e. g. it is a property of man relatively to a horse and
a dog. That nothing which may belong to anything else
than A is a convertible predicate of A is clear : for it
does not necessarily follow that if something is asleep it is 30
a man.

A genus is what is predicated in the category of essence
of a number of things exhibiting differences in kind. We
should treat as predicates in the category of essence all such
things as it would be appropriate to mention in reply to the
question, What is the object before you ? ; as, for example.

ioa a TOPICA

35 in the case of man, if asked that question, it is appropriate
to say He is an animal . The question, Is one thing in
the same genus as another or in a different one ? is also
a generic question ; for a question of that kind as well
falls under the same branch of inquiry as the genus : for
having argued that animal is the genus of man, and likewise
also of ox, we shall have argued that they are in the same
ioa b genus ; whereas if we show that it is the genus of the one
but not of the other, we shall have argued that these things
are not in the same genus.

An accident is (i) something which, though it is none
5 of the foregoing i. e. neither a definition nor a property nor
a genus yet belongs to the thing : (a) something which
may possibly either belong or not belong to any one and the
self-same thing, as (e. g.) the sitting posture may belong or
not belong to some self-same thing. Likewise also white
ness , for there is nothing to prevent the same thing being
at one time white, and at another not white. Of the defini-

10 tions of accident the second is the better : for if he adopts
the first, any one is bound, if he is to understand it, to know
already what definition and genus and property are,
whereas the second is sufficient of itself to tell us the essential
meaning of the term in question. To Accident are to be

15 attached also all comparisons of things together, when
expressed in language that is drawn in any kind of way
from what happens (accidit) to be true of them ; such as,
for example, the question, Is the honourable or the expe
dient preferable ? and Is the life of virtue or the life of
self-indulgence the pleasanter ? , and any other problem
which may happen to be phrased in terms like these. For
in all such cases the question is ( to which of the two does

20 the predicate in question happen (accidit) to belong more
closely ? It is clear on the face of it that there is nothing
to prevent an accident from becoming a temporary or a
relative property. Thus the sitting posture is an accident,
but will be a temporary property, whenever a man is the
only person sitting, while if he be not the only one sitting,
it is still a property relatively to those who are not sitting.

25 So then, there is nothing to prevent an accident from be-

BOOK I. 5 iQ2 b

coming both a relative and a temporary property ; but
a property absolutely it will never be.

6 We must not fail to observe that all remarks made in
criticism of a property and genus and accident will be
applicable to definitions as well. For when we have shown
that the attribute in question fails to belong only to the term
defined, as we do also in the case of a property, or that the 3
genus rendered in the definition is not the true genus, or that
any of the things mentioned in the phrase used does not
belong, as would be remarked also in the case of an accident,
we shall have demolished the definition ; so that, to use the
phrase previously employed, 1 all the points we have enumer
ated might in a certain sense be called definitory . But 35
we must not on this account expect to find a single line of
inquiry which will apply universally to them all : for this is
not an easy thing to find, and, even were one found, it would
be very obscure indeed, and of little service for the treatise
before us. Rather, a special plan of inquiry must be laid
down for each of the classes we have distinguished, and then,
starting from the rules that are appropriate in each case, it
will probably be easier to make our way right through the 103*
task before us. So then, as was said before, 2 we must outline

a division of our subject, and other questions we must relegate
each to the particular branch to which it most naturally
belongs, speaking of them as definitory and generic
questions. The questions I mean have practically been
already assigned to their several branches. 5

7 First of all we must define the number of senses borne
by the term Sameness . Sameness would be generally
regarded as falling, roughly speaking, into three divisions.
We generally apply the term numerically or specifically or
generically numerically in cases where there is more than
one name but only one thing, e. g. doublet and cloak ; I0
specifically, where there is more than one thing, but they
present no differences in respect of their species, as one man
and another, or one horse and another : for things like this

1 a Q. 2 IOI a 22.

3 a TOPICA

that fall under the same species are said to be specifically
the same . Similarly, too, those things are called generically
the same which fall under the same genus, such as a horse
and a man. It might appear that the sense in which water

*5 from the same spring is called the same water is somehow
different and unlike the senses mentioned above : but really
such a case as this ought to be ranked in the same class with
the things that in one way or another are called the same
in view of unity of species. For all such things seem to be
of one family and to resemble one another. For the reason

20 why all water is said to be specifically the same as all other
water is because of a certain likeness it bears to it, and the
only difference in the case of water drawn from the same
spring is this, that the likeness is more emphatic : that is
why we do not distinguish it from the things that in one
way or another are called the same in view of unity of
species. It is generally supposed that the term the same
is most used in a sense agreed on by every one when applied

25 to what is numerically one. But even so, it is apt to be
rendered in more than one sense ; its most literal and primary
use is found whenever the sameness is rendered in reference
to an alternative name or definition, as when a cloak is said
to be the same as a doublet, or an animal that walks on two
feet is said to be the same as a man : a second sense is when it
is rendered in reference to a property, as when what can
acquire knowledge is called the same as a man, and what
naturally travels upward the same as fire : while a third use
is found when it is rendered in reference to some term drawn

3 from Accident, as when the creature who is sitting, or who
is musical, is called the same as Socrates. For all these
uses mean to signify numerical unity. That what I have
just said is true may be best seen where one form of
appellation is substituted for another. For often when we
give the order to call one of the people who are sitting down,
indicating him by name, we change our description, whenever

35 the person to whom we give the order happens not to
understand us ; he will, we think, understand better from
some accidental feature ; so we bid him call to us the man
who is sitting or who is conversing over there clearly

BOOK I. 7 io3 a

supposing ourselves to be indicating the same object by its
name and by its accident.

8 Of sameness then, as has been said, 1 three senses are to iO3 b
be distinguished. Now one way to confirm that the elements
mentioned above are those out of which and through which
and to which arguments proceed, is by induction : for if
any one were to survey propositions and problems one by
one, it would be seen that each was formed either from the 5
definition of something or from its property or from its
genus or from its accident. Another way to confirm it is
through reasoning. For every predicate of a subject must

of necessity be either convertible with its subject or not :
and if it is convertible, it would be its definition or property,
for if it signifies the essence, it is the definition ; if not, it is 10
a property : for this was 2 what a property is, viz. what is
predicated convertibly, but does not signify the essence. If,
on the other hand, it is not predicated convertibly of the
thing, it either is or is not one of the terms contained in the
definition of the subject : and if it be one of those terms,
then it will be the genus or the differentia, inasmuch as the 15
definition consists of genus and differentiae ; whereas, if it
be not one of those terms, clearly it would be an accident,
for accident was said 3 to be what belongs as an attribute to
a subject without being either its definition or its genus or
a property.

9 Next, then, we must distinguish between the classes of 20
predicates in which the four orders in question are found.
These are ten in number : Essence, Quantity, Quality,
Relation, Place, Time, Position, State, Activity, Passivity.
For the accident and genus and property and definition of
anything will always be in one of these categories : for all 25
the propositions found through these signify either some
thing s essence or its quality or quantity or some one of the
other types of predicate. It is clear, too, on the face of it
that the man who signifies something s essence signifies
sometimes a substance, sometimes a quality, sometimes

1 a 7. 2 I02 a i8. 3 I02 b 4.

ioa b TOPICA

some one of the other types of predicate. For when a man
30 is set before him and he says that what is set there is a man
or an animal , he states its essence and signifies a substance;
but when a white colour is set before him and he says that
what is set there is white or is a colour , he states its
essence and signifies a quality. Likewise, also, if a magnitude
of a cubit be set before him and he says that what is set there
is a magnitude of a cubit, he will be describing its essence and
35 signifying a quantity. Likewise, also, in the other cases :
for each of these kinds of predicate, if either it be asserted
of itself, or its genus be asserted of it, signifies an essence :
if, on the other hand, one kind of predicate is asserted of
another kind, it does not signify an essence, but a quantity
or a quality or one of the other kinds of predicate. Such,
then, and so many, are the subjects on which arguments
iO4 a take place, and the materials with which they start. How
we are to acquire them, and by what means we are to
become well supplied with them, falls next to be told.

First, then, a definition must be given of a dialectical 10
proposition and a dialectical problem . For it is not
every proposition nor yet every problem that is to be set
5 down as dialectical : for no one in his senses would make
a proposition of what no one holds, nor yet make a problem
of what is obvious to everybody or to most people : for the
latter admits of no doubt, while to the former no one would
assent. Now a dialectical proposition consists in asking
something that is held by all men or by most men or by the
philosophers, i.e. either by all, or by most, or by the most
10 notable of these, provided it be not contrary to the general
opinion ; for a man would probably assent to the view of
the philosophers, if it be not contrary to the opinions of most
men. Dialectical propositions also include views which are
like those generally accepted ; also propositions which
contradict the contraries of opinions that are taken to be
generally accepted, 1 and also all opinions that are in accord-
is ance with the recognized arts. Thus, supposing it to be

1 iO4 a 13-14. Reading ravavria rois SOKOVCTIV fv86ois dvai /car" avn-
(pacnv Trp

BOOK I. 10 io 4

a general opinion that the knowledge of contraries is the
same, it might probably pass for a general opinion also
that the perception of contraries is the same : l also,
supposing it to be a general opinion that there is but one
single science of grammar, it might pass for a general
opinion that there is but one science of flute-playing as
well, whereas, if it be a general opinion that there is more
than one science of grammar, it might pass for a general
opinion that there is more than one science of flute-
playing as well : for all these seem to be alike and akin. 20
Likewise, also, propositions contradicting the contraries of
general opinions will pass as general opinions : for if it be
a general opinion that one ought to do good to one s friends,
it will also be a general opinion that one ought not to do
them harm. Here, that one ought to do harm to one s
friends is contrary to the general view, and that one ought
not to do them harm is the contradictory of that contrary.
Likewise also, if one ought to do good to one s friends, one 25
ought not to do good to one s enemies : this too is the
contradictory of the view contrary to the general view ;
the contrary being that one ought to do good to one s
enemies. Likewise, also, in other cases. Also, on comparison,
it will look like a general opinion that the contrary
predicate belongs to the contrary subject : e.g. if one ought
to do good to one s friends, one ought also to do evil to one s 3
enemies. It might appear also as if doing good to one s
friends were a contrary to doing evil to one s enemies : but
whether this is or is not so in reality as well will be stated
in the course of the discussion upon contraries. 2 Clearly
also, all opinions that are in accordance with the arts are
dialectical propositions ; for people are likely to assent to
the views held by those who have made a study of these 35
things, e.g. on a question of medicine they will agree with
the doctor, and on a question of geometry with the
geometrician ; and likewise also in other cases.

II A dialectical problem is a subject of inquiry that con- io4
tributes either to choice and avoidance, or to truth and

1 iO4 a i6f. Insert a comma after emor^r, delete the comma after
fvavriuv, and read a colon after (fravtir). 2 ii. 7.

4 b TOPICA

knowledge, and that either by itself, or as a help to the
solution of some other such problem. It must, moreover, be
something on which either people hold no opinion either way,
or the masses hold a contrary opinion to the philosophers,
5 or the philosophers to the masses, or each of them among
themselves. For some problems it is useful to know with
a view to choice or avoidance, e.g. whether pleasure is to be
chosen or not, while some it is useful to know merely with
a view to knowledge, e. g. whether the universe is eternal or
not : others, again, are not useful in and by themselves for
either of these purposes, but yet help us in regard to some

10 such problems ; for there are many things which we do not
wish to know in and by themselves, but for the sake of other
things, in order that through them we may come to know
something else. Problems also include questions in regard
to which reasonings conflict (the difficulty then being whether
so-and-so is so or not, there being convincing arguments for

15 both views) ; others also in regard to which we have no
argument because they are so vast, and we find it difficult to
give our reasons, e.g. the question whether the universe is
eternal or no : for into questions of that kind too it is
possible to inquire.

Problems, then, and propositions are to be defined as
aforesaid. 1 A thesis is a supposition of some eminent

20 philosopher that conflicts with the general opinion ; e.g. the
view that contradiction is impossible, as Antisthenes said ;
or the view of Heraclitus that all things are in motion ; or
that Being is one, as Melissus says : for to take notice when
any ordinary person expresses views contrary to men s usual
opinions would be silly. Or it may be a view about which
we have a reasoned theory contrary to men s usual opinions,

25 e.g. the view maintained by the sophists that what is need
not in every case either have come to be or be eternal : for
a musician who is a grammarian is so without ever having
come to be so, or being so eternally. For even if a man
does not accept this view, he might do so on the ground
that it is reasonable.

Now a thesis also is a problem, though a problem is

BOOK I. ii i04 b

not always a thesis, inasmuch as some problems are such 30
that we have no opinion about them either way. That
a thesis, however, also forms a problem, is clear : for it
follows of necessity from what has been said that either the
mass of men disagree with the philosophers about the thesis,
or that the one or the other class disagree among themselves,
seeing that the thesis is a supposition in conflict with general
opinion. Practically all dialectical problems indeed are now 35
called theses . But it should make no difference whichever
description is used ; for our object in thus distinguishing
them has not been to create a terminology, but to recognize
what differences happen to be found between them, 105*

Not every problem, nor every thesis, should be examined,
but only one which might puzzle one of those who need
argument, not punishment or perception. For people who 5
are puzzled to know whether one ought to honour the gods
and love one s parents or not need punishment, while those
who are puzzled to know whether snow is white or not need
perception. The subjects should not border too closely
upon the sphere of demonstration, nor yet be too far
removed from it : for the former cases admit of no doubt,
while the latter involve difficulties too great for the art of
the trainer.

12 Having drawn these definitions, we must distinguish how 10
many species there are of dialectical arguments. There is
on the one hand Induction, on the other Reasoning. Now
what reasoning is has been said before : l induction is

a passage from individuals to universals, e.g. the argument
that supposing the skilled pilot is the most effective, and
likewise the skilled charioteer, then in general the skilled 15
man is the best at his particular task. Induction is the
more convincing and clear : it is more readily learnt by
the use of the senses, and is applicable generally to the mass
of men, though Reasoning is more forcible and effective
against contradictious people.

13 The classes, then, of things about which, and of things out ao
of which, arguments are constructed, are to be distinguished

1 100*25.

ios a TOPICA

in the way we have said before. The means whereby we
are to become well supplied with reasonings 1 are four:
(i) the securing of propositions ; (2) the power to distinguish
in how many senses a particular expression is used ; (3) the
discovery of the differences of things ; (4) the investigation

25 of likeness. The last three, as well, are in a certain sense
propositions : for it is possible to make a proposition
corresponding to each of them, e.g. (i) The desirable may
mean either the honourable or the pleasant or the expedient
and (2) * Sensation differs from knowledge in that the latter
may be recovered again after it has been lost, while the

3 o former cannot ; and (3) The relation of the healthy to
health is like that of the vigorous to vigour . The first
proposition depends upon the use of one term in several
senses, the second upon the differences of things, the third
upon their likenesses.

Propositions should be selected in a number of ways 14

corresponding to the number of distinctions drawn in regard

35 to the proposition : 2 thus one may first take in hand the

opinions held by all or by most men or by the philosophers,

i.e. by all, or most, or the most notable of them ; or opinions

io5 b contrary to those that seem to be generally held ; and, again,

all opinions that are in accordance with the arts. We must

make propositions also of the contradictories of opinions

contrary to those that seem to be generally held, as was laid

down before. It is useful also to make them by selecting

not only those opinions that actually are accepted, but also

5 those that are like these, e.g. The perception of contraries

is the same the knowledge of them being so and we

see by admission of something into ourselves, not by an

emission ; for so it is, too, in the case of the other senses ;

for in hearing we admit something into ourselves ; we do not

emit ; and we taste in the same way. Likewise also in the

10 other cases. Moreover, all statements that seem to be true

in all or in most cases, should be taken as a principle or

accepted position ; for they are posited by those who do not

1 IO5 a 22. Omit Kal TUV fTrayatywv.

2 104*8-15, and perhaps also ib. 28-30.

BOOK I. 14 ios b

also see what exception there may be. 1 We should select
also from the written handbooks of argument, and should
draw up sketch-lists of them upon each several kind of
subject, putting them down under separate headings, e.g.
On Good , or On Life and that On Good should deal 15
with every form of good, beginning with the category of
essence. In the margin, too, one should indicate also the
opinions of individual thinkers, e.g. Empedocles said that
the elements of bodies were four : for any one might assent
to the saying of some generally accepted authority.

Of propositions and problems there are to comprehend
the matter in outline three divisions : for some are ethical 20
propositions, some are on natural philosophy, while some
are logical. Propositions such as the following are ethical,
e.g. Ought one rather to obey one s parents or the laws, if
they disagree ? ; such as this are logical, e.g. Is the know
ledge of opposites the same or not ? ; while such as this are
on natural philosophy, e.g. Is the universe eternal or not ? 25
Likewise also with problems. The nature of each of the
aforesaid kinds of proposition is not easily rendered in
a definition, but we have to try to recognize each of them
by means of the familiarity attained through induction,
examining them in the light of the illustrations given above.

For purposes of philosophy we must treat of these things 30
according to their truth, but for dialectic only with an eye
to general opinion. All propositions should be taken in
their most universal form ; then, the one should be made into
many. E.g. The knowledge of opposites is the same ; next,
The knowledge of contraries is the same , and that of
relative terms . In the same way these two should again
be divided, as long as division is possible, e.g. the knowledge 35
of good and evil , of white and black , or cold and hot .
Likewise also :n other cases.

15 On the formation, then, of propositions, the above remarks io6 a

are enough. As regards the number of senses a term bears,

we must not only treat of those terms which bear different

senses, but we must also try to render their definitions ;

1 Reading in 1. 12 ort TWOS.

io6 a TOPICA

e.g. we must not merely say that justice and courage are
5 called good in one sense, and that what conduces to vigour
and what conduces to health are called so in another, but
also that the former are so called because of a certain in
trinsic quality they themselves have, the latter because they
are productive of a certain result and not because of any
intrinsic quality in themselves. Similarly also in other cases.
Whether a term bears a number of specific meanings or

10 one only, may be considered by the following means. First,
look and see if its contrary bears a number of meanings,
whether the discrepancy between them be one of kind or one
of names. For in some cases a difference is at once displayed
even in the names ; e. g. the contrary of sharp in the case
of a note is flat , while in the case of a solid edge it is dull .
Clearly, then, the contrary of sharp bears several meanings,

15 and if so, so also does sharp ; for corresponding to each of
the former terms the meaning of its contrary will be different.
For sharp will not be the same when contrary to dull
and to flat , though sharp is the contrary of each. Again
fiapv ( flat , heavy ) in the case of a note has sharp as
its contrary, but in the case of a solid mass light , so that
(3apv is used with a number of meanings, inasmuch as its

20 contrary also is so used. Likewise, also, fine as applied
to a picture has ugly as its contrary, but, as applied to
a house, ramshackle ; so that fine is an ambiguous term.
In some cases there is no discrepancy of any sort in the
names used, but a difference of kind between the meanings
is at once obvious : e. g. in the case of clear and

25 obscure l : for sound is called clear and obscure , just
as colour is too. As regards the names, then, there is no
discrepancy,but the difference in kind between the meanings
is at once obvious : for colour is not called clear in a like
sense to sound. This is plain also through sensation : for
of things that are the same in kind we have the same

30 sensation, whereas we do not judge clearness by the same

sensation in the case of sound and of colour, but in the

latter case we judge by sight, in the former by hearing.

Likewise also with sharp and dull in regard to flavours

1 Lit. white (\evKos) and black (peXas).

BOOK I. 15 io6 a

and solid edges : here in the latter case we judge by touch,
but in the former by taste. For here again there is no
discrepancy in the names used, in the case either of the
original terms or of their contraries : for the contrary also 35
of sharp in either sense is dull .

Moreover, see if one sense of a term has a contrary,
while another has absolutely none ; e. g. the pleasure of
drinking has a contrary in the pain of thirst, whereas the
pleasure of seeing that the diagonal is incommensurate with
the side has none, so that pleasure is used in more than io6 b
one sense. To love also, used of the frame of mind, has
to hate as its contrary, while as used of the physical
activity (kissing) it has none : clearly, therefore, to love
is an ambiguous term. Further, see in regard to their
intermediates, if some meanings and their contraries have
an intermediate, while others have none, or if both have 5
one but not the same one, as e. g. clear and obscure in
the case of colours have grey as an intermediate, whereas
in the case of sound they have none, or, if they have, it is
harsh , as some people say that a harsh sound is inter
mediate. Clear , then, is an ambiguous term, and likewise
also obscure . See, moreover, if some of them have more
than one intermediate, while others have but one, as is the 10
case with clear and obscure , for in the case of colours
there are numbers of intermediates, whereas in regard to
sound there is but one, viz. harsh .

Again, in the case of the contradictory opposite, look and
see if it bears more than one meaning. For if this bears more
than one meaning, then the opposite of it also will be used 15
in more than one meaning ; e. g. to fail to see is a phrase
with more than one meaning, viz. (i) to fail to possess the
power of sight, (2) to fail to put that power to active use.
But if this has more than one meaning, it follows necessarily
that to see also has more than one meaning : for there
will be an opposite to each sense of to fail to see ; e. g.
the opposite of not to possess the power of sight is to
possess it, while of not to put the power of sight to active 20
use , the opposite is to put it to active use.

Moreover, examine the case of terms that denote the

io6 b TOPICA

privation or presence of a certain state : for if the one term
bears more than one meaning, then so will the remaining
term : e. g. if to have sense be used with more than one
meaning, as applied to the soul and to the body, then to
be wanting in sense too will be used with more than one

25 meaning, as applied to the soul and to the body. That the
opposition between the terms now in question depends upon
the privation or presence of a certain state is clear, since
animals naturally possess each kind of sense , both as
applied to the soul and as applied to the body.

Moreover, examine the inflected forms. For if justly

30 has more than one meaning, then just , also, will be used
with more than one meaning ; for there will be a meaning
of just corresponding to each of the meanings of justly ;
e. g. if the word justly be used of judging according to
one s own opinion, and also of judging as one ought, then
just also will be used in like manner. In the same way
also, if healthy has more than one meaning, then
healthily also will be used with more than one meaning :

35 e. g. if healthy describes both what produces health and
what preserves health and what betokens health, then
healthily also will be used to mean in such a way as to
produce or preserve or betoken health. Likewise
also in other cases, whenever the original term bears more
icy 3 - than one meaning, the inflexion also that is formed from it
will be used with more than one meaning, and vice versa.

Look also at the classes of the predicates signified by the
term, and see if they are the same in all cases. For if they
5 are not the same, then clearly the term is ambiguous : e. g.
good in the case of food means productive of pleasure ,
and in the case of medicine productive of health , whereas
as applied to the soul it means to be of a certain quality,
e. g. temperate or courageous or just : and likewise also, as
applied to man . Sometimes it signifies what happens at
a certain time, as (e. g.) the good that happens at the right
time : for what happens at the right time is called good.

jo Often it signifies what is of a certain quantity, e. g. as
applied to the proper amount : for the proper amount too
is called good. So then the term good is ambiguous.

BOOK I. 15 it>7 a

In the same way also clear , as applied to a body,
signifies a colour, but in regard to a note it denotes what is
easy to hear . Sharp , too, is in a closely similar case :
for the same term does not bear the same meaning in all
its applications : for a sharp note is a swift note, as the 15
mathematical theorists of harmony tell us, whereas a sharp
(acute) angle is one that is less than a right angle, while
a sharp dagger is one containing a sharp angle (point).

Look also at the genera of the objects denoted by the
same term, and see if they are different without being
subaltern, as (e. g.) donkey , which denotes both the animal
and the engine. For the definition of them that corre- 20
sponds to the name is different : for the one will be declared
to be an animal of a certain kind, and the other to be an
engine of a certain kind. If, however, the genera be sub
altern, there is no necessity for the definitions to be
different. Thus (e. g.) animal is the genus of raven , and
so is bird . Whenever therefore we say that the raven is
a bird, we also say that it is a certain kind of animal, so 25
that both the genera are predicated of it. Likewise also
whenever we call the raven a flying biped animal , we
declare it to be a bird : in this way, then, as well, both the
genera are predicated of raven, and also their definition.
But in the case of genera that are not subaltern this does
not happen, for whenever we call a thing an engine , we 3 o
do not call it an animal, nor vice versa.

Look also and see not only if the genera of the term
before you are different without being subaltern, but also
in the case of its contrary : for if its contrary bears several
senses, clearly the term before you does so as well. 3 -

It is useful also to look at the definition that arises from
the use of the term in combination, e. g. of a clear (lit.
white) body and of a clear note . For then if what is
peculiar in each case be abstracted, the same expression
ought to remain over. This does not happen in the case
of ambiguous terms, e. g. in the cases just mentioned. For io7 b
the former will be a body possessing such and such a
colour , while the latter will be a note easy to hear .
Abstract, then, a body and a note , and the remainder in

C 2

7 b TOPICA

each case is not the same. It should, however, have been

5 had the meaning of clear in each case been synonymous.
Often in the actual definitions as well ambiguity creeps
in unawares, and for this reason the definitions also should
be examined. If (e. g.) any one describes what betokens and
what produces 1 health as related commensurably to
health , we must not desist but go on to examine in what

10 sense he has used the term commensurably in each case,
e. g. if in the latter case it means that it is of the
right amount 2 to produce health , whereas in the former it
means that it is such as to betoken what kind of state
prevails .

Moreover, see if the terms cannot be compared as more
or less or as in like manner , as is the case (e. g.) with
a clear (lit. white) sound and a clear garment, and a

15 sharp flavour and a sharp note. For neither are these
things said to be clear or sharp in a like degree , nor yet
is the one said to be clearer or sharper than the other.
Clear , then, and sharp are ambiguous. For synonyms
are always comparable ; for they will always be used
either in like manner, or else in a greater degree in one
case.

Now since of genera that are different without being

20 subaltern the differentiae also are different in kind, e. g.
those of animal and knowledge (for the differentiae of
these are different), look and see if the meanings com
prised under the same term are differentiae of genera that
are different without being subaltern, as e. g. sharp is of
a note and a solid . For being sharp differentiates
note from note, and likewise also one solid from another.

35 Sharp , then, is an ambiguous term : for it forms differen
tiae of genera that are different without being subaltern.

Again, see if the actual meanings included under the
same term themselves have different differentiae, e. g.
colour in bodies and colour in tunes : for the differentiae
of colour in bodies are sight-piercing and sight-com-

30 pressing , whereas colour in melodies has not the same

io7 b 8. Read KCU TO

107^ ii. Read TO TOVOVTOV tivai . . .

BOOK I. 15 io7 b

differentiae. Colour, then, is an ambiguous term ; for things
that are the same have the same differentiae.

Moreover, since the species is never the differentia of
anything, look and see if one of the meanings included
under the same term be a species and another a differentia,
as (e.g.) clear (lit. white) as applied to a body is a species 35
of colour, whereas in the case of a note it is a differentia ;
for one note is differentiated from another by being clear .

16 The presence, then, of a number of meanings in a term
may be investigated by these and like means. The
differences which things present to each other should be
examined within the same genera, 1 e. g. Wherein does
justice differ from courage, and wisdom from temperance ? io8 a
for all these belong to the same genus ; and also from one
genus to another, provided they be not very much too far
apart, e. g. Wherein does sensation differ from know
ledge ? : for in the case of genera that are very far apart, 5
the differences are entirely obvious.

17 Likeness should be studied, first, in the case of things
belonging to different genera, the formulae being A : B
= C : D (e. g. as knowledge stands to the object of know
ledge, so is sensation related to the object of sensation),
and As A is in B, so is C in D (e. g. as sight is in the eye, 10
so is reason in the soul, and as is a calm in the sea, so is
windlessness in the air). Practice is more especially needed
in regard to terms that are far apart ; for in the case
of the rest, we shall be more easily able to see in one
glance the points of likeness. We should also look at
things which belong to the same genus, to see if any iden- 15
tical attribute belongs to them all, e. g. to a man and a
horse and a dog ; for in so far as they have any identical
attribute, in so far they are alike.

18 It is useful to have examined the number of meanings ot
a term both for clearness sake (for a man is more likely
to know what it is he asserts, if it has been made clear to

1 107^ 39. Read eV TO IS avro is ytvtcri.

io8 a TOPICA

20 him how many meanings it may have), and also with a view
to ensuring that our reasonings shall be in accordance with
the actual facts and not addressed merely to the term used.
For as long as it is not clear in how many senses a term
is used, it is possible that the answerer and the questioner
are not directing their minds upon the same thing : whereas
when once it has been made clear how many meanings
there are, and also upon which of them the former directs

25 his mind when he makes his assertion, the questioner would
then look ridiculous if he failed to address his argument
to this. It helps us also both to avoid being misled and
to mislead by false reasoning : for if we know the number
of meanings of a term, we shall certainly never be misled
by false reasoning, but shall know if the questioner fails to
address his argument to the same point ; and when we our-

30 selves put the questions we shall be able to mislead him, if
our answerer happens not to know the number of meanings
of our terms. This, however, is not possible in all cases,
but only when of the many senses some are true and others
are false. This manner of argument, however, does not
belong properly to dialectic ; dialecticians should therefore

35 by all means beware of this kind of verbal discussion, unless
any one is absolutely unable to discuss the subject before
him in any other way.

The discovery of the differences of things helps us both
in reasonings about sameness and difference, and also in
io8 b recognizing what any particular thing is. That it helps us
in reasoning about sameness and difference is clear : for when
we have discovered a difference of any kind whatever
between the objects before us, we shall already have shown
that they are not the same : while it helps us in recognizing
what a thing is, because we usually distinguish the expres-

5 sion that is proper to the essence of each particular thing
by means of the differentiae that are proper to it.

The examination of likeness is useful with a view both to
inductive arguments and to hypothetical reasonings, and
also with a view to the rendering of definitions. It is useful

10 for inductive arguments, because it is by means of an in
duction of individuals in cases that are alike that we claim

BOOK I. 18 io8 b

to bring the universal in evidence : for it is not easy to do
this if we do not know the points of likeness. It is useful
for hypothetical reasonings because it is a general opinion
that among similars what is true of one is true also of the
rest. If, then, with regard to any of them we are well
supplied with matter for a discussion, we shall secure a 15
preliminary admission that however it is in these cases, so
it is also in the case before us : then when we have shown
the former we shall have shown, on the strength of the
hypothesis, the matter before us as well : for we have first
made the hypothesis that however it is in these cases, so it
is also in the case before us, and have then proved the
point as regards these cases. It is useful for the rendering
of definitions because, if we are able to see in one glance 20
what is the same in each individual case of it, we shall be
at no loss into what genus we ought to put the object
before us when we define it : for of the common predicates
that which is most definitely in the category of essence
is likely to be the genus. Likewise, also, in the case of
objects widely divergent, the examination of likeness is
useful for purposes of definition, e. g. the sameness of a
calm at sea, and windlessness in the air (each being a form 25
of rest), and of a point on a line and the unit in number
each being a starting point. If, then, we render as the
genus what is common to all the cases, we shall get the
credit of defining not inappropriately. Definition-mongers
too nearly always render them in this way : for they declare
the unit to be the starting-point of number, and the point 30
the starting-point of a line. It is clear, then, that they
place them in that which is common to both as their
genus.

The means, then, whereby reasonings are effected, are
these : the commonplace rules, for the observance of which
the aforesaid means are useful, are as follows.

BOOK II
io8 b

37 OF problems some are universal, others particular. I
Universal problems are such as Every pleasure is good and
No pleasure is good ; particular problems are such as Some
iog a pleasure is good and Some pleasure is not good . The
methods of establishing and overthrowing a view universally
are common to both kinds of problems ; for when we have
shown that a predicate belongs in every case, we shall also
have shown that it belongs in some cases. Likewise, also,
5 if we show that it does not belong in any case, we shall also
have shown that it does not belong in every case. First,
then, we must speak of the methods of overthrowing
a view universally, because such are common to both
universal and particular problems, and because people more
usually introduce theses asserting a predicate than denying it,

10 while those who argue with them overthrow it. The
conversion of an appropriate name which is drawn from the
element accident is an extremely precarious thing ; for in
the case of accidents and in no other it is possible for
something to be true conditionally and not universally.
Names drawn from the elements definition and property
and genus are bound to be convertible ; e. g. if to be an
animal that walks on two feet is an attribute of S , then it

15 will be true by conversion to say that S is an animal that
walks on two feet . Likewise, also, if drawn from the genus ;
for if to be an animal is an attribute of S , then S is an
animal . The same is true also in the case of a property ;
for if to be capable of learning grammar is an attribute of
S , then S will be capable of learning grammar . For none

20 of these attributes can possibly belong or not belong in part ;
they must either belong or not belong absolutely. In the
case of accidents, on the other hand, there is nothing
to prevent an attribute (e. g. whiteness or justice) belonging
in part, so that it is not enough to show that whiteness or

BOOK II. i iog a

justice is an attribute of a man in order to show that he is
white or just ; for it is open to dispute it and say that he is
white or just in part only. Conversion, then, is not a 25
necessary process in the case of accidents.

We must also define the errors that occur in problems.
They are of two kinds, caused either by false statement or
by transgression of the established diction. For those who
make false statements, and say that an attribute belongs to
a thing which does not belong to it, commit error ; and 30
those who call objects by the names of other objects (e.g.
calling a plane-tree a man ) transgress the established
terminology.

2 Now one commonplace rule is to look and see if a man
has ascribed as an accident what belongs in some other way. 35
This mistake is most commonly made in regard to the
genera of things, e. g. if one were to say that white happens
(accidit) to be a colour for being a colour does not happen
by accident to white, but colour is its genus. The assertor
may of course define it so in so many words, saying (e. g.) that iog b
Justice happens (accidit) to be a virtue ; but often
even without such definition it is obvious that he has
rendered the genus as an accident ; e. g. suppose that one
were to say that whiteness is coloured or that walking is in
motion. For a predicate drawn from the genus is never 5
ascribed to the species in an inflected form, but always the
genera are predicated of their species literally ; for the
species take on both the name and the definition of their
genera. A man therefore who says that white is coloured
has not rendered coloured as its genus, seeing that he has
used an inflected form, nor yet as its property or as its
definition : for the definition and property of a thing belong 10
to it and to nothing else, whereas many things besides
white are coloured, e. g. a log, a stone, a man, and a horse.
Clearly then he renders it as an accident.

Another rule is to examine all cases where a predicate
has been either asserted or denied universally to belong to
something. Look at them species by species, and not
in their infinite multitude : for then the inquiry will proceed 15

iog b TOPICA

more directly and in fewer steps. You should look and
begin with the most primary groups, and then proceed
in order down to those that are not further divisible : e. g.
if a man has said that the knowledge of opposites is the
same, you should look and see whether it be so of relative
opposites and of contraries and of terms signifying the
privation or presence of certain states, and of contradictory

20 terms. Then, if no clear result be reached so far in these
cases, you should again divide these until you come to those
that are not further divisible, and see (e. g.) whether it be so
of just deeds and unjust, or of the double and the half, or of
blindness and sight, or of being and not-being : for if in any
case it be shown that the knowledge of them is not the same
we shall have demolished the problem. 1 Likewise, also, if

25 the predicate belongs in no case. This rule is convertible for
both destructive and constructive purposes : for if, when
we have suggested a division, the predicate appears to hold
in all or in a large number of cases, we may then claim that
the other should actually assert it universally, or else bring
a negative instance to show in what case it is not so : for if
he does neither of these things, a refusal to assert it will
make him look absurd.

30 Another rule is to make definitions both of an accident
and of its subject, either of both separately or else of one
of them, and then look and see if anything untrue has been
assumed as true in the definitions. Thus (e. g.) to see if it
is possible to wrong a god, ask what is to wrong ? For if
it be to injure deliberately , clearly it is not possible for a

35 god to be wronged : for it is impossible that God should be
injured. Again, to see if the good man is jealous, ask who
is the jealous man and what is jealousy . For if
jealousy is pain at the apparent success of some well-
behaved person, clearly the good man is not jealous : for
then he would be bad. Again, to see if the indignant man
is jealous, ask who each of them is : for then it will
no a be obvious whether the statement is true or false ; e. g. if he
is jealous who grieves at the successes of the good, and he
is indignant who grieves at the successes of the evil, then
1 iO9 b 23-4. Read a colon at elvm, and a full stop at

BOOK II. 2 no*

clearly the indignant man would not be jealous. A man
should substitute definitions also for the terms contained in 5
his definitions, and not stop until he comes to a familiar
term : for often if the definition be rendered whole, the point
at issue is not cleared up, whereas if for one of the terms used
in the definition a definition be stated, it becomes obvious.

Moreover, a man should make the problem into a propo- 10
sition for himself, and then bring a negative instance against
it : for the negative instance will be a ground of attack upon
the assertion. This rule is very nearly the same as the rule
to look into cases where a predicate has been attributed or
denied universally : but it differs in the turn of the
argument.

Moreover, you should define what kind of things should
be called as most men call them, and what should not. For 15
this is useful both for establishing and for overthrowing
a view : e. g. you should say that we ought to use our
terms to mean the same things as most people mean
by them, but when we ask what kind of things are or are not
of such and such a kind, we should not here go with the
multitude : e. g. it is right to call healthy whatever tends
to produce health, as do most men : but in saying whether 20
the object before us tends to produce health or not, we
should adopt the language no longer of the multitude but
of the doctor.

3 Moreover, if a term be used in several senses, and it has
been laid down that it is or that it is not an attribute of S,
you should show your case of one of its several senses, if 25
you cannot show it of both. This rule is to be observed
in cases where the difference of meaning is undetected ; for
supposing this to be obvious, then the other man will object
that the point which he himself questioned has not been
discussed, but only the other point. This commonplace
rule is convertible for purposes both of establishing and of
overthrowing a view. For if we want to establish a state
ment, we shall show that in one sense the attribute belongs, 30
if we cannot show it of both senses : whereas if we are over
throwing a statement, we shall show that in one sense

no a TOPICA

the attribute does not belong, if we cannot show it of both
senses. Of course, in overthrowing a statement there is no
need to start the discussion by securing any admission,
either when the statement asserts or when it denies
the attribute universally : for if we show that in any case
35 whatever the attribute does not belong, we shall have
demolished the universal assertion of it, and likewise also if
we show that it belongs in a single case, we shall demolish
the universal denial of it. Whereas in establishing a state
ment we ought to secure a preliminary admission that if it
belongs in any case whatever, it belongs universally,
supposing this claim to be a plausible one. For it is not
no b enough to discuss a single instance in order to show that an
attribute belongs universally ; e. g. to argue that if the
soul of man be immortal, then every soul is immortal, so
that a previous admission must be secured that if any soul
whatever be immortal, then every soul is immortal. This is
not to be done in every case, but only whenever we are
5 not easily able to quote any single argument applying to all
cases in common, as (e. g.) the geometrician can argue that
the triangle has its angles equal to two right angles.

If, again, the variety of meanings of a term be obvious,
distinguish how many meanings it has before proceeding
either to demolish or to establish it : e. g. supposing the
10 right to mean the expedient or the honourable , you
should try either to establish or to demolish both descrip
tions of the subject in question ; e. g. by showing that it is
honourable and expedient, or that it is neither honourable
nor expedient. Supposing, however, that it is impossible to
show both, you should show the one, adding an indication
that it is true in the one sense and not in the other. The
same rule applies also when the number of senses into
15 which it is divided is more than two.

Again, consider those expressions whose meanings are
many, but differ not by way of ambiguity of a term, but in
some other way : e. g. The science of many things is one :
here many things may mean the end and the means to
that end, as (e. g.) medicine is the science both of producing
health and of dieting ; or they may be both of them ends,

BOOK II. 3 no

as the science of contraries is said to be the same (for of 20
contraries the one is no more an end than the other) ;
or again they may be an essential and an accidental attribute,
as (e. g.) the essential fact that the triangle has its angles
equal to two right angles, and the accidental fact that
the equilateral figure has them so : for it is because
of the accident of the equilateral triangle happening
to be a triangle l that we know that it has its angles 25
equal to two right angles. If, then, it is not possible
in any sense of the term that the science of many things
should be the same, it clearly is altogether impossible
that it should be so ; or, if it is possible in some sense, then
clearly it is possible. Distinguish as many meanings as are
required : e. g. if we want to establish a view, we should
bring forward all such meanings as admit that view, and
should divide them only into those meanings which also are 30
required for the establishment of our case : whereas if we
want to overthrow a view, we should bring forward all that
do not admit that view, and leave the rest aside. We must
deal also in these cases as well with any uncertainty about
the number of meanings involved. Further, that one thing
is, or is not, of another should be established by means
of the same commonplace rules ; e. g. that a particular
science is of a particular thing, treated either as an end or as 35
a means to its end, or as accidentally connected with it ; or
again that it is not of it 2 in any of the aforesaid ways.
The same rule holds true also of desire and all other terms
that have more than one object. For the desire of X may
mean the desire of it as an end (e. g. the desire of health) or m a
as a means to an end (e. g. the desire of being doctored), or
as a thing desired accidentally, as, in the case of wine, the
sweet-toothed person desires it not because it is wine but
because it is sweet. For essentially he desires the sweet,
and only accidentally the wine : for if it be dry, he no 5
longer desires it. His desire for it is therefore accidental.
This rule is useful in dealing with relative terms: for cases
of this kind are generally cases of relative terms.

1 1 10*24. Read OTI ynp crv/*/3e7^Kf T< (VoTrXeiipco rpiycoyo) Tprywro) tij m.

2 no b 36. Omit ri after fivai (with C).

m a TOPICA

Moreover, it is well to alter a term into one more familiar, 4
e. g. to substitute clear for exact in describing a concep-

10 tion, and being fussy for being busy : for when the expres
sion is made more familiar, the thesis becomes easier to attack.
This commonplace rule also is available for both purposes
alike, both for establishing and for overthrowing a view.
In order to show that contrary attributes belong to the

15 same thing, look at its genus ; e. g. if we want to show that
Tightness and wrongness are possible in regard to perception,
and to perceive is to judge, while it is possible to judge
rightly or wrongly, then in regard to perception as well
Tightness and wrongness must be possible. In the present
instance the proof proceeds from the genus and relates to
the species : for to judge is the genus of to perceive ; for

20 the man who perceives judges in a certain way. But per
contra it may proceed from the species to the genus : for all
the attributes that belong to the species belong to the genus
as well ; e. g. if there is a bad and a good knowledge there
is also a bad and a good disposition : for disposition is the
genus of knowledge. Now the former commonplace argu
ment is fallacious for purposes of establishing a view, while

25 the second is true. For there is no necessity that all
the attributes that belong to the genus should belong also to
the species ; for animal is flying and quadruped, but not
so man . All the attributes, on the other hand, that
belong to the species must of necessity belong also to the
genus ; for if man is good, then animal also is good. On
the other hand, for purposes of overthrowing a view, the

30 former argument is true while the latter is fallacious ; for all
the attributes which do not belong to the genus do not belong
to the species either ; whereas all those that are wanting
to the species are not of necessity wanting to the genus.

Since those things of which the genus is predicated must
also of necessity have one of its species predicated of them,
and since those things that are possessed of the genus

35 in question, or are described by terms derived from that
genus, must also of necessity be possessed of one of its
species or be described by terms derived from one of its
species (e. g. if to anything the term scientific knowledge

BOOK II. 4 m a

be applied, then also there will be applied to it the term
grammatical or musical knowledge, or knowledge of one
of the other sciences ; and if any one possesses scientific
knowledge or is described by a term derived from science , in b
then he will also possess grammatical or musical knowledge
or knowledge of one of the other sciences, or will be
described by a term derived from one of them, e. g. as a
grammarian or a musician ) l therefore if any expression
be asserted that is in any way derived from the genus
(e. g. that the soul is in motion), look and see whether it be 5
possible for the soul to be moved with any of the species of -
motion ; whether (e. g.) it can grow or be destroyed or come
to be, and so forth with all the other species of motion. For
if it be not moved in any of these ways, clearly it does
not move at all. This commonplace rule is common for
both purposes, both for overthrowing and for establishing a
view : for if the soul moves with one of the species of 10
motion, clearly it does move ; while if it does not move
with any of the species of motion, clearly it does not move.

If you are not well equipped with an argument against
the assertion, look among the definitions, real or apparent,
of the thing before you, and if 2 one is not enough, draw
upon several. For it will be easier to attack people when 15
committed to a definition : for an attack is always more
easily made on definitions.

Moreover, look and see in regard to the thing in question,
what it is whose reality conditions the reality of the thing in
question, or what it is whose reality necessarily follows
if the thing in question be real : if you wish to establish
a view inquire what there is on whose reality the reality of
the thing in question will follow (for if the former be shown 20
to be real, then the thing in question will also have been
shown to be real) ; while if you want to overthrow a view,
ask what it is that is real if the thing in question be real, for
if we show that what follows from the thing in question is
unreal, we shall have demolished the thing in question.

1 Read a colon or comma instead of a full stop at /ZOIWIKO S (m b 4),
and for clearness put 111*36 olov . . . m b 4 /UOVO-IKOS (consisting as
it does wholly of illustrations), in a parenthesis.

2 Read KUV tl for KOI, with Vaticanus 207.

in b TOPICA

Moreover, look at the time involved, to see if there be any

25 discrepancy anywhere : e. g. suppose a man to have stated

that what is being nourished of necessity grows : for animals

are always of necessity being nourished, but they do not

always grow. Likewise, also, if he has said that knowing

is remembering : for the one is concerned with past time,

whereas the other has to do also with the present and the

future. For we are said to know things present and future

30 (e.g. that there will be an eclipse), whereas it is impossible

to remember anything save what is in the past.

Moreover, there is the sophistic turn of argument, where- 5
by we draw our opponent into the kind of statement against
which we shall be well supplied with lines of argument.
This process is sometimes a real necessity, sometimes an
apparent necessity, sometimes neither an apparent nor a real
35 necessity. It is really necessary whenever the answerer
has denied any view that would be useful in attacking
the thesis, and the questioner thereupon addresses his argu
ments to the support of this view, and when moreover
the view in question happens to be one of a kind on
which he has a good stock of lines of argument. Likewise,
also, it is really necessary whenever he (the questioner) first,
ii2 a by an induction made by means of the view laid down, 1
arrives at a certain statement and then tries to demolish
that statement : for when once this has been demolished, the
view originally laid down is demolished as well. It is an
apparent necessity, when the point to which the discussion
comes to be directed appears to be useful, and relevant
to the thesis, without being really so ; whether it be that
5 the man who is standing up to the argument has refused to
concede something, or whether he (the questioner) has first
reached it by a plausible induction based upon the thesis 2
and then tries to demolish it. The remaining case is when
the point to which the discussion comes to be directed
is neither really nor apparently necessary, and it is the
answerer s luck to be confuted on a mere side issue. You
10 should beware of the last of the aforesaid methods ; for it
1 Sc. by the answerer . z Sc. of the answerer .

BOOK II. 5 us

appears to be wholly disconnected from, and foreign to, the
art of dialectic. For this reason, moreover, the answerer
should not lose his temper, but assent to those statements
that are of no use in attacking the thesis, adding an
indication whenever he assents although he does not agree
with the view. For, as a rule, it increases the confusion of
questioners if, after all propositions of this kind have been 15
granted them, they can then draw no conclusion.

Moreover, any one who has made any statement whatever
has in a certain sense made several statements, inasmuch
as each statement has a number of necessary consequences :
e. g. the man who said X is a man has also said that it is
an animal and that it is animate and a biped and capable of
acquiring reason and knowledge, so that by the demolition ao
of any single one of these consequences, of whatever kind,
the original statement is demolished as well. But you
should beware here too of making a change to a more difficult
subject : for sometimes the consequence, and sometimes the
original thesis, is the easier to demolish.

6 In regard to subjects which must have one and one only
of two predicates, as (e.g.) a man must have either a disease 25
or health, supposing we are well supplied as regards the one
for arguing its presence or absence, we shall be well equipped
as regards the remaining one as well. This rule is convertible
for both purposes : for when we have shown that the one
attribute belongs, we shall have shown that the remaining
one does not belong ; while if we show that the one does not
belong, we shall have shown that the remaining one does 3
belong. Clearly then the rule is useful for both purposes.

Moreover, you may devise a line of attack by reinterpreting
a term in its literal meaning, with the implication that it is
most fitting so to take it rather than in its established
meaning: e.g. the expression strong at heart will suggest
not the courageous man, according to the use now established,
but the man the state of whose heart is strong ; just as also 35
the expression of a good hope may be taken to mean the
man who hopes for good things. Likewise also well-starred
may be taken to mean the man whose star is good, as

4S-28 D

iia a TOPICA

Xenocrates says well-starred is he who has a noble soul . 1
For a man s star is his soul.

ii2 b Some things occur of necessity, others usually, others
however it may chance ; if therefore a necessary event has
been asserted to occur usually, or if a usual event (or, failing
such an event itself, its contrary) has been stated to occur
. of necessity, it always gives an opportunity for attack. For
if a necessary event has been asserted to occur usually,
clearly the speaker has denied an attribute to be universal
which is universal, and so has made a mistake : and so he
has if he has declared the usual attribute to be necessary :
for then he declares it to belong universally when it does
not so belong. Likewise also if he has declared the contrary

10 of what is usual to be necessary. For the contrary of a usual
attribute is always a comparatively rare attribute : e. g. if
men are usually bad, they are comparatively seldom good,
so that his mistake is even worse if he has declared them to
be good of necessity. The same is true also if he has
declared a mere matter of chance to happen of necessity or

15 usually ; for a chance event happens neither of necessity nor
usually. If the thing happens usually, then even supposing
his statement does not distinguish whether he meant that it
happens usually or that it happens necessarily, it is open to
you to discuss it on the assumption that he meant that
it happens necessarily : e. g. if he has stated without any
distinction that disinherited persons are bad, you may

20 assume in discussing it that he means that they are so
necessarily.

Moreover, look and see also if he has stated a thing to be
an accident of itself, taking it to be a different thing because
it has a different name, as Prodicus used to divide pleasures
into joy and delight and good cheer : for all these are names
of the same thing, to wit, Pleasure. If then any one says

25 that joyfulness is an accidental attribute of cheerfulness, he
would be declaring it to be an accidental attribute of itself.

Inasmuch as contraries can be conjoined with each other 7
in six ways, and four of these conjunctions constitute a con-
1 Fr. 8 1 Heinze.

BOOK II. 7 na b

trariety, we must grasp the subject of contraries, in order
that it may help us both in demolishing and in establishing
a view. Well then, that the modes of conjunction are six 30
is clear : for either (i) each of the contrary verbs will be con
joined to each of the contrary objects ; and this gives two
modes : e.g. to do good to friends and to do evil to enemies,
or per contra to do evil to friends and to do good to enemies.
Or else (2) both verbs may be attached to one object ; and
this too gives two modes, e.g. to do good to friends and to 35
do evil to friends, or to do good to enemies and to do evil
to enemies. 1 Or (3) a single verb may be attached to both
objects: and this also gives two modes ; e.g. to do good to
friends and to do good to enemies, or to do evil to friends
and evil to enemies.

The first two then of the aforesaid conjunctions do not 113*
constitute any contrariety ; for the doing of good to friends
is not contrary to the doing of evil to enemies : for both
courses are desirable and belong to the same disposition.
Nor is the doing of evil to friends contrary to the doing of
good to enemies : for both of these are objectionable and 5
belong to the same disposition : and one objectionable thing
is not generally thought to be the contrary of another, unless
the one be an expression denoting an excess, and the other
an expression denoting a defect : for an excess is generally
thought to belong to the class of objectionable things, and
likewise also a defect. But the other four all constitute
a contrariety. For to do good to friends is contrary to the 10
doing of evil to friends : for it proceeds from the contrary
disposition, and the one is desirable, and the other objection
able. The case is the same also in regard to the other
conjunctions : for in each combination the one course is
desirable, and the other objectionable, and the one belongs
to a reasonable disposition and the other to a bad. Clearly,
then, from what has been said, the same course has more
than one contrary. For the doing of good to friends has as 15
its contrary both the doing of good to enemies and the doing
of evil to friends. Likewise, if we examine them in the
same way, we shall find that the contraries of each of the
1 H2 b 36. Read /cm TO TOVS e^povs KOKUS (with C).
D 2

3 a TOPICA

others also are two in number. Select therefore whichever
of the two contraries is useful in attacking the thesis.

30 Moreover, if the accident of a thing have a contrary, see
whether it belongs to the subject to which the accident in
question has been declared to belong: for if the latter
belongs the former could not belong; for it is impossible
that contrary predicates should belong at the same time
to the same thing.

Or again, look and see if anything has been said about
something, of such a kind that if it be true, contrary predi-

2 5 cates must necessarily belong to the thing: e.g. if he has
said that the Ideas exist in us. For then the result will
be that they are both in motion and at rest, and moreover
that they are objects both of sensation and of thought.
For according to the views of those who posit the existence
of Ideas, those Ideas are at rest and are objects of thought ;
while if they exist in us, it is impossible that they should
be unmoved : for when we move, it follows necessarily that

30 all that is in us moves with us as well. Clearly also they
are objects of sensation, if they exist in us : for it is through
the sensation of sight that we recognize the Form present
in each individual.

Again, if there be posited an accident which has a contrary,
look and see if that which admits of the accident will admit
of its contrary as well: for the same thing admits of con-

35 traries. Thus (e. g.) if he has asserted that hatred follows
anger, hatred would in that case be in the spirited faculty :
H3 b for that is where anger is. You should therefore look and
see if its contrary, to wit, friendship, be also in the spirited
faculty : for if not if friendship is in the faculty of desire
then hatred could not follow anger. Likewise also if he
has asserted that the faculty of desire is ignorant. For if
5 it were capable of ignorance, it would be capable of knowledge
as well : and this is not generally held I mean that the
faculty of desire is capable of knowledge. For purposes,
then, of overthrowing a view, as has been said, this rule
should be observed : but for purposes of establishing one,
though the rule will not help you to assert that the accident
actually belongs, it will help you to assert that it may possibly

BOOK II. 7 113"

belong. For having shown that the thing in question will
not admit of the contrary of the accident asserted, we shall
have shown that the accident neither belongs nor can possibly 10
belong ; while on the other hand ; if we show that the con
trary belongs, or that the thing is capable of the contrary,
we shall not indeed as yet have shown that the accident
asserted does belong as well ; our proof will merely have
gone to this point, that it is possible for it to belong.

8 Seeing that the modes of opposition are four in number, 15
you should look for arguments among the contradictories
of your terms, converting the order of their sequence, both
when demolishing and when establishing a view, and you
should secure them by means of induction such arguments
(e.g.) as that If man be an animal, what is not an animal
is not a man : and likewise also in other instances of con
tradictories. For in those cases the sequence is converse :
for animal follows upon man , but not-animal does not 20
follow upon not-man , but conversely not-man upon not-
animal . In all cases, therefore, a postulate of this sort
should be made, (e.g.) that l If the honourable is pleasant,
what is not pleasant is not honourable, while if the latter be
untrue, so is the former . Likewise, also, If what is not
pleasant be not honourable, then what is honourable is
pleasant . Clearly, then, the conversion of the sequence 25
formed by contradiction of the terms of the thesis is a method
convertible for both purposes.

Then look also at the case of the contraries of S and P
in the thesis, and see if the contrary of the one follows upon
the contrary of the other, either directly or conversely, both
when you are demolishing and when you are establishing
a view : secure arguments of this kind as well by means of
induction, so far as may be required. Now the sequence is 30
direct in a case such as that of courage and cowardice : for
upon the one of them virtue follows, and vice upon the other;
and upon the one it follows that it is desirable, while upon
the other it follows that it is objectionable. The sequence,
therefore, in the latter case also is direct ; for the desirable
is the contrary of the objectionable. Likewise also in other

"3 b TOPICA

cases. The sequence is, on the other hand, converse in such

35 a case as this : Health follows upon vigour, but disease
does not follow upon debility ; rather debility follows
upon disease. In this case, then, clearly the sequence
H4 a is converse. Converse sequence is, however, rare in the
case of contraries ; usually the sequence is direct. If,
therefore, the contrary of the one term does not follow
upon the contrary of the other either directly or conversely,
clearly neither does the one term follow upon the other in

5 the statement made : whereas if the one followed the other
in the case of the contraries, it must of necessity do so as well
in the original statement.

You should look also into cases of the privation or presence
of a state in like manner to the case of contraries. Only, in
the case of such privations the converse sequence does not
occur : the sequence is always bound to be direct : e. g. as

10 sensation follows sight, while absence of sensation follows
blindness. For the opposition of sensation to absence of
sensation is an opposition of the presence to the privation
of a state : for the one of them is a state, and the other the
privation of it.

The case of relative terms should also be studied
in like manner to that of a state and its privation : for

15 the sequence of these as well is direct; e.g. "if 3/1 is a
multiple, then 1/3 is a fraction : for 3/1 is relative to 1/3,
and so is a multiple to a fraction. Again, if knowledge be
a conceiving, then also the object of knowledge is an object
of conception ; and if sight be a sensation, then also the

ao object of sight is an object of sensation. An objection may
be made that there is no necessity for the sequence to take
place, in the case of relative terms, in the way described :
for the object of sensation is an object of knowledge, whereas
sensation is not knowledge. The objection is, however, not
generally received as really true ; for many people deny
that there is knowledge of objects of sensation. More
over, the principle stated is just as useful for the contrary
purpose, e.g. to show that the object of sensation is not an

2 5 object of knowledge, on the ground that neither is sensation
knowledge.

BOOK II. 9 ii4

9 Again look at the case of the co-ordinates and inflected
forms of the terms in the thesis, both in demolishing and
in establishing it. By co-ordinates are meant terms such
as the following: Just deeds and the just man are co
ordinates of justice , and courageous deeds and the
courageous man are co-ordinates of courage . Likewise
also things that tend to produce and to preserve anything
are called co-ordinates of that which they tend to produce 3
and to preserve, as e.g. healthy habits are co-ordinates of
health and a vigorous constitutional of a vigorous con
stitution and so forth also in other cases. Co-ordinate ,
then, usually describes cases such as these, whereas inflected
forms are such as the following: justly , courageously ,
healthily , and such as are formed in this way. It is usually
held that words when used in their inflected forms as well 35
are co-ordinates, as (e.g.) justly in relation to justice, and
courageously to courage ; and then co-ordinate describes
all the members of the same kindred series, e.g. justice ,
just , of a man or an act, justly . Clearly, then, when any
one member, whatever its kind, of the same kindred series
is shown to be good or praiseworthy, then all the rest as well H4
come to be shown to be so : l e.g. if justice be something
praiseworthy, then so will just , of a man or thing, and
justly connote something praiseworthy. Then justly
will be rendered also praiseworthiiy , derived by the same
inflexion from the praiseworthy whereby justly is derived 5
from justice .

Look not only in the case of the subject mentioned, but
also in the case of its contrary, for the contrary predicate :
e.g. argue that good is not necessarily pleasant ; for neither
is evil painful : or that, if the latter be the case, so is the
former. Also, if justice be knowledge, then injustice is
ignorance : and if justly means knowingly and skilfully , 10
then unjustly means ignorantly and ; unskilfully : whereas
if the latter be not true, neither is the former, as in the
instance given just now : for unjustly is more likely to
seem equivalent to skilfully than to unskilfully . This
commonplace rule has been stated before in dealing with
1 U4 b i. Read dt8fiypfi>a -yiWat, with the best MSS.

n 4 b TOPICA

the sequence of contraries ; l for all we are claiming now
15 is that the contrary of P shall follow the contrary of S.

Moreover, look at the modes of generation and destruction
of a thing, and at the things which tend to produce or to
destroy it, both in demolishing and in establishing a view.
For those things whose modes of generation rank among
good things, are themselves also good ; and if they them
selves be good, so also are their modes of generation. If,
on the other hand, their modes of generation be evil, then
they themselves also are evil. In regard to modes of destruc-
ao tion the converse is true : for if the modes of destruction
rank as good things, then they themselves rank as evil
things ; whereas if the modes of destruction count as evil,
they themselves count as good. The same argument applies
also to things tending to produce and destroy : for things
whose productive causes are good, themselves also rank as
good ; whereas if causes destructive of them are good, they
themselves rank as evil.

25 Again, look at things which are like the subject in question, IO
and see if they are in like case; e.g. if one branch of know
ledge has more than one object, so also will one opinion ;
and if to possess sight be to see, then also to possess hearing
will be to hear. Likewise also in the case of other things,
both those which are and those which are generally held to
be like. The rule in question is useful for both purposes ;

30 for if it be as stated in the case of some one like thing, it is
so with the other like things as well, whereas if it be not so
in the case of some one of them, neither is it so in the case
of the others. Look and see also whether the cases are alike
as regards a single thing and a number of things : for
sometimes there is a discrepancy. Thus, if to know a thing
be to think of it, then also to know many things is to
be thinking of many things ; whereas this is not true;
for it is possible to know many things but not to be thinking

35 of them. If, then, the latter proposition be not true, neither
was the former that dealt with a single thing, viz. that to
know a thing is to think of it

BOOK II. 10 n 4 b

Moreover, argue from greater and less degrees. In regard
to greater degrees l there are four commonplace rules. One
is : See whether a greater degree of the predicate follows
a greater degree of the subject: e.g. if pleasure be good,
see whether also a greater pleasure be a greater good : and
if to do a wrong be evil, see whether also to do a greater 115"
wrong is a greater evil. Now this rule is of use for both
purposes : for if an increase of the accident follows an
increase of the subject, as we have said, clearly the accident
belongs ; while if it does not follow, the accident does not 5
belong. You should establish this by induction. Another
rule is: If one predicate be attributed to two subjects;
then supposing it does not belong to the subject to which it is
the more likely to belong, neither does it belong where it is
less likely to belong ; while if it does belong where it is less
likely to belong, then it belongs as well where it is more likely.
Again : If two predicates be attributed to one subject, then
if the one which is more generally thought to belong does not
belong, neither does the one that is less generally thought 10
to belong ; or, if the one that is less generally thought
to belong does belong, so also does the other. Moreover :
If two predicates be attributed to two subjects, then if the
one which is more usually thought to belong to the one
subject does not belong, neither does the remaining predicate
belong to the remaining subject; or, if the one which is less
usually thought to belong to the one subject does belong, so
too does the remaining predicate to the remaining subject.

Moreover, you can argue from the fact that an attri- 15
bute belongs, or is generally supposed to belong, in a
like degree, in three ways, viz. those described in the last
three rules given in regard to a greater degree. 2 For sup
posing that one predicate belongs, or is supposed to
belong, to two subjects in a like degree, then if it does not
belong to the one, neither does it belong to the other ; while
if it belongs to the one, it belongs to the remaining one as
well. Or, supposing two predicates to belong in a like degree
to the same subjecl;, then, if the one does not belong, neither 20

1 H4 b 37-8. Omit not rtrrov before TOXOI. with the best MSS.

2 11. 6-14.

ii5 a TOPICA

does the remaining one ; while if the one does belong, the
remaining one belongs as well. The case is the same also
if two predicates belong in a like degree to two subjects ;
for if the one predicate does not belong to the one subject,
neither does the remaining predicate belong to the remaining
subject, while if the one predicate does belong to the one
subject, the remaining predicate belongs to the remaining
subject as well.

25 You can argue, then, from greater or less or like degrees n
of truth in the aforesaid number of ways. Moreover, you
should argue from the addition of one thing to another.
If the addition of one thing to another makes that other
good or white, whereas formerly it was not white or good,
then the thing added will be white or good it will possess
the character it imparts to the whole as well. Moreover,

30 if an addition of something to a given object intensifies the
character which it had as given, then the thing added will
itself as well be of that character. Likewise, also, in the
case of other attributes. The rule is not applicable in all
cases, but only in those in which the excess described as an
increased intensity is found to take place. The above
rule is, however, not convertible for overthrowing a view.
For if the thing added does not make the other good, it is

35 not thereby made clear whether in itself it may not be good :
ii5 b for the addition of good to evil does not necessarily make
the whole good, any more than the addition of white to
black makes the whole white.

Again, any predicate of which we can speak of greater or
less degrees belongs also absolutely : for greater or less
degrees of good or of white will not be attributed to what
5 is not good or white : for a bad thing will never be said to
have a greater or less degree of goodness than another, but
always of badness. This rule is not convertible, either, for
the purpose of overthrowing a predication : for several predi
cates of which we cannot speak of a greater degree belong
absolutely : for the term man is not attributed in greater

10 and less degrees, but a man is a man for all that.

You should examine in the same way predicates attributed

BOOK II. II ii5 b

in a given respect, and at a given time and place : for if the
predicate be possible in some respect, it is possible also
absolutely. Likewise, also, is what is predicated at a given
time or place: for what is absolutely impossible is not
possible either in any respect or at any place or time. An
objection may be raised that in a given respect people may J 5
be good by nature, e.g. they may be generous or temperately
inclined, while absolutely they are not good by nature,
because no one is prudent by nature. Likewise, also, it is
possible for a destructible thing to escape destruction at
a given time, whereas it is not possible for it to escape
absolutely. In the same way also it is a good thing at
certain places to follow such and such a diet, e.g. in infected 20
areas, though it is not a good thing absolutely. Moreover,
in certain places it is possible to live singly and alone, but
absolutely it is not possible to exist singly and alone. In
the same way also it is in certain places honourable to
sacrifice one s father, e. g. among the Triballi, whereas,
absolutely, it is not honourable. Or possibly this may
indicate a relativity not to places but to persons : for it is
all the same wherever they may be : for everywhere it will 2;)
be held honourable among the Triballi themselves, just
because they are Triballi. Again, at certain times it is
a good thing to take medicines, e.g. when one is ill, but it
is not so absolutely. Or possibly this again may indicate
a relativity not to a certain time, but to a certain state of
health : for it is all the same whenever it occurs, if only
one be in that state. A thing is absolutely so which
without any addition you are prepared to say is honourable 3
or the contrary. Thus (e.g.) you will deny that to sacrifice
one s father is honourable : it is honourable only to certain
persons : it is not therefore honourable absolutely. On the
other hand, to honour the gods you will declare to be
honourable without adding anything, because that is honour
able absolutely. So that whatever without any addition is
generally accounted to be honourable or dishonourable or
anything else of that kind, will be said to be so absolutely . 35

BOOK III
n6 a

THE question which is the more desirable, or the better, I
of two or more things, should be examined upon the
following lines : only first of all it must be clearly laid
down that the inquiry we are making concerns not things
5 that are widely divergent and that exhibit great differences
from one another (for nobody raises any doubt whether
happiness or wealth is more desirable), but things that are
nearly related and about which we commonly discuss for
which of the two we ought rather to vote, because we do not
see any advantage on either side as compared with the other.

10 Clearly, then, in such cases if we can show a single advan
tage, or more than one, our judgement will record our
assent that whichever side happens to have the advantage
is the more desirable.

First, then, that which is more lasting or secure is more
desirable than that which is less so : and so is that which is
more likely to be chosen by the prudent or by the good

15 man or by the right law, or by men who are good in any
particular line, when they make their choice as such, or by
the experts in regard to any particular class of things ; i. e.
either whatever most of them or what all of them would
choose ; e. g. in medicine or in carpentry those things are
more desirable which most, or all, doctors would choose ;
or, in general, whatever most men or all men or all things
would choose, e.g. the good: for everything aims at the

20 good. You should direct the argument you intend to
employ to whatever purpose you require. Of what is
better or more desirable the absolute standard is the
verdict of the better science, though relatively to a given
individual the standard may be his own particular science.
In the second place, that which is known as an x is
more desirable than that which does not come within the
genus x e. g. justice than a just man ; for the former

BOOK III. I "6 a

falls within the genus good , whereas the other does not,
and the former is called a good , whereas the latter is not : 25
for nothing which does not happen to belong to the genus
in question is called by the generic name ; e. g. a white
man is not a colour . Likewise also in other cases.

Also, that which is desired for itself is more desirable
than that which is desired for something else ; e. g. health
is more desirable than gymnastics : for the former is desired 3
for itself, the latter for something else. Also, that which is
desirable in itself is more desirable than what is desirable
per accidens ; e. g. justice in our friends than justice in our
enemies : for the former is desirable in itself, the latter per
accidens : for we desire that our enemies should be just
per accidens, in order that they may do us no harm. This
last principle is the same as the one that precedes it, with, 35
however, a different turn of expression. For we desire
justice in our friends for itself, even though it will make
no difference to us, and even though they be in India ;
whereas in our enemies we desire it for something else, in
order that they may do us no harm.

Also, that which is in itself the cause of good is more n6 b
desirable than what is so per accidens, e. g. virtue than
luck (for the former is in itself, and the latter per accidens,
the cause of good things), 1 and so in other cases of the
same kind. Likewise also in the case of the contrary ; for
what is in itself the cause of evil is more objectionable than 5
what is so per accidens, e. g. vice and chance : for the one is
bad in itself, whereas chance is so per accidens.

Also, what is good absolutely is more desirable than what
is good for a particular person, e. g. recovery of health than
a surgical operation ; for the former is good absolutely, the
latter only for a particular person, viz. the man who needs 10
an operation. So too what is good by nature is more
desirable than the good that is not so by nature, e. g. justice
than the just man ; for the one is good by nature, whereas
in the other case the goodness is acquired. Also the attribute
is more desirable which belongs to the better and more

1 Ii6 b 2~3. Treat 17 p.kv yap . . . TO>V ayadav as a parenthesis, with
Wallies.

n6 b TOPICA

honourable subject, e.g. to a god rather than to a man, and to
the soul rather than to the body. So too the property of the
better thing is better than the property of the worse ; e. g.

15 the property of God than the property of man : for whereas
in respect of what is common in both of them they do not
differ at all from each other, in respect of their properties
the one surpasses the other. Also that is better which is
inherent in things better or prior or more honourable : thus
(e. g.) health is better than strength and beauty : for the
former is inherent in the moist and the dry, and the hot
and the cold, in fact in all the primary constituents of an
animal, whereas the others are inherent in what is secondary,

20 strength being a feature of the sinews and bones, while
beauty is generally supposed to consist in a certain sym
metry of the limbs. Also the end is generally supposed to
be more desirable than the means, and of two means, that
which lies nearer the end. In general, too, a means directed
towards the end of life is more desirable than a means to

25 anything else, e. g. that which contributes to happiness
than that which contributes to prudence. Also the com
petent is more desirable than the incompetent. Moreover,
of two productive agents that one is more desirable whose
end is better ; while between a productive agent and an end
we can decide by a proportional sum whenever the excess
of the one end over the other is greater than that of the
latter over its own productive means : e. g. supposing the
excess of happiness over health to be greater than that of

30 health over what produces health, then what produces
happiness is better than health. For what produces happi
ness exceeds what produces health just as much as happiness
exceeds health. But health exceeds what produces health
by a smaller amount ; ergo y the excess of what produces
happiness over what produces health is greater than that of
health over what produces health. Clearly, therefore, what

35 produces happiness is more desirable than health : for it
exceeds the same standard by a greater amount.

Moreover, what is in itself nobler and more precious and
praiseworthy is more desirable than what is less so, e. g.
friendship than wealth, and justice than strength. For the

BOOK III. i n6 l

former belong in themselves to the class of things precious
and praiseworthy, while the latter do so not in themselves n? 8
but for something else : for no one prizes wealth for itself
but always for something else, whereas we prize friendship
for itself, even though nothing else is likely to come to us
from it.

2 Moreover, whenever two things are very much like one 5
another, 1 and we cannot see any superiority in the one over
the other of them, we should look at them from the stand
point of their consequences. For the one which is followed
by the greater good is the more desirable : or, if the con
sequences be evil, that is more desirable which is followed
by the less evil. For though both may be desirable, yet
there may possibly be some unpleasant consequence T
involved to turn the scale. Our survey from the point of
view of consequences lies in two directions, for there are
prior consequences and later consequences : e. g. if a man
learns, it follows that he was ignorant before and knows
afterwards. As a rule, the later consequence is the better
to consider. You should take, therefore, whichever of the
consequences suits your purpose. 15

Moreover, a greater number of good things is more
desirable than a smaller, either absolutely or when the one is
included in the other, viz. the smaller number in the greater.
An objection maybe raised suppose in some particular case
the one is valued for the sake of the other ; for then the
two together are not more desirable than the one ; e. g.
recovery of health and health, than health alone, inasmuch 20
as we desire recovery of health for the sake of health. Also
it is quite possible for what is not good, together with what
is, to be more desirable than a greater number of good
things, 2 e. g. the combination of happiness and something
else which is not good may be more desirable than the

1 1 17* 5. Read avro ts for U\\TJ\OIS.

I I7 a 21. Read *l p.r] ayada /ier ayciQatv ovdev KoAvei dvai aiperutTtpa
(sc. -n\fi6vtov aya65>v}. Or, keeping the MS. reading, trans. Also it is
quite possible for what are not good things to be more desirable than
what are : happiness plus a not-good thing are not good things :
only one of them is good.

n7 a TOPICA

combination of justice and courage. Also, the same things
are more valuable if accompanied than if unaccompanied
by pleasure, and likewise when free from pain than when

25 attended with pain.

Also, everything is more desirable at the season when it
is of greater consequence ; e. g. freedom from pain in old
age more than in youth : for it is of greater consequence in
old age. On the same principle also/ prudence is more
desirable in old age ; for no man chooses the young to

30 guide him, because he does not expect them to be prudent.
With courage, the converse is the case, for it is in youth
that the active exercise of courage is more imperatively
required. Likewise also with temperance ; for the young
are more troubled by their passions than are their elders.

35 Also, that is more desirable which is more useful at every
season or at most seasons, e.g. justice and temperance
rather than courage : for they are always useful, while
courage is only useful at times. Also, that one of two
things which if all possess, we do not need the other thing,
is more desirable than that which all may possess and still
we want the other one as well. Take the case of justice
and courage ; if everybody were just, there would be no use
H7 b for courage, whereas all might be courageous, and still
justice would be of use.

Moreover, judge by the destructions and losses and
generations and acquisitions and contraries of things : for
5 things whose destruction is more objectionable are them
selves more desirable. Likewise also with the losses and
contraries of things ; for a thing whose loss or whose
contrary is more objectionable is itself more desirable.
With the generations or acquisitions of things the opposite
is the case : for things whose acquisition or generation is
more desirable are themselves also desirable.

10 Another commonplace rule is that what is nearer to the
good is better and more desirable, 2 i. e. what more nearly
resembles the good : thus justice is better than a just man.
Also, that which is more like than another thing to some-

1 117*28. Read Kara Tavra 8f.

2 H7 b II. Read a comma only, not a full stop, after aiperurfpov.

BOOK III. 2 ii7 b

thing better than itself, as e. g. some say that Ajax was
a better man than Odysseus because he was more like
Achilles. An objection maybe raised to this that it is not
true : for it is quite possible that Ajax did not resemble
Achilles more nearly than Odysseus in the points which 15
made Achilles the best of them, and that Odysseus was a
good man, though unlike Achilles. Look also to see
whether the resemblance be that of a caricature, like the
resemblance of a monkey to a man, whereas a horse bears
none : for the monkey is not the more handsome creature,
despite its nearer resemblance to a man. Again, in the
case of two things, if one is more like the better thing 20
while another is more like the worse, then that is likely to
be better which is more like the better. This too, how
ever, admits of an objection : for quite possibly the one
only slightly resembles the better, while the other strongly
resembles the worse, e. g. supposing the resemblance of
Ajax to Achilles to be slight, while that of Odysseus to
Nestor is strong. Also it may be that the one which is 25
like the better type shows a degrading likeness, whereas
the one which is like the worse type improves upon it:
witness the likeness of a horse to a donkey, and that of a
monkey to a man.

Another rule is that the more conspicuous good is more
desirable than the less conspicuous, and the more difficult
than the easier : for we appreciate better the possession of
things that cannot be easily acquired. Also the more 30
personal possession is more desirable than the more widely
shared. Also, that which is more free from connexion
with evil : for what is not attended by any unpleasantness
is more desirable than what is so attended.

Moreover, if A be without qualification better than B,
then also the best of the members of A is better than the
best of the members of B ; e. g. if Man be better than
Horse, then also the best man is better than the best horse. 35
Also, if the best in A be better than the best in B, then also
A is better than B without qualification ; e. g. if the best
man be better than the best horse, then also Man is better
than Horse without qualification.

n8 a TOPIC A

u8 a Moreover, things which our friends can share are more
desirable than those they cannot. Also, things which we
like rather to do to our friend are more desirable than those
we like to do to the man in the street, e. g. just dealing
and the doing of good rather than the semblance of them :
5 for we would rather really do good to our friends than seem
to do so, whereas towards the man in the street the converse
is the case.

Also, superfluities are better than necessities, and are
sometimes more desirable as well : for the good life is
better than mere life, and good life is a superfluity, whereas
mere life itself is a necessity. Sometimes, though, what is
better is not also more desirable : for there is no necessity

10 that because it is better it should also be more desirable :
at least to be a philosopher is better than to make money,
but it is not more desirable for a man who lacks the neces
sities of life. The expression superfluity applies when
ever a man possesses the necessities of life and sets to
work to secure as well other noble acquisitions. Roughly

15 speaking, perhaps, necessities are more desirable, while
superfluities are better.

Also, what cannot be got from another is more desirable
than what can be got from another as well, as (e. g.) is the
case of justice compared with courage. Also, A is more
desirable if A is desirable without B, but not B without A :
power (e. g.) is not desirable without prudence, but prudence

20 is desirable without power. Also, if of two things we
repudiate the one in order to be thought to possess the
other, then that one is more desirable which we wish to be
thought to possess ; thus (e. g.) we repudiate the love of
hard work in order that people may think us geniuses.
Moreover, that is more desirable in whose absence it is

35 less blameworthy for people to be vexed ; and that is more
desirable in whose absence it is more blameworthy for
a man not to be vexed.

Moreover, of things that belong to the same species one 3
which possesses the peculiar virtue of the species is more
desirable than one which does not. If both possess it, then

BOOK III. 3 n8 a

the one which possesses it in a greater degree is more
desirable.

Moreover, if one thing makes good whatever it touches,
while another does not, the former is more desirable, just 30
as also what makes things warm is warmer than what does
not. If both do so, then that one is more desirable which
does so in a greater degree, or if it render good the better
and more important object if (e. g.), the one makes good
the soul, and the other the body.

Moreover, judge things by their inflexions and uses and
actions and works, and judge these by them : for they go 35
with each other: e.g. if justly means something more
desirable than courageously , then also justice means
something more desirable than courage ; and if justice be
more desirable than courage, then also justly means
something more desirable than courageously . Similarly
also in the other cases.

Moreover, if one thing exceeds while the other falls short n8 b
of the same standard of good, the one which exceeds is the
more desirable ; or if the one exceeds an even higher
standard. Nay more, if there be two things both prefer
able to something, the one which is more highly preferable
to it is more desirable than the less highly preferable.
Moreover, when the excess of a thing is more desirable than 5
the excess of something else, that thing is itself also more
desirable than the other, as (e. g.) friendship than money :
for an excess of friendship is more desirable than an excess
of money. So also that of which a man would rather that
it were his by his own doing is more desirable than what he
would rather get by another s doing, e. g. friends than money.

Moreover, judge by means of an addition, and see if the 10
addition of A to the same thing as B makes the whole more
desirable than does the addition of B. You must, how
ever, beware of adducing a case in which the common term
uses, or in some other way helps the case of, one of the
things added to it, but not the other, as (e. g.) if you took
a saw and a sickle in combination with the art of carpentry :
for in the combination the saw is a more desirable thing, 15
but it is not a more desirable thing without qualification.

E 2

n8 b TOPICA

Again, a thing is more desirable if, when added to a lesser
good, it makes the whole a greater good. Likewise, also,
you should judge by means of subtraction : for the thing
upon whose subtraction the remainder is a lesser good may
be taken to be a greater good, whichever it be whose l sub
traction makes the remainder a lesser good.

20 Also, if one thing be desirable for itself, and the other
for the look of it, the former is more desirable, as (e. g.)
health than beauty. A thing is defined as being desired
for the look of it if, supposing no one knew of it, you would
not care to have it. Also, it is more desirable if it be desirable
both for itself and for the look of it, while the other thing
is desirable on the one ground alone. Also, whichever is
the more precious for itself, is also better and more desirable.

25 A thing may be taken to be more precious in itself which
we choose rather for itself, without anything else being
likely to come of it.

Moreover, you should distinguish in how many senses
desirable is used, and with a view to what ends, e.g.
expediency or honour or pleasure. For what is useful for
all or most of them may be taken to be more desirable

30 than what is not useful in like manner. If the same
characters belong to both things you should look and see
which possesses them more markedly, i. e. which of the two
is the more pleasant or more honourable or more expe
dient. Again, that is more desirable which serves the better
purpose, e. g. that which serves to promote virtue more
than that which serves to promote pleasure. Likewise also
in the case of objectionable things ; for that is more
objectionable which stands more in the way of what is

35 desirable, e. g. disease more than ugliness : for disease
is a greater hindrance both to pleasure and to being
good.

Moreover, argue by showing that the thing in question is
in like measure objectionable and desirable : for a thing of
such a character that a man might well desire and object
to it alike is less desirable than the other which is desirable
only.

1 Il8 b i9. Read o

BOOK III. 4 ng

4 Comparisons of things together should therefore be con- n g a
ducted in the manner prescribed. The same commonplace
rules are useful also for showing that anything is simply
desirable or objectionable : for we have only to subtract

the excess of one thing over another. For if what is more
precious be more desirable, then also what is precious is
desirable ; and if what is more useful be more desirable, 5
then also what is useful is desirable. Likewise, also, in the
case of other things which admit of comparisons of that
kind. For in some cases in the very course of comparing
the things together we at once assert also that each of
them, or the one of them, is desirable, e. g. whenever we
call the one good by nature and the other not by nature :
for clearly what is good by nature is desirable. 10

5 The commonplace rules relating to comparative degrees
and amounts ought to be taken in the most general possible
form : for when so taken they are likely to be useful in
a larger number of instances. It is possible to render some
of the actual rules given above more universal by a slight 15
alteration of the expression, e.g. that what by nature
exhibits such and such a quality exhibits that quality in a
greater degree than what exhibits it not by nature. Also, if
one thing does, and another does not, impart such and such

a quality to that which possesses it, or to which it belongs,
then whichever does impart it is of that quality in greater
degree than the one which does not impart it ; and if both
impart it, then that one exhibits it in a greater degree
which imparts it in a greater degree.

Moreover, if in any character one thing exceeds and 20
another falls short of the same standard ; also, if the one
exceeds something which exceeds a given standard, while
the other does not reach that standard, 1 then clearly the
first-named thing exhibits that character in a greater
degree. Moreover, you should judge by means of addition,
and see if A when added to the same thing as B imparts to
the whole such and such a character in a more marked

1 II9 a 2I. Read Ka\ fl TO fi(i> p.a\\ov TOIOVTOU p.a\\ov TOIOVTO, TO dt p.i}
TOIOVTO.

tig* TOPICA

degree than B, or if, when added to a thing which exhibits
that character in a less degree, it imparts that character to

25 the whole in a greater degree. Likewise, also, you may
judge by means of subtraction : for a thing upon whose
subtraction the remainder exhibits such and such a character
in a less degree, itself exhibits that character in a greater
degree. Also, things exhibit such and such a character in
a greater degree if more free from admixture with their
contraries ; e. g. that is whiter which is more free from
admixture with black. Moreover, apart from the rules
given above, that has such and such a character in greater
degree which admits in a greater degree of the definition

30 proper to the given character ; e.g. if the definition of white
be a colour which pierces the vision , then that is whiter
which is in a greater degree a colour that pierces the vision.

If the question be put in a particular and not in a universal 6
form, in the first place the universal constructive or destruc
tive commonplace rules that have been given may all be
brought into use. For in demolishing or establishing a
35 thing universally we also show it in particular : for if it be
true of all, it is true also of some, and if untrue of all,
it is untrue of some. Especially handy and of general
application are the commonplace rules that are drawn from
the opposites and co-ordinates and inflexions of a thing :
for public opinion grants alike the claim that if all pleasure
be good, then also all pain is evil, and the claim that if
H9 b some pleasure be good, then also some pain is evil. More
over, if some form of sensation be not a capacity, then also
some form of failure of sensation is not a failure of capacity.
Also, if the object of conception is in some cases an object
of knowledge, then also some form of conceiving is know
ledge. Again, if what is unjust be in some cases good,
5 then also what is just is in some cases evil ; and if what
happens justly is in some cases evil, then also what happens
unjustly is in some cases good. Also, if what is pleasant
is in some cases objectionable, then pleasure is in some
cases an objectionable thing. On the same principle, also,
if what is pleasant is in some cases beneficial, then pleasure

BOOK III. 6 ng b

is in some cases a beneficial thing. The case is the same
also as regards the things that destroy, and the processes of
generation and destruction. For if anything that destroys
pleasure or knowledge be in some cases good, then we may 10
take it that pleasure or knowledge is in some cases an evil
thing. Likewise, also, if the destruction of knowledge be
in some cases a good thing or its production an evil thing,
then knowledge will be in some cases an evil thing ; e. g. if
for a man to forget his disgraceful conduct be a good thing,
and to remember it be an evil thing, then the knowledge of
his disgraceful conduct may be taken to be an evil thing. 15
The same holds also in other cases : in all such cases the
premiss and the conclusion are equally likely to be
accepted.

Moreover, you should judge by means of greater or
smaller or like degrees : for if some member of another
genus exhibit such and such a character in a more marked
degree than your object, while no member of that genus
exhibits that character at all, then you may take it that
neither does the object in question exhibit it ; e. g. if some
form of knowledge be good in a greater degree than
pleasure, while no form of knowledge is good, then you may 20
take it that pleasure is not good either. Also, you should
judge by a smaller or like degree in the same way : for so
you will find it possible both to demolish and to establish
a view, except that whereas both are possible by means of
like degrees, by means of a smaller degree it is possible
only to establish, not to overthrow. For if a certain form
of capacity be good in a like degree to knowledge, and
a certain form of capacity be good, then so also is know- 25
ledge ; while if no form of capacity be good, then neither
is knowledge. If, too, a certain form of capacity be good
in a less degree than knowledge, and a certain form of
capacity be good, then so also is knowledge ; but if no
form of capacity be good, there is no necessity that no
form of knowledge either should be good. Clearly, then,
it is only possible to establish a view by means of a less 30
degree.

Not only by means of another genus can you overthrow

iig b TOPICA

a view, but also by means of the same, if you take the most
marked instance of the character in question ; e. g. if it be
maintained that some form of knowledge is good, then,
suppose it to be shown that prudence is not good, neither
will any other kind be good, seeing that not even the kind
upon which there is most general agreement is so. More-

35 over, you should go to work by means of an hypothesis ;
you should claim that the attribute, if it belongs or does
not belong in one case, does so in a like degree in all, e. g.
that if the soul of man be immortal, so are other souls as
well, while if this one be not so, neither are the others. If,
then, it be maintained that in some instance the attribute
belongs, you must show that in some instance it does not
belong : for then it will follow, by reason of the hypothesis,
that it does not belong in any instance at all. If, on the
i2O a other hand, it be maintained that it does not belong in
some instance, you must show that it does belong in some
instance, for in this way" it will follow that it belongs in all
instances. It is clear that the maker of the hypothesis
universalizes the question, whereas it was stated in a par
ticular form : for he claims that the maker of a particular
admission should make a universal admission, inasmuch as

5 he claims that if the attribute belongs in one instance, it
belongs also in all instances alike.

If the problem be indefinite, it is possible to overthrow a
statement in only one way ; e. g. if a man has asserted that
pleasure is good or is not good, without any further defini
tion. For if he meant that a particular pleasure is good,
you must show universally that no pleasure is good, if the

10 proposition in question is to be demolished. And likewise,
also, if he meant that some particular pleasure is not good
you must show universally that all pleasure is good : it is
impossible to demolish it in any other way. For if we show
that some particular pleasure is not good or is good, the
proposition in question is not yet demolished. It is clear,
then, that it is possible to demolish an indefinite statement in

15 one way only, whereas it can be established in two ways :
for whether we show universally that all pleasure is good,
or whether we show that a particular pleasure is good, the

BOOK III. 6 120*

proposition in question will have been proved. Likewise,
also, supposing we are required to argue that some particular
pleasure is not good, if we show that no pleasure is good
or that a particular pleasure is not good, we shall have
produced an argument in both ways, both universally and
in particular, to show that some particular pleasure is not 20
good. If, on the other hand, the statement made be
definite, it will be possible to demolish it in two ways ; e. g.
if it be maintained that it is an attribute of some particular
pleasure to be good, while of some it is not : for whether it
be shown that all pleasure, or that no pleasure, is good, the
proposition in question will have been demolished. If,
however, he has stated that only one single pleasure is
good, it is possible to demolish it in three ways : for by
showing that all pleasure, or that no pleasure, or that more 25
than one pleasure, is good, we shall have demolished the
statement in question. If the statement be made still more
definite, e.g. that prudence alone of the virtues is knowledge,
there are four ways of demolishing it : for if it be shown
that all virtue is knowledge, or that no virtue is so, or that
some other virtue (e.g. justice) is so, or that prudence 30
itself is not knowledge, the proposition in question will have
been demolished.

It is useful also to take a look at individual instances, in
cases where some attribute has been said to belong or not
to belong, as in the case of universal questions. Moreover,
you should take a glance among genera, dividing them by
their species until you come to those that are not further 35
divisible, as has been said before : l for whether the attribute
is found to belong in all cases or in none, you should, after
adducing several instances, claim that he should either
admit your point universally, or else bring an objection
showing in what case it does not hold. Moreover, in cases
where it is possible to make the accident definite either
specifically or numerically, you should look and see whether
perhaps none of them belongs, showing e. g. that time is not
moved, nor yet is a movement, by enumerating how many iao b
species there are of movement : for if none of these belong

1 log 13 15.

iao b TOPICA

to time, clearly it does not move, nor yet is a movement.
Likewise, also, you can show that the soul is not a number, 1
by dividing all numbers into either odd or even : for then, if
the soul be neither odd nor even, clearly it is not a number.
In regard then to Accident, you should set to work by
means like these, and in this manner.

1 Cf. Xenocrates, fr. 60 Heinze.

BOOK IV

ISO*

I NEXT we must go on to examine questions relating to 12
Genus and Property. These are elements in the questions
that relate to definitions, but dialecticians seldom address
their inquiries to these by themselves. If, then, a genus be 15
suggested for something that is, first take a look at all
objects which belong to the same genus as the thing men
tioned, and see whether the genus suggested is not predi
cated of one of them, as happens in the case of an accident :
e - g- if good be laid down to be the genus of pleasure ,
see whether some particular pleasure be not good : for, if so,
clearly good is not the genus of pleasure : for the genus is
predicated of all the members of the same species. Secondly, 20
see whether it be predicated not in the category of essence,
but as an accident, as white is predicated of snow , or
self-moved of the soul. For snow is not a kind of
white , and therefore white is not the genus of snow, nor
is the soul a kind of moving object : its motion is an
accident of it, as it often is of an animal to walk or to be 25
walking. Moreover, moving does not seem to indicate
the essence, but rather a state of doing or of having some
thing done to it. Likewise, also, white : for it indicates
not the essence of snow, but a certain quality of it. So
that neither of them is predicated in the category of
essence .

Especially you should take a look at the definition of 30
Accident, and see whether it fits the genus mentioned,
as (e. g.) is also the case in the instances just given. For it
is possible for a thing to be and not to be self-moved, and
likewise, also, for it to be and not to be white. So that
neither of these attributes is the genus but an accident,
since we were saying 1 that an accident is an attribute
which can belong to a thing and also not belong. 35

1 102*6.

iao b TOPICA

Moreover, see whether the genus and the species be not
found in the same division, but the one be a substance while
the other is a quality, or the one be a relative while the
other is a quality, as (e. g.) snow and swan are each
a substance, while white is not a substance but a quality,
so that white is not the genus either of snow or of
iai a swan . Again, knowledge is a relative, while good and
1 noble are each a quality, so that good, or noble, is not
the genus of knowledge. For the genera of relatives ought
themselves also to be relatives, as is the case with double :
5 for multiple , which is the genus of double , is itself also
a relative. To speak generally, the genus ought to fall
under the same division as the species : for if the species be
a substance, so too should be the genus, and if the species
be a quality, so too the genus should be a quality ; e. g. if
white be a quality, so too should colour be. Likewise, also,
in other cases.

10 Again, see whether it be necessary or possible for the
genus to partake of the object which has been placed in
the genus. To partake is defined as to admit the defini
tion of that which is partaken. Clearly, therefore, the
species partake of the genera, but not the genera of the
species : for the species admits the definition of the genus,
whereas the genus does not admit that of the species. You

15 must look, therefore, and see whether the genus rendered
partakes or can possibly partake of the species, e. g. if any
one were to render anything as genus of being or of
unity : for then the result will be that the genus partakes
of the species : for of everything that is, being and unity
are predicated, and therefore their definition as well.

20 Moreover, see if there be anything of which the species
rendered is true, while the genus is not so, e. g. supposing
being or object of knowledge were stated to be the
genus of object of opinion . For object of opinion will
be a predicate of what does not exist ; for many things
which do not exist are objects of opinion ; whereas that
being or object of knowledge is not predicated of what
does not exist is clear. So that neither being nor object

35 of knowledge is the genus of object of opinion : for of

BOOK IV. i iai a

the objects of which the species is predicated, the genus
ought to be predicated as well.

Again, see whether the object placed in the genus be
quite unable to partake of any of its species: for it is
impossible that it should partake of the genus if it do not
partake of any of its species, except it be one of the species
reached by the first division : these do partake of the genus 30
alone. If, therefore, Motion be stated as the genus of
pleasure, you should look and see if pleasure be neither
locomotion nor alteration, nor any of the rest of the given
modes of motion : for clearly you may then take it that it
does not partake of any of the species, and therefore not of
the genus either, since what partakes of the genus must
necessarily partake of one of the species as well : so that 35
pleasure could not be a species of Motion, nor yet be one
of the individual phenomena comprised under the term
motion \ l For individuals as well partake in the genus
and the species, as (e.g.) an individual man partakes of both
man and animal .

Moreover, see if the term placed in the genus has a wider iai b
denotation than the genus, as (e.g.) object of opinion has,
as compared with being : for both what is and what is not
are objects of opinion, so that object of opinion could not
be a species of being : for the genus is always of wider
denotation than the species. Again, see if the species and its
genus have an equal denotation ; suppose, for instance, that 5
of the attributes which go with everything, one were to be
stated as a species and the other as its genus, as for example
Being and Unity: for everything has being and unity, so
that neither is the genus of the other, since their denotation
is equal. Likewise, also, if the first of a series and the
beginning were to be placed one under the other: 2 for
the beginning is first and the first is the beginning, so that 10
either both expressions are identical or at any rate neither
is the genus of the other. The elementary principle in
regard to all such cases is that the genus has a wider
denotation than the species and its differentia : for the

1 I2I a 36. Read ov8e TO>V drd^wv T>V r

2 I2i b 9. Reading vn aX\rj\ a .

iai b TOPICA

differentia as well has a narrower denotation than the
genus.

15 See also whether the genus mentioned fails, or might
be generally thought to fail, to apply to some object which
is not specifically different from the thing in question ; or, if
your argument be constructive, whether it does so apply.
For all things that are not specifically different have the
same genus. If, therefore, it be shown to apply to one,
then clearly it applies to all, and if it fails to apply to one,
clearly it fails to apply to any ; e. g. if any one who assumes
indivisible lines were to say that the indivisible is their

ao genus. For the aforesaid term is not the genus of divisible
lines, and these do not differ as regards their species from
indivisible : for straight lines are never different from each
other as regards their species.

Look and see, also, if there be any other genus of the 2
25 given species which neither embraces the genus rendered
nor yet falls under it, e. g. suppose any one were to lay
down that knowledge is the genus of justice. For virtue
is its genus as well, and neither of these genera embraces
the remaining one, so that knowledge could not be the
genus of justice: for it is generally accepted that whenever
one species falls under two genera, the one is embraced
30 by the other. Yet a principle of this kind gives rise to
a difficulty in some cases. For some people hold that
prudence is both virtue and knowledge, and that neither of
its genera is embraced by the other : although certainly
not everybody admits that prudence is knowledge. If, how
ever, any one were to admit the truth of this assertion, yet
35 it would still be generally agreed to be necessary that the
genera of the same object must at any rate be subordinate
either the one to the other or both to the same, as actually
is the case with virtue and knowledge. For both fall under
the same genus ; for each of them is a state and a disposi
tion. You should look, therefore, and see whether neither of
these things is true of the genus rendered ; for if the genera
i22 a be subordinate neither the one to the other nor both to the
same, then what is rendered could not be the true genus.

BOOK IV. 2 I22 E

Look, also, at the genus of the genus rendered, and so
continually at the next higher genus, and see whether all
are predicated of the species, and predicated in the category 5
of essence : for all the higher genera should be predicated
of the species in the category of essence. If, then, there be
anywhere a discrepancy, clearly what is rendered is not the
true genus. [Again, see whether either the genus itself, or
one of its higher genera, partakes of the species : for the
higher genus does not partake of any of the lower.] l If, then,
you are overthrowing a view, follow the rule as given : if 10
establishing one, then suppose that what has been named
as genus be admitted to belong to the species, only it be
disputed whether it belongs as genus it is enough to show
that one of its higher genera is predicated of the species in
the category of essence. For if one of them be predicated
in the category of essence, all of them, both higher and lower
than this one, if predicated at all of the species, will be pre- 15
dicated of it in the category of essence : so that what has
been rendered as genus is also predicated in the category of
essence. The premiss that when one genus is predicated
in the category of essence, all the rest, if predicated at all,
will be predicated in the category of essence, should be
secured by induction. Supposing, however, that it be dis
puted whether what has been rendered as genus belongs at jo
all, it is not enough to show that one of the higher genera
is predicated of the species in the category of essence : e. g. if
any one has rendered locomotion as the genus of walking,
it is not enough to show that walking is motion in order
to show that it is locomotion , seeing that there are other
forms of motion as well ; but one must show in addition that
walking does not partake of any of the species of motion 25
produced by the same division except locomotion. For of
necessity what partakes of the genus partakes also of one of
the species produced by the first division of the genus. If, there
fore, walking does not partake either of increase or decrease
or of the other kinds of motion, clearly it would partake of
locomotion, so that locomotion would be the genus of walking. 30
Again, look among the things of which the given species
1 An irrelevant interruption here : it merely repeats 121* 10 foil.

i22 a TOPICA

is predicated as genus, and see if what is rendered as its
genus be also predicated in the category of essence of the
very things of which the species is so predicated, and like
wise if all the genera higher than this genus are so predi
cated as well. For if there be anywhere a discrepancy,

35 clearly what has been rendered is not the true genus : for
had it been the genus, then both the genera higher than it,
and it itself, would all have been predicated in the category
of essence of those objects of which the species too is predi
cated in the category of essence. If, then, you are over
throwing a view, it is useful to see whether the genus fails
to be predicated in the category of essence of those things
of which the species too is predicated. If establishing a
i22 b view, it is useful to see whether it is predicated in the
category of essence : for if so, the result will be that the
genus and the species will be predicated of the same object
in the category of essence, so that the same object falls
under two genera : the genera must therefore of necessity
be subordinate one to the other, and therefore if it be shown
5 that the one we wish to establish as genus is not subordinate
to the species, clearly the species would be subordinate to
it, so that you may take it as shown that it is the genus.

Look, also, at the definitions of the genera, and see
whether they apply both to the given species and to the
objects which partake of the species. For of necessity
the definitions of its genera must be predicated of the

10 species and of the objects which partake of the species:
if, then, there be anywhere a discrepancy, clearly what has
been rendered is not the genus.

Again, see if he has rendered the differentia as the genus,
e. g. immortal as the genus of God . For immortal is
a differentia of living being , seeing that of living beings
some are mortal and others immortal. Clearly, then, a bad

15 mistake has been made ; for the differentia of a thing is
never its genus. And that this is true is clear : for a thing s
differentia never signifies its essence, but rather some quality,
as do walking and biped .

Also, see whether he has placed the differentia inside the
genus, e.g. by taking odd as a number . For odd is

BOOK IV. 2 I22 b

a differentia of number, not a species. Nor is the differentia ao
generally thought to partake of the genus : for what par
takes of the genus is always either a species or an individual,
whereas the differentia is neither a species nor an indi
vidual. Clearly, therefore, the differentia does not partake
of the genus, so that odd too is no species but a differentia,
seeing that it does not partake of the genus.

Moreover, see whether he has placed the genus inside the 25
species, e.g. by taking contact to be a juncture , or
mixture a fusion , or, as in Plato s definition, 1 loco
motion to be the same as carriage . For there is no
necessity that contact should be juncture: rather, con
versely, juncture must be contact : for what is in contact is
not always joined, though what is joined is always in con
tact. Likewise, also, in the remaining instances : for 30
mixture is not always a fusion (for to mix dry things
does not fuse them), nor is locomotion always carriage .
For walking is not generally thought to be carriage : for
carriage is mostly used of things that change one place
for another involuntarily, as happens in the case of in
animate things. Clearly, also, the species, in the instances 35
given, has a wider denotation than the genus, whereas it
ought to be vice versa.

Again, see whether he has placed the differentia inside
the species, by taking (e. g.) immortal to be a god . For
the result will be that the species has an equal or wider
denotation : and this cannot be, for always the differentia
has an equal or a wider denotation than the species. More- i23 a
over, see whether he has placed the genus inside the
differentia, by making colour (e. g.) to be a thing that
pierces , or number a thing that is odd . Also, see if
he has mentioned the genus as differentia : for it is possible
for a man to bring forward a statement of this kind as well,
e.g. that mixture is the differentia of fusion , or that
change of place is the differentia of carriage . All such 5
cases should be examined by means of the same principles :
for they depend upon common rules : for the genus should
have a wider denotation than its differentia, and also should
1 Theaet. 181 D.

i2 3 a TOPICA

not partake of its differentia ; whereas, if it be rendered in
this manner, neither of the aforesaid requirements can be
satisfied : for the genus will both have a narrower denota-

10 tion than its differentia, and will partake of it.

Again, if no differentia belonging to the genus be predi
cated of the given species, neither will the genus be
predicated of it ; e. g. of soul neither odd nor even
is predicated : neither therefore is number . Moreover,
see whether the species is naturally prior and abolishes the

15 genus along with itself: for the contrary is the general
view. Moreover, if it be possible for the genus stated, or
for its differentia, to be absent from the alleged species,
e. g. for movement to be absent from the soul , or truth
and falsehood from opinion , then neither of the terms
stated could be its genus or its differentia : for the general
view is that the genus and the differentia accompany the
species, as long as it exists.

30 Look and see, also, if what is placed in the genus 3
partakes or could possibly partake of any contrary of the
genus : for in that case the same thing will at the same
time partake of contrary things, seeing that the genus is
never absent from it, while it partakes, or can possibly
partake, of the contrary genus as well. Moreover, see
whether the species shares in any character which it is
utterly impossible for any member of the genus to have.

35 Thus (e. g.) if the soul has a share in life, while it is im
possible for any number to live, then the soul could not be
a species of number.

You should look and see, also, if the species be a homonym
of the genus, and employ as your elementary principles
those already stated for dealing with homonymity : J for the
genus and the species are synonymous.

30 Seeing that of every genus there is more than one
species, look and see if it be impossible that there should
be another species than the given one belonging to the
genus stated : for if there should be none, then clearly what
has been stated could not be a genus at all.

1 io6 a 9ff.

BOOK IV. 3 i2 3 a

Look and see, also, if he has rendered as genus a meta
phorical expression, describing (e. g.) temperance as a
harmony : for a genus is always predicated of its species 35
in its literal sense, whereas harmony is predicated of
temperance not in a literal sense but metaphorically : for
a harmony always consists in notes.

Moreover, if there be any contrary of the species, examine i23 b
it. The examination may take different forms ; first of all
see if the contrary as well be found in the same genus as
the species, supposing the genus to have no contrary : for
contraries ought to be found in the same genus, if there be
no contrary to the genus. Supposing, on the other hand, 5
that there is a contrary to the genus, see if the contrary of
the species be found in the contrary genus : for of necessity
the contrary species must be in the contrary genus, if there
be any contrary to the genus. Each of these points is
made plain by means of induction. Again, see whether the
contrary of the species be not found in any genus at all,
but be itself a genus, e. g. good : for if this be not found
in any genus, neither will its contrary be found in any 10
genus, but will itself be a genus, as happens in the case of
good and evil : for neither of these is found in a genus,
but each of them is a genus. Moreover, see if both genus
and species be contrary to something, and one pair of
contraries have an intermediary, but not the other. For if
the genera have an intermediary, so should their species as
well, and if the species have, so should their genera as well, 15
as is the case with (i) virtue and vice and (2) justice and
injustice : for each pair has an intermediary. An objection
to this is that there is no intermediary between health and
disease, although there is one between evil and good. Or
see whether, though there be indeed an intermediary between
both pairs, i. e. both between the species and between the
genera, yet it be not similarly related, but in one case be
a mere negation of the extremes, whereas in the other case ao
it is a subject. For the general view is that the relation
should be similar in both cases, as it is in the cases of virtue
and vice and of justice and injustice : for the intermediaries
between both are mere negations. Moreover, whenever the

F 2

i2 3 b TOPICA

genus has no contrary, look and see not merely whether the
contrary of the species be found in the same genus, but the

25 intermediate as well : for the genus containing the extremes
contains the intermediates as well, as (e. g.) in the case of
white and black : for colour is the genus both of these and
of all the intermediate colours as well. An objection may
be raised that defect and excess are found in the same
genus (for both are in the genus evil ), whereas moderate
amount , the intermediate between them, is found not in

30 evil but in good . Look and see also whether, while the
genus has a contrary, the species has none ; for if the genus
be contrary to anything, so too is the species, as virtue to vice
and justice to injustice. Likewise, also, if one were to look at
other instances, one would come to see clearly a fact like this.
An objection may be raised in the case of health and disease :

35 for health in general is the contrary of disease, whereas a
particular disease, being a species of disease, e.g. fever and
ophthalmia and any other particular disease, has no contrary.
124* If> therefore, you are demolishing a view, there are all
these ways in which you should make your examination :
for if the aforesaid characters do not belong to it, clearly
what has been rendered is not the genus. If, on the other
hand, you are establishing a view, there are three ways :
in the first place, see whether the contrary of the species be
found in the genus stated, suppose the genus have no
5 contrary : for if the contrary be found in it, clearly the
species in question is found in it as well. Moreover, see if
the intermediate species is found in the genus stated : for
whatever genus contains the intermediate contains the
extremes as well. Again, if the genus have a contrary,
look and see whether also the contrary species is found
in the contrary genus : for if so, clearly also the species in
question is found in the genus in question.

I0 Again, consider in the case of the inflexions and the
co-ordinates of species and genus, and see whether they
follow likewise, both in demolishing and in establishing
a view. For whatever attribute belongs or does not belong
to one belongs or does not belong at the same time to all ;
e. g. if justice be a particular form of knowledge, then also

BOOK IV. 3 i2 4 s

justly is knowingly and the just man is a man of
knowledge : whereas if any of these things be not so, then
neither is any of the rest of them.

4 Again, consider the case of things that bear a like relation 15
to one another. Thus (e. g.) the relation of the pleasant
to pleasure is like that of the useful to the good : for in
each case the one produces the other. If therefore pleasure
be a kind of good , then also the pleasant will be a kind
of useful : for clearly it may be taken to be productive of
good, seeing that pleasure is good. In the same way also 20
consider the case of processes of generation and destruc
tion ; if (e. g.) to build be to be active, then to have built
is to have been active, and if to learn be to recollect,
then also to have learnt is to have recollected, and if to
be decomposed be to be destroyed, then to have been
decomposed is to have been destroyed, and decomposition
is a kind of destruction. Consider also in the same way the
case of things that generate or destroy, and of the capacities 25
and uses of things ; and in general, both in demolishing
and in establishing an argument, you should examine things
in the light of any resemblance of whatever description, as
we were saying in the case of generation and destruction.
For if what tends to destroy tends to decompose, then also
to be destroyed is to be decomposed : and if what tends to
generate tends to produce, then to be generated is to be 30
produced, and generation is production. Likewise, also, in
the case of the capacities and uses of things : for if a
capacity be a disposition, then also to be capable of some
thing is to be disposed to it, and if the use of anything be
an activity, then to use it is to be active, and to have used
it is to have been active.

If the opposite of the species be a privation, there are 35
two ways of demolishing an argument, first of all by looking
to see if the opposite be found in the genus rendered : for
either the privation is to be found absolutely nowhere in
the same genus, or at least not in the same ultimate genus :
e. g. if the ultimate genus containing sight be sensation,
then blindness will not be a sensation. Secondly, if there

i24 b TOPICA

i24 b be a privation opposed to both genus and species, but the
opposite of the species be not found in the opposite of
the genus, then neither could the species rendered be in
the genus rendered. If, then, you are demolishing a view,
you should follow the rule as stated ; but if establishing
one there is but one way : for if the opposite species be

5 found in the opposite genus, then also the species in question
would be found in the genus in question : e. g. if blind
ness be a form of insensibility , then sight is a form of
sensation .

Again, look at the negations of the genus and species
and convert the order of terms, according to the method
described in the case of Accident : l e. g. if the pleasant be
a kind of good, what is not good is not pleasant. For were

10 this not so, something not good as well would then be
pleasant. That, however, cannot be, 2 for it is impossible, if
good be the genus of pleasant, that anything not good
should be pleasant : for of things of which the genus is
not predicated, none of the species is predicated either.
Also, in establishing a view, you should adopt the same
method of examination : for if what is not good be not
pleasant, then what is pleasant is good, so that good is
the genus of pleasant .

15 If the species be a relative term, see whether the genus
be a relative term as well : for if the species be a relative
term, so too is the genus, as is the case with double and
multiple : for each is a relative term. If, on the other
hand, the genus be a relative term, there is no necessity
that the species should be so as well : for knowledge is
a relative term, but not so grammar . Or possibly not. even

20 the first statement would be generally considered true : for
virtue is a kind of noble and a kind of good thing, and
yet, while virtue is a relative term, good and noble
are not relatives but qualities. Again, see whether the
species fails to be used in the same relation when called
by its own name, and when called by the name of its
genus : e. g. if the term double be used to mean the

25 double of a half, then also the term multiple ought to

1 H3 b 15-26. 2 I24 b lo. Read ativvarov yap.

BOOK IV. 4 i24 b

be used to mean multiple of a half. Otherwise multiple
could not be the genus of double .

Moreover, see whether the term fail to be used in the
same relation both when called by the name of its genus,
and also when called by those of all the genera of its genus.
For if the double be a multiple of a half, then in excess of 3
will also be used in relation to a half: and, in general,
the double will be called by the names of all the higher
genera in relation to a half. An objection may be raised
that there is no necessity for a term to be used in the same
relation when called by its own name and when called by
that of its genus : for knowledge is called knowledge of
an object , whereas it is called a state and disposition
not of an object but of the soul .

Again, see whether the genus and the species be used in 35
the same way in respect of the inflexions they take, e.g.
datives and genitives and all the rest. For as the species is
used, so should the genus be as well, as in the case of
double and its higher genera : for we say both double
of and multiple of a thing. Likewise, also, in the case
of knowledge : for both knowledge itself and its genera, 125*
e.g. disposition and state , are said to be of some
thing. An objection may be raised that in some cases it is
not so : for we say superior to and contrary to so and so,
whereas other , which is the genus of these terms, demands
not to but than : for the expression is other than so
and so.

Again, see whether terms used in like case-relationships 5
fail to yield a like construction when converted, as do
double and multiple . For each of these terms takes a
genitive both in itself and in its converted form : for we
say both a half of and a fraction of something. The
case is the same also as regards both knowledge and
conception : for these take a genitive, and by conversion 10
an object of knowledge and an object of conception are
both alike 1 used with a dative. If, then, in any cases the
constructions after conversion be not alike, clearly the one
term is not the genus of the other.

1 125*11. Take away the colon after O

5 a TOPICA

Again, see whether the species and the genus fail to be
used in relation to an equal number of things : for the

15 general view is that the uses of both are alike and equal in
number, as is the case with present and grant . For
a present is of something or to some one, and also a
grant is of something and to some one : and grant is the
genus of present , for a present is a grant that need not
be returned . In some cases, however, the number of
relations in which the terms are used happens not to be

20 equal, for while double is double of something, we speak
of in excess or greater in something, as well as of or
than something : for what is in excess or greater is always
in excess in something, as well as in excess of something.
Hence the terms in question are not the genera of double ,
inasmuch as they are not used in relation to an equal number
of things with the species. Or possibly it is not universally
true that species and genus are used in relation to an equal
number of things.

25 See, also, if the opposite of the species have the opposite
of the genus as its genus, e. g. whether, if multiple be the
genus of double , fraction be also the genus of half .
For the opposite of the genus should always be the genus
of the opposite species. If, then, any one were to assert
that knowledge is a kind of sensation, then also the object
of knowledge will have to be a kind of object of sensation,
whereas it is not : for an object of knowledge is not always

30 an object of sensation : for objects of knowledge include
some of the objects of intuition as well. Hence object of
sensation is not the genus of object of knowledge : and if
this be so, neither is sensation the genus of knowledge .
Seeing that of relative terms some are of necessity found
in, or used of, the things in relation to which they happen at

35 any time to be used ( l e. g. disposition and state and
balance ; for in nothing else can the aforesaid terms
possibly be found except in the things in relation to which
they are used), while others need not be found in the things
in relation to which they are used at any time, though they
still may be (e.g. if the term object of knowledge be
1 125*35. Beginning the bracket at nlov . . . instead of at ev. -

BOOK IV. 4 i25 a

applied to the soul : for it is quite possible that the know
ledge of itself should be possessed by the soul itself, but it
is not necessary, for it is possible for this same knowledge 40
to be found in some one else), while for others, again, it is I25 b
absolutely impossible that they should be found in the things
in relation to which they happen at any time to be used
(as e. g. that the contrary should be found in the contrary
or knowledge in the object of knowledge, unless the object
of knowledge happen to be a soul or a man) J you should
look, therefore, and see whether he places a term of one 5
kind inside a genus that is not of that kind, e. g. suppose he
has said that memory is the abiding of knowledge . For
abiding is always found in that which abides, and is used
of that, so that the abiding of knowledge also will be found
in knowledge. Memory, then, is found in knowledge, seeing
that it is the abiding of knowledge. But this is impossible,
for memory is always found in the soul. The aforesaid 10
commonplace rule is common to the subject of Accident as
well : for it is all the same to say that abiding is the
genus of memory, or to allege that it is an accident of it.
For if in any way whatever memory be the abiding of
knowledge, the same argument in regard to it will apply.

5 Again, see if he has placed what is a state inside the 15
genus activity , or an activity inside the genus state ,
e. g. by defining sensation as movement communicated
through the body : for sensation is a state , whereas
movement is an activity . Likewise, also, if he has said
that memory is a state that is retentive of a conception ,
for memory is never a state, but rather an activity.

They also make a bad mistake who rank a state within 20
the capacity that attends it, e. g. by defining good temper
as the control of anger , and courage and justice as
control of fears and of gains : for the terms courageous
and good-tempered are applied to a man who is immune
from passion, whereas ( self-controlled describes the man
who is exposed to passion and not led by it. Quite possibly,
indeed, each of the former is attended by a capacity such

1 Bracketing I25 b 2-4 olov . . . avdpvnos ov.

i25 b TOPICA

25 that, if he were exposed to passion, he would control it and
not be led by it : but, for all that, this is not what is meant
by being courageous in the one case, and good-tempered
in the other ; what is meant is an absolute immunity from
any passions of that kind at all.

Sometimes,also, people state any kind of attendant feature
as the genus, e. g. pain as the genus of anger and con-
so ception as that of conviction . For both of the things in
question follow in a certain sense upon the given species, but
neither of them is genus to it. For when the angry man feels
pain, the pain has appeared in him earlier than the anger: for
his anger is not the cause of his pain, but his pain of his anger,
so that anger emphatically is not pain. By the same reasoning, 1
35 neither is conviction conception : for it is possible to have the
same conception even without being convinced of it, whereas
this is impossible if conviction be a species of conception :
for it is impossible for a thing still to remain the same if it
be entirely transferred out of its species, just as neither
could the same animal at one time be, and at another not be,
4 o a man. If, on the other hand, any one says that a man who has
a conception must of necessity be also convinced of it, then
ia6 a conception and conviction will be used with an equal de
notation, so that not even so could the former be the genus
of the latter : for the denotation of the genus should be wider.
See, also, whether both naturally come to be anywhere in
the same thing : for what contains the species contains the
genus as well : e.g. what contains white contains colour
5 as well, and what contains knowledge of grammar con
tains knowledge as well. If, therefore, any one says that
shame is fear , or that anger is pain , the result will
be that genus and species are not found in the same thing :
for shame is found in the reasoning faculty, whereas fear
is in the spirited faculty, and pain is found in the faculty
10 of desires (for in this pleasure also is found), whereas
anger is found in the spirited faculty. Hence the
terms rendered are not the genera, seeing that they do not
naturally come to be in the same faculty as the species.
Likewise, also, if friendship be found in the faculty of
1 I 35 b 35- Read ravrd.

BOOK IV. 5 ia6 a

desires, you may take it that it is not a form of wishing :
for wishing is always found in the reasoning faculty. This
commonplace rule is useful also in dealing with Accident :
for the accident and that of which it is an accident are both 15
found in the same thing, so that if they do not appear in the
same thing, clearly it is not an accident.

Again, see if the species partakes of the genus attributed
only in some particular respect : for it is the general view
that the genus is not thus imparted only in some particular
respect: for a man is not an animal in a particular respect,
nor is grammar knowledge in a particular respect only.
Likewise also in other instances. Look, therefore, and see 20
if in the case of any of its species the genus be imparted
only in a certain respect ; e.g. if animal has been described
as an object of perception or of sight . For an animal
is an object of perception or of sight in a particular respect
only ; for it is in respect of its body that it is perceived
and seen, not in respect of its soul, so that object of sight
and object of perception could not be the genus of animal . 25

Sometimes also people place the whole inside the part
without detection, defining (e.g.) animal as an animate
body ; whereas the part is not predicated in any sense of
the whole, so that body could not be the genus of animal,
seeing that it is a part.

See also if he has put anything that is blameworthy or 30
objectionable into the class 4 capacity or capable , e.g. by
defining a sophist or a slanderer , or a thief as one
who is capable of secretly thieving other people s property . 1
For none of the aforesaid characters is so called because he
is capable in one of these respects : for even God and the
good man are capable of doing bad things, but that is not 35
their character : for it is always in respect of their choice
that bad men are so called. Moreover, a capacity is always
a desirable thing : for even the capacities for doing bad
things are desirable, and therefore it is we say that even
God and the good man possess them ; for they are capable
(we say) of doing evil. So then capacity can never be the
genus of anything blameworthy. Else, the result will be ia6 b

1 126*32. Read TOV dvt>up.(t>ov \ddpa dXXdrpia K\firTtiv.

i26 b TOPICA

that what is blameworthy is sometimes desirable : for there
will be a certain form of capacity that is blameworthy.

Also, see if he has put anything that is precious or desir
able for its own sake into the class capacity or capable
5 or productive of anything. For capacity, and what is
capable or productive of anything, is always desirable for
the sake of something else.

Or see if he has put anything that exists in two genera or
more into one of them only. For some things it is im
possible to place in a single genus, e.g. the cheat and the
slanderer : for neither he who has the will without the

10 capacity, nor he who has the capacity without the will, is a
slanderer or cheat, but he who has both of them. Hence
he must be put not into one genus, but into both the afore
said genera.

Moreover, people sometimes in converse order render
genus as differentia, and differentia as genus, defining (e.g.)

15 astonishment as excess of wonderment and conviction as
vehemence of conception . For neither excess nor
vehemence is the genus, but the differentia : for astonish
ment is usually taken to be an excessive wonderment , and
conviction to be a vehement conception . so that wonder
ment and conception are the genus, while excess and
vehemence are the differentia. Moreover, if any one

30 renders excess and vehemence as genera, 1 then inani
mate things will be convinced and astonished. For vehe
mence and excess of a thing are found in a thing which
is thus vehement and in excess. If, therefore, astonishment
be excess of wonderment the astonishment will be found in
the wonderment, so that wonderment will be astonished !

25 Likewise, also, conviction will be found in the conception, if
it be vehemence of conception , so that the conception will
be convinced. Moreover, a man who renders an answer in
this style will in consequence find himself calling vehemence
vehement and excess excessive : for there is such a thing as
a vehement conviction : if then conviction be vehemence ,

3 o there would be a vehement vehemence . Likewise, also,
there is such a thing as excessive astonishment : if then

1 I26 b 20. Read yivr).

BOOK IV. 5 i26 b

astonishment be an excess, there would be an excessive
excess . Whereas neither of these things is generally
believed, any more than that knowledge is a knovver l or
motion a moving thing.

Sometimes, too, people make the bad mistake of putting
an affection into that which is affected, as its genus, e.g. 35
those who say that immortality is everlasting life : for
immortality seems to be a certain affection or accidental
feature of life. That this saying is true would appear clear
if any one were to admit that a man can pass from being
mortal and become immortal : for no one will assert that
he takes another life, but that a certain accidental feature or
affection enters into this one as it is. So then life is not 127*
the genus of immortality.

Again, see if to an affection he has ascribed as genus the
object of which it is an affection, by defining (e. g.) wind as
air in motion . Rather, wind is a movement of air :
for the same air persists both when it is in motion and when 5
it is still. Hence wind is not air at all : for then there
would also have been wind when the air was not in motion,
seeing that the same air which formed the wind persists.
Likewise, also, in other cases of the kind. Even, then, if
we ought in this instance to admit the point that wind
is air in motion , yet we should accept a definition of the 10
kind, not about all those things of which the genus is not
true, but only in cases where the genus rendered is a true
predicate. For in some cases, e. g. mud or snow , it is
not generally held to be true. For people tell you that
snow is frozen water and mud is earth mixed with
moisture , whereas snow is not water, nor mud earth, so 15
that neither of the terms rendered could be the genus : for
the genus should be true of all its species. Likewise
neither is wine fermented water , as Empedocles speaks of
water fermented in wood : 2 for it simply is not water at
all.

6 Moreover, see whether the term rendered fail to be the 20

genus of anything at all ; for then clearly it also fails to be

1 I26 b 33. Read eVicmj/x?; eVtorfj/ioi/. 2 Fr. 8l.

? a TOPICA

the genus of the species mentioned. Examine the point by
seeing whether the objects that partake of the genus fail
to be specifically different from one another, e.g. white
objects : for these do not differ specifically from one another,
whereas of a genus the species are always different, so that

35 white could not be the genus of anything.

Again, see whether he has named as genus or differentia
some feature that goes with everything : for the number of
attributes that follow everything is comparatively large :
thus (e.g.) Being and Unity are among the number of
attributes that follow everything. If, therefore, he has
rendered Being as a genus, clearly it would be the genus
of everything, seeing that it is predicated of everything ; for

30 the genus is never predicated of anything except of its
species. Hence Unity, inter alia, will be a species of Being.
The result, therefore, is that of all things of which the genus
is predicated, the species is predicated as well, seeing that
Being and Unity are predicates of absolutely everything,
whereas the predication of the species ought to be of narrower

35 range. If, on the other hand, he has named as differentia
some attribute that follows everything, clearly the denota
tion of the differentia will be equal to, or wider than, that
of the genus. For if the genus, too, be some attribute that
follows everything, the denotation of the differentia will be
equal to its denotation, while if the genus do not follow
everything, it will be still wider.

y b Moreover, see if the description inherent in S be used
of the genus rendered in relation to its species, as it is used
of white in the case of snow, thus showing clearly that it
could not be the genus : for true of S is the only descrip
tion used of the genus in relation to its species.
5 Look and see also if the genus fails to be synonymous
with its species. For the genus is always predicated of its
species synonymously.

Moreover, beware, whenever both species and genus have
a contrary, and he places the better of the contraries inside
the worse genus : for the result will be that the remaining

10 species will be found in the remaining genus, seeing that
contraries are found in contrary genera, so that the better

BOOK IV. 6 i27 b

species will be found in the worse genus and the worse in
the better : whereas the usual view is that of the better
species the genus too is better. Also see if he has placed
the species inside the worse and not inside the better genus,
when it is at the same time related in like manner to both,
as (e.g.) if he has defined the soul as a form of motion X 5
or a form of moving thing . For the same soul is usually
thought to be a principle alike of rest and of motion, so
that, if rest is the better of the two, this is the genus into
which the soul should have been put.

Moreover, judge by means of greater and less degrees :
if overthrowing a view, see whether the genus admits of a
greater degree, whereas neither the species itself does so,
nor any term that is called after it: e.g. if virtue admits of 20
a greater degree, so too does justice and the just man : for
one man is called more just than another . If, therefore,
the genus rendered admits of a greater degree, whereas
neither the species does so itself nor yet any term called
after it, then what has been rendered could not be the
genus. 2 5

Again, if what is more generally, or as generally, thought
to be the genus be not so, clearly neither is the genus
rendered. The commonplace rule in question is useful
especially in cases where the species appears to have several
predicates in the category of essence, and where no distinc
tion has been drawn between them, and we cannot say
which of them is genus ; e.g. both pain and the concep- 30
tion of a slight are usually thought to be predicates of
anger in the category of essence : for the angry man is
both in pain and also conceives that he is slighted. The
same mode of inquiry may be applied also to the case of
the species, by comparing it with some other species : for if
the one which is more generally, or as generally, thought to
be found in the genus rendered be not found therein, then 35
clearly neither could the species rendered be found therein.

In demolishing a view, therefore, you should follow the
rule as stated. In establishing one, on the other hand, the
commonplace rule that you should see if both the genus
rendered and the species admit of a greater degree will not 128*

8 a TOPICA

serve : for even though both admit it, it is still possible for
one not to be the genus of the other. For both beautiful
and white admit of a greater degree, and neither is the
genus of the other. On the other hand, the comparison of

5 the genera and of the species one with another is of use :
e. g. supposing A and B to have a like claim to be genus,
then if one be a genus, so also is the other. Likewise also,
if what has less claim be a genus, so also is what has
more claim : e. g. if capacity have more claim than
virtue to be the genus of self-control, and virtue be the
genus, so also is capacity. The same observations will

[ apply also in the case of the species. For instance, supposing
A and B to have a like claim to be a species of the genus in
question, then if the one be a species, so also is the other : and
if that which is less generally thought to be so be a species,
so also is that which is more generally thought to be so.

Moreover, to establish a view, you should look and see if
the genus is predicated in the category of essence of those
things of which it has been rendered as the genus, suppos-

15 ing the species rendered to be not. one single species but
several different ones : for then clearly it will be the genus.
If, on the other, the species rendered be single, look and see
whether the genus be predicated in the category of essence
of other species as well : for then, again, the result will be
that it is predicated of several different species.

20 Since some people think that the differentia, too, is a
predicate of the various species in the category of essence,
you should distinguish the genus from the differentia by
employing the aforesaid elementary principles (a) that
the genus has a wider denotation than the differentia ;
(b) that in rendering the essence of a thing it is more
fitting to state the genus than the differentia : for any one

25 who says that man is an animal shows what man is
better than he who describes him as walking ; also (c) that
the differentia always signifies a quality of the genus,
whereas the genus does not do this of the differentia : for
he who says walking describes an animal of a certain
quality, whereas he who says animal does not describe
a walking thing of a certain quality.

BOOK IV. 6 128

The differentia, then, should be distinguished from the 30
genus in this manner. Now seeing it is generally held that
if 1 what is musical, in being musical, possesses knowledge
in some respect, then also music is a particular kind of
knowledge ; and also that if what walks is moved in
walking, then walking is a particular kind of movement ;
you should therefore examine in the aforesaid manner any
genus in which you want to establish the existence of some
thing : e. g., if you wish to prove that knowledge is a form 35
of conviction , see whether the knower in knowing is con
vinced : for then clearly knowledge would be a particular
kind of conviction. You should proceed in the same way
also in regard to the other cases of this kind.

Moreover, seeing that it is difficult to distinguish what
ever always follows along with a thing, and is not con
vertible with it, from its genus, if A follows B universally,
whereas B does not follow A universally as e.g. rest ia8 b
always follows a calm and divisibility follows number ,
but not conversely (for the divisible is not always a number,
nor rest a calm) you may yourself assume in your treat
ment of them that the one which always follows is the
genus, whenever the other is not convertible with it : if, on 5
the other hand, some one else puts forward the proposition,
do not accept it universally. An objection to it is that not-
being always follows what is coming to be (for what is
coming to be is not) and is not convertible with it (for
what is not is not always coming to be), and that still
not-being is not the genus of coming to be : for not-
being has not any species at all.

Questions, then, in regard to Genus should be investi- 10
gated in the ways described.

1 128*31, adopting Imelman s restoration (at which I had arrived
independently) f nfl dt BOKI I <^fi) TO povcriKbi/ . . . l-ni<jTr\\jj>v ri OTI, KO.I fj

BOOK V

I28 b

14 THE question whether the attribute stated is or is not I
a property, should be examined by the following methods :
Any property rendered is always either essential and
permanent or relative and temporary : e. g. it is an essential
property of man to be by nature a civilized animal :
a relative property is one like that of the soul in relation
to the body, viz. that the one is fitted to command, and the
other to obey : a permanent property is one like the
20 property which belongs to God, of being an immortal
living being : a temporary property is one like the
property which belongs to any particular man of walking
in the gymnasium.

1 [The rendering of a property relatively gives rise
either to two problems or to four. For if he at the same
time render this property of one thing and deny it of
another, only two problems arise, as in the case of a state-
as ment that it is a property of a man, in relation to a horse,
to be a biped. For one might try both to show that a man
is not a biped, and also that a horse is a biped : in both
ways the property would be upset. 2 If on the other hand
he render one apiece of two attributes to each of two things,
and deny it in each case of the other, there will then be four
problems ; as in the case of a statement that it is a property
30 of a man in relation to a horse for the former to be a biped
and the latter a quadruped. For then it is possible to try
to show both that a man is not naturally a biped, and that
he is a quadruped, and also that the horse both is a biped,
and is not a quadruped. If you show any of these at all,
the intended attribute is demolished.]

An essential property is one which is rendered of a thing
35 in comparison with everything else and distinguishes the

1 128 22-33. The natural place of this paragraph is after 129* 16.

2 I28 b 27. Read KIVQITO TO ldioi>.

BOOK V. i ia8 b

said thing from everything else, as does a mortal living being
capable of receiving knowledge in the case of man. A rela
tive property is one which separates its subject off not from
everything else but only from a particular definite thing, as
does the property which virtue possesses, in comparison with
knowledge, viz. that the former is naturally produced in
more than one faculty, whereas the latter is produced in
that of reason alone, and in those who have a reasoning
faculty. A permanent property is one which is true at
every time, and never fails, like being compounded of soul 129*
and body , in the case of a living creature. A temporary
property is one which is true at some particular time, and
does not of necessity always follow ; as, of some particular
man, that he walks in the market-place. 5

To render a property relatively to something else means
to state the difference between them as it is found either
universally and always, or generally and in most cases:
thus a difference that is found universally and always, is
one such as man possesses in comparison with a horse,
viz. being a biped : for a man is always and in every case
a biped, whereas a horse is never a biped at any time. On 10
the other hand, a difference that is found generally and in
most cases, is one such as the faculty of reason possesses
in comparison with that of desire and spirit, in that the
former commands, while the latter obeys : for the reasoning
faculty does not always command, but sometimes also is
under command, nor is that of desire and spirit always
under command, but also on occasion assumes the command, 15
whenever the soul of a man is vicious.

Of properties the most arguable are the essential and
permanent and the relative. For a relative property gives
rise, as we said before, 1 to several questions : for of necessity 20
the questions arising are either two or four, so that argu
ments in regard to these are several. An essential and
a permanent property you can discuss in relation to many
things, or can observe in relation to many periods of time:
if essential , discuss it in comparison with many things:
for the property ought to belong to its subject in compari- 25

1 I28 b 22.
G 2

i2 9 a TOPICA

son with every single thing that is, so that if the subject be
not distinguished by it in comparison with everything else,
the property could not have been rendered correctly. So
a permanent property you should observe in relation to
many periods of time ; for if it does not or did not, or is
not going to, belong, it will not be a property. On the
other hand, about a temporary property we do not inquire
further than in regard to the time called the present ; and

30 so arguments in regard to it are not many ; whereas an
arguable question is one in regard to which it is possible
for arguments both numerous and good to arise.

The so-called relative property, then, should be examined
by means of the commonplace arguments relating to Acci
dent, to see whether it belongs to the one thing and not to
the other: on the other hand, permanent and essential

35 properties should be considered by the following methods.

i29 b First, see whether the property has or has not been 2
rendered correctly. Of a rendering being incorrect or
correct, one test is to see whether the terms in which the
property is stated are not or are more intelligible for
destructive purposes, whether they are not so, and for con-
5 structive purposes, whether they are so. Of the terms not
being more intelligible, one test is to see whether the
property which he renders is altogether more unintelligible
than the subject whose property he has stated : for, if so,
the property will not have been stated correctly. For the
object of getting a property constituted is to be intelligible :
the terms therefore in which it is rendered should be more
intelligible: for in that case it will be possible to conceive
10 it more adequately, e. g. any one who has stated that it is
a property of fire to bear a very close resemblance to the
soul , uses the term soul , which is less intelligible than
fire for we know better what fire is than what soul is ,
and therefore a very close resemblance to the soul could
not be correctly stated to be a property of fire. Another
test is to see whether the attribution of A (property) to
B (subject) fails to be more intelligible. For not only
should the property be more intelligible than its subject,

BOOK V. 2 i2Q b

but also it should be something whose attribution to the 15
particular subject is a more intelligible attribution. For
he who does not know whether it is an attribute of the
particular subject at all, will not know either whether it
belongs to it alone, so that whichever of these results
happens, its character as a property becomes obscure.
Thus (e. g.) a man who has stated that it is a property of
fire to be the primary element wherein the soul is naturally
found , has introduced a subject which is less intelligible
than fire , viz. whether the soul is found in it, and whether ao
it is found there primarily ; and therefore to be the primary
element in which the soul is naturally found could not be
correctly stated to be a property of fire . On the other
hand, for constructive purposes, see whether the terms in
which the property is stated are more intelligible, and if
they are more intelligible in each of the aforesaid ways.
For then the property will have been correctly stated in
this respect : for of constructive arguments, showing the 25
correctness of a rendering, some will show the correctness
merely in this respect, while others will show it without
qualification. Thus (e. g.) a man who has said that the
possession of sensation is a property of animal has both
used more intelligible terms and has rendered the property
more intelligible in each of the aforesaid senses ; so that to
1 possess sensation would in this respect have been correctly
rendered as a property of animal .

Next, for destructive purposes, see whether any of the 30
terms rendered in the property is used in more than one
sense, or whether the whole expression too signifies more
than one thing. For then the property will not have been
correctly stated. Thus (e. g.) seeing that to be sentient
signifies more than one thing, viz. (i) to possess sensation,
(2) to use one s sensation, being naturally sentient could 35
not be a correct statement of a property of animal . The i3o a
reason why the term you use, or the whole expression
signifying the property, should not bear more than one
meaning is this, that an expression bearing more than one
meaning makes the object described obscure, because the
man who is about to attempt an argument is in doubt which

3o* TOPICA

of the various senses the expression bears : and this will not
do, for the object of rendering the property is that he may
5 understand. Moreover, in addition to this, it is inevitable
that those who render a property after this fashion should
be somehow refuted whenever any one addresses his syllo
gism to that one of the term s several meanings which does
not agree. For constructive purposes, on the other hand,
see whether both all the terms and also the expression as
10 a whole avoid bearing more than one sense : for then the
property will have been correctly stated in this respect.
Thus (e. g.) seeing that body does not bear several
meanings, nor quickest to move upwards in space , nor
yet the whole expression made by putting them together,
it would be correct in this respect to say that it is a property
of fire to be the body quickest to move upwards in space .

15 Next, for destructive purposes, see if the term of which
he renders the property is used in more than one sense,
and no distinction has been drawn as to which of them it is
whose property he is stating : for then the property will
not have been correctly rendered. The reasons why this is
so are quite clear from what has been said above : l for the
same results are bound to follow. Thus (e. g.) seeing that

30 the knowledge of this signifies many things for it means
(i) the possession of knowledge by it, (2) the use of its
knowledge by it, (3) the existence of knowledge about it,
(4) the use of knowledge about it no property of the
knowledge of this could be rendered correctly unless he
draw a distinction as to which of these it is whose property
he is rendering. For constructive purposes, a man should
see if the term of which he is rendering the property avoids

35 bearing many senses and is one and simple : for then the
property will have been correctly stated in this respect.
Thus (e. g.) seeing that man is used in a single sense,
naturally civilized animal would be correctly stated as
a property of man.

Next, for destructive purposes, see whether the same term

30 has been repeated in the property. For people often do
this undetected in rendering properties also, just as they

BOOK V. 2 130*

do in their definitions as well : but a property to which
this has happened will not have been correctly stated : for
the repetition of it confuses the hearer; thus inevitably
the meaning becomes obscure, and further, such people are
thought to babble. Repetition of the same term is likely
to happen in two ways : one is, when a man repeatedly uses 35
the same word, as would happen if any one were to render,
as a property of fire, the body which is the most rarefied
of bodies (for he has repeated the word body ) ; the second
is, if a man replaces words by their definitions, as would
happen if any one were to render, as a property of earth, i3O b
the substance which is by its nature most easily of all
bodies borne downwards in space , and were then to substi
tute substances of such and such a kind for the word
bodies : for body and a substance of such and such
a kind mean one and the same thing. For he will have
repeated the word substance , and accordingly neither of
the properties would be correctly stated. For constructive 5
purposes, on the other hand, see whether he avoids ever
repeating the same term ; for then the property will in this
respect have been correctly rendered. Thus (e. g.) seeing
that he who has stated animal capable of acquiring know
ledge as a property of man has avoided repeating the same
term several times, the property would in this respect have 10
been correctly rendered of man.

Next, for destructive purposes, see whether he has
rendered in the property any such term as is a universal
attribute. For one which does not distinguish its subject
from other things is useless, and it is the business of the
language of properties , as also of the language of defini
tions, to distinguish. In the case contemplated, therefore, rs
the property will not have been correctly rendered. Thus
(e. g.) a man who has stated that it is a property of
knowledge to be a conception incontrovertible by argu
ment, because of its unity , has used in the property a term
of that kind. viz. unity , which is a universal attribute;
and therefore the property of knowledge could not have
been correctly stated. For constructive purposes, on the
other hand, see whether he has avoided all terms that are

i30 b TOPICA

common to everything and used a term that distinguishes
the subject from something: for then the property will in

ao this respect have been correctly stated. Thus (e.g.) inasmuch
as he who has said that it is a property of a living creature
to have a soul has used no term that is common to every
thing, it would in this respect have been correctly stated to
be a property of a living creature to have a soul .

Next, for destructive purposes see whether he renders
more than one property of the same thing, without a definite
proviso that he is stating more than one : for then the

25 property will not have been correctly stated. For just as
in the case of definitions too there should be no further
addition beside the expression which shows the essence, so
too in the case of properties nothing further should be
rendered beside the expression that constitutes the property
mentioned : for such an addition is made to no purpose.
Thus (e. g.) a man who has said that it is a property of fire

3 to be the most rarefied and lightest body has rendered
more than one property (for each term is a true predicate
of fire alone) ; and so it could not be a correctly stated
property of fire to be the most rarefied and lightest body .
On the other hand, for constructive purposes, see whether
he has avoided rendering more than one property of the
same thing, and has rendered one only : for then the
property will in this respect have been correctly stated.

35 Thus (e. g.) a man who has said that it is a property of
a liquid to be a body adaptable to every shape has
rendered as its property a single character and not several,
and so the property of liquid would in this respect
have been correctly stated.

Next, for destructive purposes, see whether he has em- 3
ployed either the actual subject whose property he is
rendering, or any of its species : for then the property will
I3i a not have been correctly stated. For the object of rendering
the property is that people may understand : now the
subject itself is just as unintelligible as it was to start with,
while any one of its species is posterior to it, and so is no
more intelligible. Accordingly it is impossible to under-

BOOK V. 3 131*

stand anything further by the use of these terms. Thus
(e. g.) any one who has said that it is a property of animal
to be the substance to which " man " belongs as a species
has employed one of its species, and therefore the property 5
could not have been correctly stated. For constructive
purposes, on the other hand, see whether he avoids intro
ducing either the subject itself or any of its species : for
then the property will in this respect have been correctly
stated. Thus (e. g.) a man who has stated that it is a
property of a living creature to be compounded of soul
and body has avoided introducing among the rest either
the subject itself or any of its species, and therefore in 10
this respect the property of a living creature would have
been correctly rendered.

You should inquire in the same way also in the case of
other terms that do or do not make the subject more intelli
gible : thus, for destructive purposes, see whether he has
employed anything either opposite to the subject or, in
general, anything simultaneous by nature with it or pos- 15
terior to it : for then the property will not have been
correctly stated. For an opposite is simultaneous by
nature with its opposite, and what is simultaneous by
nature or is posterior to it does not make its subject more
intelligible. Thus (e.g.) any one who has said that it is
a property of good to be the most direct opposite of
evil , has employed the opposite of good, and so the pro
perty of good could not have been correctly rendered, ao
For constructive purposes, on the other hand, see whether
he has avoided employing anything either opposite to, or,
in general, simultaneous by nature with the subject, or
posterior to it : for then the property will in this respect
have been correctly rendered. Thus (e. g.) a man who has
stated that it is a property of knowledge to be the most
convincing conception has avoided employing anything
either opposite to, or simultaneous by nature with, or
posterior to, the subject ; and so the property of knowledge 35
would in this respect have been correctly stated.

Next, for destructive purposes, see whether he has ren
dered as property something that does not always follow

i3i a TOPICA

the subject but sometimes ceases to be its property : for
then the property will not have been correctly described. For

30 there is no necessity either that the name of the subject must
also be true of anything to which we find such an attribute
belonging ; nor yet that the name of the subject will be
untrue of anything to which such an attribute is found not
to belong. Moreover, in addition to this, even after he has
rendered the property it will not be clear whether it belongs,
seeing that it is the kind of attribute that may fail : and

35 so the property will not be clear. Thus (e.g.) a man who
has stated that it is a property of animal sometimes to
move and sometimes to stand still has rendered the kind
of property which sometimes is not a property, and so the
property could not have been correctly stated. For con
structive purposes, on the other hand, see whether he has
rendered something that of necessity must always be a
I3i b property: for then the property will have been in this
respect correctly stated. Thus (e.g.) a man who has stated
that it is a property of virtue to be what makes its
possessor good has rendered as property something that
always follows, and so the property of virtue would in this
respect have been correctly rendered.

5 Next, for destructive purposes, see whether in rendering
the property of the present time he has omitted to make a
definite proviso that it is the property of the present time
which he is rendering : for else the property will not have
been correctly stated. For in the first place, any unusual
procedure always needs a definite proviso : and it is the
usual procedure for everybody to render as property some

10 attribute that always follows. In the second place, a man
who omits to provide definitely whether it was the property
of the present time which he intended to state, is obscure :
and one should not give any occasion for adverse criticism.
Thus (e. g.) a man who has stated it as the property of
a particular man to be sitting with a particular man ,
states the property of the present time, and so he cannot
have rendered the property correctly, seeing that he has
described it without any definite proviso. For constructive
purposes, on the other hand, see whether, in rendering the

BOOK V. 3 131

property of the present time, he has, in stating it, made 15
a definite proviso that it is the property of the present time
that he is stating : for then the property will in this respect
have been correctly stated. Thus (e.g.) a man who has
said that it is the property of a particular man to be
walking now , has made this distinction in his statement,
and so the property would have been correctly stated.

Next, for destructive purposes, see whether he has ren
dered a property of the kind whose appropriateness is not 20
obvious except by sensation : for then the property will not
have been correctly stated. For every sensible attribute,
once it is taken beyond the sphere of sensation, becomes
uncertain. For it is not clear whether it still belongs,
because it is evidenced only by sensation. This principle
will be true in the case of any attributes that do not always 35
and necessarily follow. Thus (e. g.) any one who has stated
that it is a property of the sun to be the brightest star
that moves over the earth , has used in describing the
property an expression of that kind, viz. to move over the
earth , which is evidenced by sensation ; and so the sun s
property could not have been correctly rendered : for it will
be uncertain, whenever the sun sets, whether it continues to
move over the earth, because sensation then fails us. For 30
constructive purposes, on the other hand, see whether he
has rendered the property of a kind that is not obvious to
sensation, or, if it be sensible, must clearly belong of
necessity : for then the property will in this respect have
been correctly stated. Thus (e.g.) a man who has stated
that it is a property of a surface to be the primary thing
that is coloured , has introduced amongst the rest a sensible
quality, to be coloured , but still a quality such as mani- 35
festly always belongs, and so the property of surface
would in this respect have been correctly rendered.

Next, for destructive purposes, see whether he has ren
dered the definition as a property : for then the property
will not have been correctly stated : for the property of
a thing ought not to show its essence. Thus (e. g.) a man 132*
who has said that it is the property of man to be a walking,
biped animal has rendered a property of man so as to

ja a TOPICA

signify his essence, and so the property of man could not
have been correctly rendered. For constructive purposes,
on the other hand, see whether the property which he has
rendered forms a predicate convertible with its subject,
5 without, however, signifying its essence : for then the
property will in this respect have been correctly rendered.
Thus (e. g.) he who has stated that it is a property of
man to be a naturally civilized animal has rendered the
property so as to be convertible with its subject, without,
however, showing its essence, and so the property of man
would in this respect have been correctly rendered.

10 Next, for destructive purposes, see whether he has rendered
the property without having placed l the subject within its
essence. For of properties, as also of definitions, the first
term to be rendered should be the genus, and then the rest
of it should be appended immediately afterwards, and
should distinguish its subject from other things. Hence
a property which is not stated in this way could not

15 have been correctly rendered. Thus (e. g.) a man who has
said that it is a property of a living creature to have a
soul has not placed living creature within its essence,
and so the property of a living creature could not have
been correctly stated. For constructive purposes, on the
other hand, see whether a man first places within its
essence the subject whose property he is rendering, and
then appends the rest : for then the property will in this
respect have been correctly rendered. Thus (e. g.) he who has

20 stated that it is a property of man to be an animal capable
of receiving knowledge , has rendered the property after
placing the subject within its essence, and so the property
of man would in this respect have been correctly rendered.

The inquiry, then, whether the property has been cor- 4
rectly rendered or no, should be made by these means.
The question, on the other hand, whether what is stated is
25 or is not a property at all, you should examine from the
following points of view. For the commonplace arguments
which establish absolutely that the property is accurately
1 132* 10. Omitting 6 before deis.

BOOK V. 4 132*

stated will be the same as those that constitute it a property at
all : accordingly they will be described in the course of them.

Firstly, then, for destructive purposes, take a look at
each subject of which he has rendered the property, and
see (e.g.) if it fails to belong to any of them at all, or to be
true of them in that particular respect, or to be a property
of each of them in respect of that character of which he 30
has rendered the property : for then what is stated to be a
property will not be a property. Thus, for example, inas
much as it is not true of the geometrician that he cannot
be deceived by an argument (for a geometrician is deceived
when his figure is misdrawn), it could not be a property of
the man of science that he is not deceived by an argument.
For constructive purposes, on the other hand, see whether 35
the property rendered be true of every instance, and true
in that particular respect : for then what is stated not to be
a property l will be a property. Thus, for example, inas
much as the description an animal capable of receiving i32 b
knowledge is true of every man, and true of him qua man,
it would be a property of man to be an animal capable of
receiving knowledge . [This commonplace rule means
for destructive purposes, see if the description fails to be 5
true of that of which the name is true ; and if the name fails
to be true of that of which the description is true: for
constructive purposes, on the other hand, see if the descrip
tion too is predicated of that of which the name is pre
dicated, and if the name too is predicated of that of which
the description is predicated.] 2

Next, for destructive purposes, see if the description fails
to apply to that to which the name applies, and if the name
fails to apply to that to which the description applies: for 10
then what is stated to be a property will not be a property.
Thus (e. g.) inasmuch as the description a living being that
partakes of knowledge is true of God, while man is not
predicated of God, to be a living being that partakes of

1 132*36. Read TO Ktiptvov ^ tlvm "8iov, with A, B, Pacius, Waitz,
and Strache as in the subsequent examples.

2 I think, with Pacius (though for a different reason), that this sen
tence (i32 b 3-8) is probably an addition by a later hand.

2 b TOPICA

knowledge could not be a property of man. For con
structive purposes, on the other hand, see if the name as
well be predicated of that of which the description is pre
dicated, and if the description as well be predicated of that

15 of which the name is predicated. For then what is stated
not to be a property will be a property. Thus (e. g.) the
predicate living creature is true of that of which having
a soul is true, and having a soul is true of that of which
the predicate living creature is true; and so having a
soul would be a property of living creature .

Next, for destructive purposes, see if he has rendered

20 a subject as a property of that which is described as in
the subject : for then what has been stated to be a property
will not be a property. Thus (e. g.) inasmuch as he who
has rendered fire as the property of the body with the
most rarefied particles , has rendered the subject as the
property of its predicate, fire could not be a property of
the body with the most rarefied particles . The reason
why the subject will not be a property of that which is

35 found in the subject is this, that then the same thing will
be the property of a number of things that are specifically
different. For the same thing has quite a number of
specifically different predicates that belong to it alone,
and the subject will be a property of all of these, if
any one states the property in this way. For construc
tive purposes, on the other hand, see if he has rendered
what is found in the subject as a property of the sub-

30 ject : for then what has been stated not to be a property
will be a property, if it be predicated only of the things of
which it has been stated to be the property. Thus (e. g.)
he who has said that it is a property of earth to be
specifically the heaviest body has rendered of the subject
as its property something that is said of the thing in ques
tion alone, and is said of it in the manner in which a
property is predicated, and so the property of earth would
have been rightly stated.

?5 Next, for destructive purposes, see if he has rendered the
property as partaken of: for then what is stated to be a pro
perty will not be a property. For an attribute of which the

BOOK V. 4 i33

subject partakes is a constituent part of its essence : and an i33 c
attribute of that kind would be a differentia applying to
some one species. E.g., inasmuch as he who has said that
walking on two feet is a property of man has rendered
the property as partaken of, walking on two feet could 5
not be a property of man . For constructive purposes, on
the other hand, see if he has avoided rendering the property
as partaken of, or as showing the essence, though the subject
is predicated convertibly with it : for then what is stated
not to be a property will be a property. Thus (e. g.) he who
has stated that to be naturally sentient is a property of
animal has rendered the property neither as partaken
of nor as showing the essence, though the subject is predicated 10
convertibly with it ; and so to be naturally sentient would
be a property of animal .

Next, for destructive purposes, see if the property cannot
possibly belong simultaneously, but must belong either as
posterior or as prior to the attribute described in the name
for then what is stated to be a property will not be a
property either never, or not always. Thus (e.g.) inasmuch 15
as it is possible for the attribute walking through the
market-place to belong to an object as prior and as posterior
to the attribute man , walking through the market-place
could not be a property of man either never, or not
always. For constructive purposes, on the other hand, see if
it always and of necessity belongs simultaneously, without
being either a definition or a differentia : for then what is
stated not to be a property will be a property. Thus (e. g.) 20
the attribute : an animal capable of receiving knowledge
always and of necessity belongs simultaneously with the
attribute man , and is neither differentia nor definition of
its subject, and so an animal capable of receiving knowledge
would be a property of man .

Next, for destructive purposes, see if the same thing fails
to be a property of things that are the same as the subject, 25
so far as they are the same : for then what is stated to be
a property will not be a property. Thus, for example, in
asmuch as it is no property of a proper object of pursuit
to appear good to certain persons , it could not be a property

i33 a TOPICA

of the desirable either to appear good to certain persons :
for proper object of pursuit and desirable mean the same.
For constructive purposes, on the other hand, see if the same
thing be a property of something that is the same as the
subject, in so far as it is the same. For then what is stated

30 not to be a property will be a property. Thus (e. g.) inas
much as it is called a property of a man, in so far as he is
a man, to have a tripartite soul , it would also be a property
of a mortal, in so far as he is a mortal, to have a
tripartite soul. This commonplace rule is useful also in
dealing with Accident : for the same attributes ought either
to belong or not belong to the same things, in so far as they
are the same.

35 Next, for destructive purposes, see if the property of
things that are the same in kind as the subject fails to be
always the same in kind as the alleged property : for then
i33 b neither will what is stated to be the property be the property
of the subject in question. Thus (e. g.) inasmuch as a man
and a horse are the same in kind, and it is not always
a property of a horse to stand by its own initiative, it could
not be a property of a man to move by his own initiative ;
for to stand and to move by his own initiative are the
5 same in kind, because they belong to each of them in so far
as each is an animal . For constructive purposes, on the
other hand, see if of things that are the same in kind as the
subject the property that is the same as the alleged property
is always true : for then what is stated not to be a property
will be a property. Thus (e. g.) since l it is a property of man
to be a walking biped , it would also be a property of

10 a bird to be a flying biped : for each of these is the same
in kind, in so far as the one pair have the sameness of species
that fall under the same genus, being under the genus
animal , while the other pair have that of differentiae of the
genus, viz. of animal . This commonplace rule is deceptive
whenever one of the properties mentioned belongs to some
one species only while the other belongs to many, as does
walking quadruped .

15 Inasmuch as same and different are terms used in
1 *33 b 7- f>7re O r perhaps finep, if indeed . . .

BOOK V. 4 i33 b

several senses, it is a job to render to a sophistical questioner
a property that belongs to one thing and that only. For
an attribute that belongs to something qualified by an
accident will also belong to the accident taken along with
the subject which it qualifies ; e. g. an attribute that belongs
to man will belong also to white man , if there be a white 20
man, and one that belongs to white man will belong also
to ( man . One might, then, bring captious criticism against
the majority of properties, by representing the subject as
being one thing in itself, and another thing when combined
with its accident, saying, for example, that man is one
thing, and white man another, and moreover by represent
ing as different a certain state and what is called after that 25
state. For an attribute that belongs to the state will belong
also to what is called after that state, and one that belongs
to what is called after a state will belong also to the state :
e. g. inasmuch as the condition of the scientist is called after
his science, it could not be a property of science that it is
incontrovertible by argument ; for then the scientist also
will be incontrovertible by argument. For constructive 30
purposes, however, you should say that the subject of an
accident is not absolutely different from the accident taken
along with its subject ; though it is called another thing
because the mode of being of the two is different : for it is
not the same thing for a man to be a man and for a white 35
man to be a white man. Moreover, you should take a look
along at the inflections, and say that the description of the
man of science is wrong : one should say not it but he is i34 a
incontrovertible by argument ; while the description of
Science is wrong too : one should say not it but she is
incontrovertible by argument . For against an objector
who sticks at nothing the defence should stick at nothing.

5 Next, for destructive purposes, see if, while intending to 5
render an attribute that naturally belongs, he states it in his
language in such a way as to indicate one that invariably
belongs : for then it would be generally agreed that what
has been stated to be a property is upset. Thus (e. g.) the
man who has said that biped is a property of man intends

H

i34 a TOPICA

10 to render the attribute that naturally belongs, but his
expression actually indicates one that invariably belongs :
accordingly, biped could not be a property of man : for
not every man is possessed of two feet. For constructive
purposes, on the other hand, see if he intends to render the
property that naturally belongs, and indicates it in that way
in his language : for then the property will not be upset in
this respect. Thus (e. g.) he who renders as a property of
15 man the phrase an animal capable of receiving knowledge
both intends, and by his language indicates, the property
that belongs by nature, and so an animal capable of receiving
knowledge would not be upset or shown in that respect not
to be a property of man.

Moreover, as regards all the things that are called as they
are primarily after something else, or primarily in themselves,
it is a job to render the property of such things. For if you
20 render a property as belonging to the subject that is so called
after something else, then it will be true of its primary
subject as well ; whereas if you state it of its primary subject,
then it will be predicated also of the thing that is so called
after this other. Thus (e. g.) if any one renders coloured
as the property of surface , coloured will be true of body
as well ; whereas if he render it of body , it will be pre
ss dicated also of surface . Hence the name as well will not
be true of that of which the description is true. 1

In the case of some properties it mostly happens that
some error is incurred because of a failure to define how as
well as to what things the property is stated to belong.
For every one tries to render as the property of a thing
something that belongs to it either naturally, as biped
30 belongs to man , or actually, as having four fingers
belongs to a particular man, or specifically, as consisting of
most rarefied particles belongs to fire , or absolutely, as
life to living being , or one that belongs to a thing only
as called after something else, as wisdom to the f soul ,

1 The name surface will not be true of everything of which the
description coloured* is true, since a body is coloured but is not
a surface. The name body will not be true of everything of which
the description coloured is true, since a surface is coloured but is
not a body.

BOOK V. 5 i34 a

or on the other hand primarily, as wisdom to the rational
faculty , or because the thing is in a certain state, as
incontrovertible by argument belongs to a scientist (for 35
simply and solely by reason of his being in a certain state
will he be incontrovertible by argument ), or because it is
the state possessed by something, as incontrovertible by
argument belongs to science , or because it is partaken i34 b
of, as sensation belongs to animal (for other things as
well have sensation, e. g. man, but they have it because they
already partake of animal ), or because it partakes of
something else, as life belongs to a particular kind of living
being . Accordingly he makes a mistake if he has failed to 5
add the word naturally , because what belongs naturally
may fail to belong to the thing to which it naturally belongs,
as (e. g.) it belongs to a man to have two feet : so too he
errs if he does not make a definite proviso that he is
rendering what actually belongs, because one day that
attribute will not be what it now is, 1 e.g. the man s possession
of four fingers. So he errs if he has not shown that he states 10
a thing to be such and such primarily, or that he calls it so
after something else, because then its name too will not be
true of that of which the description is true, as is the case
with coloured , whether rendered as a property of surface
or of body . So he errs if he has not said beforehand that
he has rendered a property to a thing either because that
thing possesses a state, or because it is a state possessed by
something ; because then it will not be a property. For, sup
posing he renders the property to something as being a state 15
possessed, it will belong to what possesses that state ; while
supposing he renders it to what possesses the state, it will
belong to the state possessed, as did incontrovertible by
argument when stated as a property of science or of the
scientist . So he errs if he has not indicated beforehand
that the property belongs because the thing partakes of, or is
partaken of by, something; because then the property will
belong to certain other things as well. For if he renders it 20
because its subject is partaken of. it will belong to the things

1 Or (reading olov inrdpxeiv c/mpa, with A) because one day that
attribute will not be such as can belong to that subject .

H 2

i34 b TOPICA

which partake of it ; whereas if he renders it because its sub
ject partakes of something else, it will belong to the things
partaken of, as (e. g.) if he were to state life to be a property
of a particular kind of living being , or just of living being .
So he errs if he has not expressly distinguished the property
that belongs specifically, because then it will belong only to
one of the things that fall under the term of which he states
the property : for the superlative belongs only to one of

35 them, e. g. lightest as applied to fire . Sometimes, too,
a man may even add the word specifically , and still make
a mistake. For the things in question should all be of one
species, whenever the word specifically is added : and in
some cases this does not occur, as it does not, in fact, in the
case of fire. For fire is not all of one species ; for live coals
and flame and light are each of them fire , but are of

30 different species. The reason why, whenever specifically
is added, there should not be any species other than the one
mentioned, is this, that if there be, then the property in
question will belong to some of them in a greater and to
others in a less degree, as happens with consisting of most
rarefied particles in the case of fire : for light consists of
more rarefied particles than live coals and flame. And this

35 should not happen unless the name too be predicated in
a greater degree of that of which the description is truer ;
otherwise the rule that where the description is truer the
i35 a name too should be truer is not fulfilled. Moreover, in
addition to this, the same attribute will be the property both
of the term which has it absolutely and of that element
therein which has it l in the highest degree, as is the con
dition of the property consisting of most rarefied particles
in the case of fire : for this same attribute will be the

5 property of light as well : for it is light that consists of
the most rarefied particles . If, then, any one else renders
a property in this way one should attack it ; for oneself, one
should not give occasion for this objection, but should define
in what manner one states the property at the actual time
of making the statement.

Next, for destructive purposes, see if he has stated a thing
1 135*3. Read TOIOVTOV (with A, B, and u) for roioirrw.

BOOK V. 5 i35 a

as a property of itself: for then what has been stated to be 10
a property will not be a property. For a thing itself always
shows its own essence, and what shows the essence is not
a property but a definition. Thus (e. g.) he who has said
that becoming is a property of beautiful has rendered the
term as a property of itself (for beautiful and becoming
are the same) ; and so becoming could not be a property
of beautiful . For constructive purposes, on the other 15
hand, see if he has avoided rendering a thing as a property
of itself, but has yet stated a convertible predicate : for then
what is stated not to be a property will be a property. Thus
he who has stated animate substance as a property of
living-creature has not stated living-creature as a property
of itself, but has rendered a convertible predicate, so that
animate substance would be a property of living-creature .

Next, in the case of things consisting of like parts, you 20
should look and see, for destructive purposes, if the property
of the whole be not true of the part, or if that of the part be
not predicated of the whole : for then what has been stated
to be the property will not be a property. In some cases
it happens that this is so : for sometimes in rendering a
property in the case of things that consist of like parts 25
a man may have his eye on the whole, while sometimes he
may address himself to what is predicated of the part : and
then in neither case will it have been rightly rendered.
Take an instance referring to the whole : the man who has
said that it is a property of the sea to be the largest
volume of salt water , has stated the property of something
that consists of like parts, but has rendered an attribute of
such a kind as is not true of the part (for a particular sea is 30
not the largest volume of salt water ) ; and so the largest
volume of salt water could not be a property of the sea .
Now take one referring to the part : the man who has
stated that it is a property of air to be breathable has
stated the property of something that consists of like parts,
but he has stated an attribute such as, though true of some 35
air, is still not predicable of the whole (for the whole of the
air is not breathable) ; and so breathable could not be
a property of air . For constructive purposes, on the i35 b

i35 b TOPICA

other hand, see whether, while it is true of each of the
things with similar parts, it is on the other hand a property
of them taken as a collective whole : for then what has
been stated not to be a property will be a property.
Thus (e. g.) while it is true of earth everywhere that it
5 naturally falls downwards, it is a property of the various
particular pieces of earth taken as the Earth , 1 so that it
would be a property of earth naturally to fall downwards .

Next, look from the point of view of the respective oppo- 6
sites, and first (a) from that of the contraries, and see, for
destructive purposes, if the contrary of the term rendered
fails to be a property of the contrary subject. For then
neither will the contrary of the first be a property of the

10 contrary of the second. Thus (e.g.) inasmuch as injustice
is contrary to justice, and the lowest evil to the highest
good, but to be the highest good is not a property of
justice , therefore to be the lowest evil could not be
a property of injustice . For constructive purposes, on
the other hand, see if the contrary is the property of the
contrary : for then also the contrary of the first will be
the property of the contrary of the second. Thus (e. g.)

15 inasmuch as evil is contrary to good, and objectionable
to desirable, and desirable is a property of good ,
objectionable would be a property of evil .

Secondly (b) look from the point of view of relative
opposites and see, for destructive purposes, if the correlative
of the term rendered fails to be a property of the correla
tive of the subject : for then neither will the correlative of
the first be a property of the correlative of the second.

20 Thus (e.g.) inasmuch as double is relative to half,
and in excess to exceeded , while in excess is not
a property of double , exceeded could not be a property
of half. For constructive purposes, on the other hand, see
if the correlative of the alleged property is a property of the
subject s correlative : for then also the correlative of the
first will be a property of the correlative of the second :

1 I 35 b 4~S- Read in 1. 4, Kara Truo-rjs yrjs, and in 1. 5, not TTJS KU\ rrjs
TIVOS yfjs KOTO, rrjv ~fyv.

BOOK V. 6 i35 b

e.g. inasmuch as double is relative to half, and the
proportion I : 2 is relative to the proportion 2 : I, 1 while it 25
is a property of double to be in the proportion of 2 to i ,
it would be a property of half to be in the proportion of
i to 2 .

Thirdly (c) for destructive purposes, see if an attribute
described in terms of a state (X) fails to be a property of
the given state (Y) : for then neither will the attribute
described in terms of the privation (of X) be a property of
the privation (of Y). Also if, on the other hand, an attri
bute described in terms of the privation (of X) be not a 3
property of the given privation (of Y), neither will the
attribute described in terms of the state (X) be a property
of the state (Y). Thus, for example, inasmuch as it is not
predicated as a property of deafness to be a lack of
sensation , neither could it be a property of hearing to
be a sensation . For constructive purposes, on the other
hand, see if an attribute described in terms of a state (X) is
a property of the given state (Y) : for then also the attribute
that is described in terms of the privation (of X) will be
a property of the privation (of Y). Also, if an attribute 35
described in terms of a privation (of X) be a property of
the privation (of Y), then also the attribute that is described
in terms of the state (X) will be a property of the state (Y).
Thus (e. g.) inasmuch as to see is a property of sight , in
asmuch as we have sight, failure to see would be a property
of blindness , inasmuch as we have not got the sight we
should naturally have.

Next, look from the point of view of positive and negative 5
terms ; and first (a) from the point of view of the predicates
taken by themselves. This common-place rule is useful
only for a destructive purpose. Thus (e.g.) see if the positive
term or the attribute described in terms of it is a property
of the subject : for then the negative term or the attribute
described in terms of it will not be a property of the subject. 10
Also if, on the other hand, the negative term or the attribute
described in terms of it is a property of the subject, then the
positive term or the attribute described in terms of it will not

1 135^ 24. Read (after I^IOTI) rd 8 tt> npos 8vo npos TO dvo npbs ei>.

TOPICA

be a property of the subject : e. g. inasmuch as animate is
a property of living creature , inanimate could not be
a property of living creature .

Secondly (b} look from the point of view of the predicates,

15 positive or negative, and their respective subjects ; " and see,
for destructive purposes, if the positive term fails to be a
property of the positive subject : for then neither will the
negative term be a property of the negative subject. Also,
if the negative term fails to be a property of the negative
subject, neither will the positive term be a property of the
positive subject. Thus (e.g.) inasmuch as animal is not
a property of man , neither could not-animal be a pro-

20 perty of not-man . Also if not-animal seems not to be
a property of not-man , neither will animal be a property
of man . For constructive purposes, on the other hand,
see if the positive term is a property of the positive subject :
for then the negative term will be a property of the nega
tive subject as well. Also if the negative term be a property
of the negative subject, the positive will be a property of

25 the positive as well. Thus (e. g.) inasmuch as it is a property
of not-living being not to live , it would be a property of
living being to live : also if it seems to be a property
of living being to live , it will also seem to be a property
of not-living being not to live .

Thirdly (c) look from the point of view of the subjects
taken by themselves, and see, for destructive purposes, if

30 the property rendered is a property of the positive subject :
for then the same term will not be a property of the nega
tive subject as well. Also, if the term rendered be a property
of the negative subject, it will not be a property of the
positive. Thus (e. g.) inasmuch as animate is a property
of living creature , animate could not be a property of
not-living creature . For constructive purposes, 2 on the
other hand, if the term rendered fails to be a property of

35 the affirmative subject it would be a property of the nega
tive. This commonplace rule is, however, deceptive: for
a positive term is not a property of a negative, or a negative

1 I36 a 15. Read K<U e a>v Karr/yopelrm.

2 I36 a 34. Read Karao-Keuafoj/Tt.

BOOK V. 6 i36

of a positive. For a positive term does not belong at all
to a negative, while a negative term, though it belongs to
a positive, does not belong as a property.

Next, look from the point of view of the co-ordinate
members of a division, and see, for destructive purposes, if
none of the co-ordinate members (parallel with the property
rendered) be a property of any of the remaining set of
co-ordinate members (parallel with the subject) : for then 5
neither will the term stated be a property of that of which
it is stated to be a property. Thus (e. g.) inasmuch as
sensible living being is not a property of any of the other
living beings, 1 intelligible living being could not be a
property of God. For constructive purposes, on the other
hand, see if some one or other of the remaining co-ordinate
members (parallel with the property rendered) be a property
of each of these co-ordinate members (parallel with the
subject) : for then the remaining one too will be a property 10
of that of which it has been stated not to be a property.
Thus (e. g.) inasmuch as it is a property of wisdom to be
essentially the natural virtue of the rational faculty , then,
taking each of the other virtues as well in this way, it would
be a property of temperance to be essentially the natural
virtue of the faculty of desire .

7 Next, look from the point of view of the inflexions, and 15
see, for destructive purposes, if the inflexion of the property
rendered fails to be a property of the inflexion of the sub
ject: for then neither will the other inflexion be a property
of the other inflexion. Thus (e. g.) inasmuch as beautifully
is not a property of justly , neither could beautiful be
a property of just . For constructive purposes, on the
other hand, see if the inflexion of the property rendered
is a property of the inflexion of the subject : for then also
the other inflexion will be a property of the other inflexion.
Thus (e.g.) inasmuch as walking biped is a property of ao
man, it would also be any one s property as a man to be
described as a walking biped . Not only in the case of
the actual term mentioned should one look at the inflexions,
1 I36 b 6. Omit 6vr]Tuv.

TOPICA

but also in the case of its opposites, just as has been laid
down in the case of the former commonplace rules as well. 1

25 Thus, for destructive purposes, see if the inflexion of the
opposite of the property rendered fails to be the property
of the inflexion of the opposite of the subject : for then
neither will the inflexion of the other opposite be a property
of the inflexion of the other opposite. Thus (e. g.) inasmuch
as well is not a property of justly , neither could badly
be a property of unjustly . For constructive purposes, on
the other hand, see if the inflexion of the opposite of the
property originally suggested is a property of the inflexion

30 of the opposite of the original subject : for then also the
inflexion of the other opposite will be a property of the
inflexion of the other opposite. Thus (e. g.) inasmuch as
best is a property of the good , worst also will be a
property of the evil .

Next, look from the point of view of things that are in
a like relation, and see, for destructive purposes, if what is
in a relation like that of the property rendered fails to be
a property of what is in a relation like that of the subject:
for then neither will what is in a relation like that of the

35 first be a property of what is in a relation like that of
the second. Thus (e. g.) inasmuch as the relation of the
builder towards the production of a house is like that of
the doctor towards the production of health, and it is not
i37 a a property of a doctor to produce health, it could not be
a property of a builder to produce a house. For con
structive purposes, on the other hand, see if what is in
a relation like that of the property rendered is a property
of what is in a relation like that of the subject : for then
also what is in a relation like that of the first will be
a property of what is in a relation like that of the second.
Thus (e. g.) inasmuch as the relation of a doctor towards
the possession of ability to produce health is like that of
5 a trainer towards the possession of ability to produce
vigour, and it is a property of a trainer to possess the
ability to produce vigour, it would be a property of
a doctor to possess the ability to produce health.
1 ii4 b 6-15.

BOOK V. 7 i37 f

Next look from the point of view of things that are
identically related, and see, for destructive purposes, if the
predicate that is identically related towards two subjects
fails to be a property of the subject which is identically
related to it as the subject in question ; for then neither
will the predicate that is identically related to both subjects 10
be a property of the subject which is identically related to
it as the first. If, on the other hand, the predicate which
is identically related to two subjects is the property of the
subject which is identically related to it as the subject in
question, then it will not be a property of that of which it
has been stated to be a property. [Thus (e. g.) inasmuch
as prudence is identically related to both the noble and the
base, since it is knowledge of each of them, and it is not
a property of prudence to be knowledge of the noble, it
could not be a property of prudence to be knowledge of 15
the base. If, on the other hand, it is a property of prudence
to be the knowledge of the noble, it could not be a property
of it to be the knowledge of the base. 1 ] For it is impossible
for the same thing to be a property of more than one subject.
For constructive purposes, on the other hand, this common
place rule is of no use : for what is identically related is
a single predicate in process of comparison with more than 20
one subject.

Next, for destructive purposes, see if the predicate quali
fied by the verb to be fails to be a property of the subject
qualified by the verb to be : for then neither will the
destruction of the one be a property of the other qualified
by the verb to be destroyed , nor will the becoming the
one be a property of the other qualified by the verb to
become . Thus (e. g.) inasmuch as it is not a property
of man to be an animal, neither could it be a property of
becoming a man to become an animal ; nor could the 25
destruction of an animal be a property of the destruction of
a man. In the same way one should derive arguments also
from becoming to being and being destroyed , and from
being destroyed to being and to becoming , exactly as

1 I37 a i2 olov firfl ... 17 tlvai ala-xpov. These illustrations are
bracketed, with Pacius, as a later and inept addition.

i37 a TOPICA

30 they have just been given from being to becoming and
being destroyed . For constructive purposes, on the other
hand, see if the subject set down as qualified by the verb
to be has the predicate set down as so qualified, as its
property : for then also the subject qualified by the verb
to become will have the predicate qualified by to become
as its property, and the subject qualified by the verb to be
destroyed will have as its property the predicate rendered
with this qualification. Thus, for example, inasmuch as it

35 is a property of man to be a mortal, it would be a property
of becoming a man to become a mortal, and the destruction
of a mortal would be a property of the destruction of a man.
i37 b In the same way one should derive arguments also from
becoming and being destroyed both to being and to
the conclusions that follow from them, exactly as was
directed also for the purpose of destruction.

Next take a look at the idea of the subject stated, and
see, for destructive purposes, if the suggested property fails
to belong to the idea in question, or fails to belong to it
5 in virtue of that character which causes it to bear the
description of which the property was rendered : for then
what has been stated to be a property will not be a property.
Thus (e. g.) inasmuch as being motionless does not belong
to man-himself qua man , but qua idea , it could not
be a property of man to be motionless. For constructive
purposes, on the other hand, see if the property in question
belongs to the idea, and belongs to it in that respect in
virtue of which there is predicated of it that character l of

10 which the predicate in question has been stated not to be
a property: for then what has been stated not to be a
property will be a property. Thus (e. g.) inasmuch as it
belongs to living-creature-itself to be compounded of soul
and body, and further this belongs to it qua living-creature ,
it would be a property of living-creature to be compounded
of soul and body.

Next look from the point of view of greater and less 8
15 degrees, and first (a) for destructive purposes, see if what
1 I37 b 10. Adopting Mr. W. D. Ross s emendation e/cetco.

BOOK V. 8 i37 b

is more-P fails to be a property of what is more-S : for then
neither will what is less-P be a property of what is less-S,
nor least-P of least-S, nor most-P of most-S, nor P simply
of S simply. Thus (e. g.) inasmuch as being more highly
coloured is not a property of what is more a body, neither
could being less highly coloured be a property of what is 20
less a body, nor being coloured be a property of body
at all. For constructive purposes, on the other hand, see if
what is more-P is a property of what is more-S : for then
also what is less-P will be a property of what is less-S, and
least-P of least-S, and most-P of most-S, and P simply of
S simply. Thus (e. g.) inasmuch as a higher degree of
sensation is a property of a higher degree of life, a lower
degree of sensation also would be a property of a lower 25
degree of life, and the highest of the highest and the lowest
of the lowest degree, and sensation simply of life simply.

Also you should look at the argument from a simple
predication to the same qualified types of predication, and
see, for destructive purposes, if P simply fails to be a
property of S simply ; for then neither will more-P be 30
a property of more-S, nor less-P of less-S, nor most-P of
most-S, nor least-P of least-S. Thus (e.g.) inasmuch as
virtuous is not a property of man , neither could more
virtuous be a property of what is more human . For
constructive purposes, on the other hand, see if P simply is
a property of S simply: for then more-P also will be
a property of more-S, and less-P of less-S, and least-P of 35
least-S, and most-P of most-S. Thus (e. g.) a tendency to
move upwards by nature is a property of fire, and so also
a greater tendency to move upwards by nature would be i38 a
a property of what is more fiery. In the same way too
one should look at all these matters from the point of view
of the others as well.

Secondly (b) for destructive purposes, see if the more
likely property fails to be a property of the more likely
subject : for then neither will the less likely property be 5
a property of the less likely subject. Thus (e. g.) inasmuch
as perceiving is more likely to be a property of animal
than knowing of man , and perceiving is not a property

8 a TOPICA

of animal , knowing could not be a property of man .
For constructive purposes, on the other hand, see if the less
likely property is a property of the less likely subject ; for
then too the more likely property will be a property of the

10 more likely subject. Thus (e. g.) inasmuch as to be naturally
civilized is less likely to be a property of man than to live
of an animal, and it is a property of man to be naturally
civilized, it would be a property of animal to live.

Thirdly (c) for destructive purposes, see if the predicate
fails to be a property of that of which it is more likely to
be a property : for then neither will it be a property of that
of which it is less likely to be a property: while if it is

15 a property of the former, it will not be a property of the
latter. Thus (e. g.) inasmuch as to be coloured is more
likely to be a property of a surface than of a body , and
it is not a property of a surface, to be coloured could not
be a property of body ; while if it is a property of a
surface , it could not be a property of a body . For
constructive purposes, on the other hand, this commonplace

ao rule is not of any use : for it is impossible for the same
thing to be a property of more than one thing.

Fourthly (d] for destructive purposes, see if what is more
likely to be a property of a given subject fails to be its
property : for then neither will what is less likely to be
a property of it be its property. Thus (e. g.) inasmuch as
sensible is more likely than divisible to be a property
of animal , and sensible is not a property of animal,

25 divisible could not be a property of animal. For con
structive purposes, on the other hand, see if what is less
likely to be a property of it is a property ; for then what is
more likely to be a property of it will be a property as well.
Thus, for example, inasmuch as sensation is less likely to
be a property of animal than life , and sensation is
a property of animal, life would be a property of
animal.

30 Next, look from the point of view of the attributes that
belong in a like manner, and first (a) for destructive pur
poses, see if what is as much a property fails to be a
property of that of which it is as much a property: for

BOOK V. 8 i38 a

then neither will that which is as much a property as it be
a property of that of which it is as much a property.
Thus (e. g.) inasmuch as desiring is as much a property
of the faculty of desire as reasoning is a property of
the faculty of reason, and desiring is not a property of the 35
faculty of desire, reasoning could not be a property of
the faculty of reason. For constructive purposes, on the
other hand, see if what is as much a property is a property
of that of which it is as much a property : for then also
what is as much a property as it will be a property of that i38 b
of which it is as much a property. Thus (e. g.) inasmuch
as it is as much a property of the faculty of reason to be
the primary seat of wisdom as it is of the faculty of
desire to be the primary seat of temperance , and it is
a property of the faculty of reason to be the primary seat
of wisdom, it would be a property of the faculty of desire
to be the primary seat of temperance. 5

Secondly (b] for destructive purposes, see if what is as
much a property of anything fails to be a property of it :
for then neither will what is as much a property be a
property of it. Thus (e. g.) inasmuch as seeing is as
much a property of man as hearing , and seeing is not
a property of man, hearing could not be a property of
man. For constructive purposes, on the other hand, see if 10
what is as much a property of it is its property : for then
what is as much a property of it as the former will be its
property as well. Thus (e. g.) it is as much a property of
the soul to be the primary possessor of a part that desires
as of a part that reasons, and it is a property of the soul to
be the primary possessor of a part that desires, and so it
would be a property of the soul to be the primary possessor 15
of a part that reasons.

Thirdly (c] for destructive purposes, see if it fails to be
a property of that of which it is as much a property : for
then neither will it be a property of that of which it is as
much a property as of the former, while if it be a property
of the former, it will not be a property of the other. Thus
(e. g.) inasmuch as to burn is as much a property of
flame as of live coals , and to burn is not a property

TOPICA

ao of flame, to burn could not be a property of live coals:
while if it is a property of flame, it could not be a property
of Jive coals. For constructive purposes, on the other hand,
this commonplace rule is of no use.

The rule based on things that are in a like relation l differs
from the rule based on attributes that belong in a like
manner, 2 because the former point is secured by analogy,

25 not from reflection on the belonging of any attribute, while
the latter is judged by a comparison based on the fact that
an attribute belongs.

Next, for destructive purposes, see if in rendering the
property potentially, he has also through that potentiality
rendered the property relatively to something that does
not exist, when the potentiality in question cannot belong

30 to what does not exist : for then what is stated to be
a property will not be a property. Thus (e. g.) he who has
said that breathable is a property of air has, on the
one hand, rendered the property potentially (for that is
breathable which is such as can be breathed), and on the
other hand has also rendered the property relatively to
what does not exist : for while air may exist, even though
there exist no animal so constituted as to breathe the air,

35 it is not possible to breathe it if no animal exist : so that it
will not, either, be a property of air to be such as can be
breathed at a time when there exists no animal such as to
breathe it and so it follows that breathable could not
be a property of air.

i3g a For constructive purposes, see if in rendering the property
potentially he renders the property either relatively to some
thing that exists, or to something that does not exist, when
the potentiality in question can belong to what does not
exist : for then what has been stated not to be a property
will be a property. Thus (e. g.) he who renders it as a
5 property of being to be capable of being acted upon
or of acting , in rendering the property potentially, has
rendered the property relatively to something that exists :
for when being exists, it will also be capable of being
acted upon or of acting in a certain way : so that to be

BOOK V. 8 i39 E

capable of being acted upon or of acting would be
a property of being .

Next, for destructive purposes, see if he has stated the
property in the superlative : for then what has been stated 10
to be a property will not be a property. For people who
render the property in that way find that of the object of
which the description is true, the name is not true as well :
for though the object perish the description will continue in
being none the less ; for it belongs most nearly to some
thing that is in being. An example would be supposing
any one were to render the lightest body as a property of
fire : for, though fire perish, there will still be some form 15
of body that is the lightest, so that the lightest body
could not be a property of fire. For constructive purposes,
on the other hand, see if he has avoided rendering the
property in the superlative : for then the property will
in this respect have been correctly stated. Thus (e. g.)
inasmuch as he who states a naturally civilized animal
as a property of man has not rendered the property in the
superlative, the property would in this respect have been ao
correctly stated.

BOOK VI

J39 a THE discussion of Definitions falls into five parts. For
25 you have to show either (i) that it is not true at all to
apply the expression as well to that to which the term is
applied (for the definition of Man ought to be true of every
man) ; or (a) that though the object has a genus, he has
failed to put the object defined into the genus, or to put it
into the appropriate genus (for the framer of a definition
should first place the object in its genus, and then append
30 its differences : for of all the elements of the definition the
genus is usually supposed to be the principal mark of the
essence of what is defined) : or (3) that the expression is
not peculiar to the object (for, as we said above as well, 1
a definition ought to be peculiar) 2 : or else (4) see if, though
he has observed all the aforesaid cautions, he has yet failed
to define the object, that is, to express its essence. (5) It
remains, apart from the foregoing, to see if he has defined it,
35 but defined it incorrectly.

Whether, then, the expression be not also true of that of
which the term is true you should proceed to examine
according to the commonplace rules that relate to Acci
dent. For there too the question is always Is so and so
true or untrue? : for whenever we argue that an accident

i39 b belongs, we declare it to be true, while whenever we argue
that it does not belong, we declare it to be untrue. If,
again, he has failed to place the object in the appropriate
genus, or if the expression be not peculiar to the object, we
must go on to examine the case according to the common-
5 place rules that relate to genus and property.

It remains, then, to prescribe how to investigate whether
the object has been either not defined at all, or else defined
incorrectly. First, then, we must proceed to examine if it
has been defined incorrectly : for with anything it is easier
to do it than to do it correctly. Clearly, then, more mistakes

1 ioi b 19.

2 The bracket which begins at 8et yap ... (1. 31) should be closed
after ei /j^rui (1. 32).

BOOK VI. I i39 b

are made in the latter task on account of its greater difficulty.
Accordingly the attack becomes easier in the latter case than 10
in the former.

Incorrectness falls into two branches : (i) first, the use of
obscure language (for the language of a definition ought to
be the very clearest possible, seeing that the whole purpose
of rendering it is to make something known) ; (2) secondly, 15
if the expression used be longer than is necessary : for all
additional matter in a definition is superfluous. Again,
each of the aforesaid branches is divided into a number of
others.

2 One commonplace rule, then, in regard to obscurity is,
See if the meaning intended by the definition involves an 20
ambiguity with any other, e. g. Becoming is a passage into
being , or Health is the balance of hot and cold elements ; .
Here passage and balance are ambiguous terms: it is
accordingly not clear which of the several possible senses of
the term he intends to convey. Likewise also, if the term
defined be used in different senses and he has spoken without
distinguishing between them : for then it is not clear to 25
which of them the definition rendered applies, and one can
then bring a captious objection on the ground that the
definition does not apply to all the things whose definition
he has rendered : and this kind of thing is particularly easy
in the case where the definer does not see the ambiguity of
his terms. Or, again, the questioner may himself distinguish
the various senses of the term rendered in the definition,
and then institute his argument against each : for if the 30
expression used be not adequate to the subject in any of
its senses, it is clear that he cannot have defined it in any
sense aright.

Another rule is, See if he has used a metaphorical
expression, as, for instance, if he has defined knowledge
as imsupplantable , or the earth as a nurse , or temperance
as a harmony . For a metaphorical expression is always
obscure. It is possible, also, to argue sophistically against 35
the user of a metaphorical expression 1 as though he had
1 139^35 Resd TO^ nfruffoopav (Inovra.
I 2

i39 b TOPICA

used it in its literal sense : for the definition stated will not
apply to the term defined, e. g. in the case of temperance :
for harmony is always found between notes. Moreover, if
harmony be the genus of temperance, then the same object
i4O a will occur in two genera of which neither contains the other :
for harmony does not contain virtue, nor virtue harmony.
Again, see if he uses terms that are unfamiliar, as when
Plato describes l the eye as brow-shaded , or a certain spider
5 as poison-fanged , or the marrow as bone-formed . For
an unusual phrase is always obscure.

Sometimes a phrase is used neither ambiguously, nor yet
metaphorically, nor yet literally, as when the law is said to
be the measure or image of the things that are by nature
just. Such phrases are worse than metaphor ; for the latter
does make its meaning to some extent clear because of the

I0 likeness involved ; for those who use metaphors do so always
in view of some likeness : whereas this kind of phrase makes
nothing clear ; for there is no likeness to justify the descrip
tion * measure or image , as applied to the law, nor is the
law ordinarily so called in a literal sense. So then, if a man
says that the law is literally a measure or an image , he

15 speaks falsely : for an image is something produced by
imitation, and this is not found in the case of the law.
If, on the other hand, he does not mean the term literally,
it is clear that he has used an unclear expression, and one
that is worse than any sort of metaphorical expression.

Moreover, see if from the expression used the definition of
the contrary be not clear; for definitions that have been
correctly rendered also indicate their contraries as well.

20 Or, again, see if, when it is merely stated by itself, it is not
evident what it defines : just as in the works of the old
painters, unless there were an inscription, the figures used
to be unrecognizable.

If, then, the definition be not clear, you should proceed to 3
examine on lines such as these. If, on the other hand, he
has phrased the definition redundantly, first of all look

1 Not in his extant works ; perhaps in his early poems. Or the
reference may be to Plato the comic poet.

BOOK VI. 3 H

and see whether he has used any attribute that belongs 25
universally, either to real objects in general, or to all that
fall under the same genus as the object defined : for the
mention of this is sure to be redundant. For the genus
ought to divide the object from things in general, and the
differentia from any of the things contained in the same
genus. Now any term that belongs to everything separates
off the given object from absolutely nothing, while any that
belongs to all the things that fall under the same genus 30
does not separate it off from the things contained in the
same genus. Any addition, then, of that kind will be
pointless.

Or see if, though the additional matter may be peculiar
to the given term, yet even when it is struck out the rest of
the expression too is peculiar and makes clear the essence
of the term. Thus, in the definition of man, the addition 35
capable of receiving knowledge is superfluous ; for strike
it out, and still the expression is peculiar and makes clear
his essence. Speaking generally, everything is superfluous i4
upon whose removal the remainder still makes the term
that is being defined clear. Such, for instance, would also
be the definition of the soul, assuming it to be stated as
a self-moving number ; 1 for the soul is just the self-
moving , as Plato defined it. 2 Or perhaps the expression
used, though appropriate, yet does not declare the essence,
if the word number be eliminated. Which of the two is 5
the real state of the case it is difficult to determine clearly :
the right way to treat the matter in all cases is to be guided
by convenience. Thus (e.g.) it is said that the definition of
phlegm is the undigested moisture that comes first off food .
Here the addition of the word undigested is superfluous,
seeing that the first is one and not many, so that even when
undigested is left out the definition will still be peculiar 10
to the subject : for it is impossible that both phlegm and
also something else should both be the first to arise from
the food. Or perhaps the phlegm is not absolutely the
first thing to come off the food, but only the first of the
undigested matters, so that the addition undigested is
1 Xenocrates, fr. 60 Heinze. " Phaedr. 245 E.

i4Q b TOPICA

required ; for stated the other way the definition would not

15 be true unless the phlegm comes first of all.

Moreover, see if anything contained in the definition fails
to apply to everything that falls under the same species :
for this sort of definition is worse than those which include
an attribute belonging to all things universally. For in
that case, if the remainder of the expression be peculiar,
the whole too will be peculiar : for absolutely always, if to

20 something peculiar anything whatever that is true be added,
the whole too becomes peculiar. Whereas if any part of
the expression do not apply to everything that falls under
the same species, it is impossible that the expression as
a whole should be peculiar : for it will not be predicated
convertibly with the object ; e. g. a walking biped animal
six feet high : for an expression of that kind is not predi-

25 cated convertibly with the term, because the attribute six
feet high does not belong to everything that falls under
the same species.

Again, see if he has said the same thing more than once,
saying (e. g.) desire is a conation for the pleasant . For
desire is always for the pleasant , so that what is the
same as desire will also be for the pleasant . Accordingly

3 o our definition of desire becomes conation-for-the-pleasant
for the pleasant : for the word desire is the exact equi
valent of the words conation-for-the-pleasant , so that both
alike will be for the pleasant . Or perhaps there is no
absurdity in this ; for consider this instance : Man is a
biped : therefore, what is the same as man is a biped : but
a walking biped animal is the same as man, and therefore

35 a walking biped animal is a biped . But this involves no

real absurdity. For biped is not a predicate of walking

animal : if it were, then we should certainly have biped

predicated twice of the same thing ; but as a matter of fact

i4i a the subject said to be a biped is a walking biped animal ,

so that the word biped is only used as a predicate once.

Likewise also in the case of desire as well : for it is not

4 conation that is said to be for the pleasant , but rather

the whole idea, so that there too the predication is only

5 made once. Absurdity results, not when the same word is

BOOK VI. 3 i4i

uttered twice, but when the same thing is more than once
predicated of a subject; e.g. if he says, like Xenocrates, 1
that wisdom defines and contemplates reality : 2 for defini
tion is a certain type of contemplation, so that by adding
the words and contemplates over again he says the same
thing twice over. Likewise, too, those fail who say that
cooling is the privation of natural heat . For all priva- 10
tion is a privation of some natural attribute, so that the
addition of the word natural is superfluous : it would
have been enough to say privation of heat , for the word
privation shows of itself that the heat meant is natural
heat.

Again, see if a universal have been mentioned and then 15
a particular case of it be added as well, e. g. Equity is
a remission of what is expedient and just ; for what is
just is a branch of what is expedient and is therefore
included in the latter term : its mention is therefore redun
dant, an addition of the particular after the universal has
been already stated. So also, if he defines medicine as
knowledge of what makes for health in animals and men ,
or the law as the image of what is by nature noble and a
just ; for what is just is a branch of what is noble, so that
he says the same thing more than once.

4 Whether, then, a man defines a thing correctly or incor
rectly you should proceed to examine on these and similar
lines. But whether he has mentioned and defined its essence
or no, should be examined as follows : 25

First of all, see if he has failed to make the definition
through terms that are prior and more intelligible. For
the reason why the definition is rendered is to make known
the term stated, and we make things known by taking not
any random terms, but such as are prior and more intelli
gible, as is done in demonstrations (for so it is with all 30
teaching and learning) ; accordingly, it is clear that a man
who does not define through terms of this kind has not
defined at all. Otherwise, there will be more than one
definition of the same thing : for clearly he who defines
1 141*6. Read CHOP tl is SfvoKpdTTjs. J Fr. ^ Heinze.

i a TOPICA

through terms that are prior and more intelligible has also
framed a definition, and a better one, so that both would
then be definitions of the same object. This sort of view,

35 however, does not generally find acceptance : for of each
real object the essence is single: if, then, there are to be
a number of definitions of the same thing, the essence of
the object will be the same as it is represented to be in
each of the definitions, and these representations are not

lb the same, inasmuch as the definitions are different. Clearly,
then, any one who has not defined a thing through terms
that are prior and more intelligible has not defined it at all.
The statement that a definition has not been made through
more intelligible terms may be understood in two senses,
either supposing that its terms are absolutely less intelli-
5 gible, or supposing that they are less intelligible to us : for
either sense is possible. Thus absolutely the prior is more
intelligible than the posterior, a point, for instance, than
a line, a line than a plane, and a plane than a solid ; just as
also a unit is more intelligible than a number ; for it is the
prius and starting-point of all number. Likewise, also,
a letter is more intelligible than a syllable. Whereas to us
it sometimes happens that the converse is the case : for

10 the solid falls under perception most of all more than
a plane l and a plane more than a line, and a line more
than a point ; for most people learn things like the former
earlier than the latter ; for any ordinary intelligence can
grasp them, whereas the others require an exact and
exceptional understanding.

15 Absolutely, then, it is better to try to make what is
posterior known through what is prior, inasmuch as such
a way of procedure is more scientific. Of course, in dealing
with persons who cannot recognize things through terms
of that kind, it may perhaps be necessary to frame the
expression through terms that are intelligible to them.
Among definitions of this kind are those of a point, a line,

20 and a plane, all of which explain the prior by the posterior ;
for they say that a point is the limit of a line, a line of
a plane, a plane of a solid. One must, however, not fail to

1 141^11. Read TTtTJTft e7ri7r Sov.

BOOK VI. 4 i4i b

observe that those who define in this way cannot show the
essential nature of the term they define, unless it so happens
that the same thing is more intelligible both to us and also 2 5
absolutely, since a correct definition must define a thing
through its genus and its differentiae, and these belong to
the order of things which are absolutely more intelligible
than, and prior to, the species. For annul the genus and
differentia, and the species too is annulled, so that these are
prior to the species. They are also more intelligible ; for
if the species be known, the genus and differentia must of 3
necessity be known as well (for any one who knows what
a man is knows also what animal and walking are),
whereas if the genus or the differentia be known it does
not follow of necessity that the species is known as well :
thus the species is less intelligible. Moreover, those who
say that such definitions, viz. those which proceed from 35
what is intelligible to this, that, or the other man, are really
and truly definitions, will have to say that there are several
definitions of one and the same thing. For, as it happens,
different things are more intelligible to different people, not
the same things to all ; and so a different definition would 142*
have to be rendered to each several person, if the definition
is to be constructed from what is more intelligible to par
ticular individuals. Moreover, to the same people different
things are more intelligible at different times ; first of all
the objects of sense ; then, as they become more sharp-
witted, the converse ; so that those who hold that a defini
tion ought to be rendered through what is more intelligible 5
to particular individuals would not have to render the same
definition at all times even to the same person. It is clear,
then, that the right way to define is not through terms of
that kind, but through what is absolutely more intelligible:
for only in this way could the definition come always to be
one and the same. Perhaps, also, what is absolutely intelli
gible is what is intelligible, not to all, but to those who are 10
in a sound state of understanding, just as what is absolutely
healthy is what is healthy to those in a sound state of body.
All such points as this ought to be made very precise, and
made use of in the course of discussion as occasion requires.

i42 a TOPICA

The demolition of a definition will most surely win a general
15 approval if the definer happens to have framed his expression

neither from what is absolutely more intelligible nor yet from

what is so to us.

One form, then, of the failure to work through more

intelligible terms is the exhibition of the prior through the

posterior, as we remarked before. 1 Another form occurs if

we find 2 that the definition has been rendered of what is at
20 rest and definite through what is indefinite and in motion :

for what is still and definite is prior to what is indefinite

and in motion.

Of the failure to use terms that are prior there are three

forms :

(1) The first is when an opposite has been defined through
its opposite, e. g. good through evil : for opposites are always
simultaneous by nature. Some people think, also, that both

25 are objects of the same science, so that the one is not even
more intelligible than the other. One must, however, observe
that it is perhaps not possible to define some things in any
other way, c. g. the double without the half, and all the
terms that are essentially relative : for in all such cases the
essential being is the same as a certain relation to some-

30 thing, so that it is impossible to understand the one term
without the other, and accordingly in the definition of the
one the other too must be embraced. One ought to learn
up all such points as these, and use them as occasion may
seem to require.

(2) Another is if he has used the term defined itself.
This passes unobserved when the actual name of the object

35 is not used, e. g. supposing any one had defined the sun as

i42 b a star that appears by day . 3 For in bringing in day he

brings in the sun. To detect errors of this sort, exchange

the word for its definition, e.g. the definition of day as

the passage of the sun over the earth . Clearly, whoever

has said the passage of the sun over the earth has said

5 the sun , so that in bringing in the day he has brought

in the sun.

1 141*26. 2 I42 a 2o. Read r^iiiv after 6 Xdyo?.

3 Cf. PI. Def. 41 1 A.

BOOK VI. 4 142"

(3) Again, see if he has defined one co-ordinate member
of a division by another, e. g. an odd number as that
which is greater by one than an even number . For the
co-ordinate members of a division that are derived from
the same genus are simultaneous by nature, and odd and
even are such terms : for both are differentiae of number. 10

Likewise also, see if he has defined a superior through
a subordinate term, e.g. An "even number" is "a number
divisible into halves " , or " the good " is a " state of
virtue" . For half is derived from two , and two is
an even number : virtue also is a kind of good, so that the
latter terms are subordinate to the former. Moreover, in 15
using the subordinate term one is bound to use the other as
well : for whoever employs the term virtue employs the
term good , seeing that virtue is a certain kind of good :
likewise, also, whoever employs the term half employs
the term even , for to be divided in half means to be
divided into two, and two is even.

Generally speaking, then, one commonplace rule relates 20
to the failure to frame the expression by means of terms
that are prior and more intelligible: and of this the sub
divisions arc those specified above. A second is, see
whether, though the object is in a genus, it has not been
placed in a genus. This sort of error is always found
where the essence of the object does not stand first in the
expression, e. g. the definition of body as that which has
three dimensions , or the definition of man , supposing 35
any one to give it, as that which knows how to count :
for it is not stated what it is that has three dimensions, or
what it is that knows how to count : whereas the genus is
meant to indicate just this, and is submitted first of the
terms in the definition.

Moreover, see if, while the term to be defined is used in 30
relation to many things, he has failed to render it in rela
tion to all of them ; as (e. g.) if he define grammar as the
knowledge how to write from dictation : for he ought
also to say that it is a knowledge how to read as well.
For in rendering it as knowledge of writing he has no

i42 b TOPICA

more defined it than by rendering it as knowledge of
reading : neither in fact has succeeded, but only he who
mentions both these things, since it is impossible that there

35 should be more than one definition of the same thing. It is
i43 a only, however, in some cases that what has been said corre
sponds to the actual state of things : in some it does not,
e. g. all those terms which are not used essentially in rela
tion to both things : as medicine is said to deal with the
production of disease and health ; for it is said essentially
to do the latter, but the former only by accident : for it is
5 absolutely alien to medicine to produce disease. Here,
then, the man who renders medicine as relative to both of
these things has not defined it any better than he who
mentions the one only. In fact he has done it perhaps
worse, for any one else besides the doctor is capable of
producing disease.

Moreover, in a case where the term to be defined is used

10 in relation to several things, see if he has rendered it as
relative to the worse rather than to the better ; for every
form of knowledge and potentiality is generally thought
to be relative to the best.

Again, if the thing in question be not placed in its
own proper genus, one must examine it according to the
elementary rules in regard to genera, as has been said
before. 1

15 Moreover, see if he uses language which transgresses 2 the
genera of the things he defines, defining, e. g., justice as
a state that produces equality or distributes what is
equal : for by defining it so he passes outside the sphere
of virtue, and so by leaving out the genus of justice he
fails to express its essence : for the essence of a thing must
in each case bring in its genus. It is the same thing if the

20 object be not put into its nearest genus ; for the man who
puts it into the nearest one has stated all the higher genera,
seeing that all the higher genera are predicated of the lower.
Either, then, it ought to be put into its nearest genus, or else
to the higher genus all the differentiae ought to be appended
whereby the nearest genus is defined. For then he would
1 I 39 b 3 2 I 43 a I S Read 4irt

BOOK VI. 5 i43 a

not have left out anything : but would merely have men- 35
tioned the subordinate genus by an expression instead of
by name. On the other hand, he who mentions merely
the higher genus by itself, does not state the subordinate
genus as well : in saying plant a man docs not specify
a tree .

6 Again, in regard to the differentiae, we must examine in
like manner whether the differentiae, too, that he has stated 3
be those of the genus. For if a man has not defined the
object by the differentiae peculiar to it, or has mentioned
something such as is utterly incapable of being a differentia
of anything, e. g. animal or substance , clearly he has
not defined it at all : for the aforesaid terms do not
differentiate anything at all. Further, we must see whether
the differentia stated possesses anything that is co-ordinate
with it in a division ; for, if not, clearly the one stated could 35
not be a differentia of the genus. For a genus is always
divided by differentiae that are co-ordinate members of a
division, as, for instance, animal by the terms walking , i43 b
flying , aquatic , and biped . Or see if, though the
contrasted differentia exists, it yet is not true of the
genus ; for then, clearly, neither of them could be a
differentia of the genus ; for differentiae that are co-or
dinates in a division with the differentia of a thing are
all true of the genus to which the thing belongs. Likewise, 5
also, see if, though it be true, yet the addition of it to the
genus fails to make a species. For then, clearly, this could
not be a specific differentia of the genus : for a specific
differentia, if added to the genus, always makes a species.
If, however, this be no true differentia, no more is the one
adduced, seeing that it is a co-ordinate member of a division 10
with this.

Moreover, see if he divides the genus by a negation, as
those do who define a line as length without breadth : for
this means simply that it has not any breadth. The genus
will then be found to partake of its own species : for,
since of everything either an affirmation or its negation is 15
true, length must always either lack breadth or possess it,

i43 b TOPICA

so that length as well, i.e. the genus of line , will be
either with or without breadth. But length without
breadth is the definition of a species, as also is length
with breadth : for without breadth and with breadth
are differentiae, and the genus and differentia constitute the

20 definition of the species. Hence the genus would admit of
the definition of its species. Likewise, also, it will admit
of the definition of the differentia, seeing that one or the
other of the aforesaid differentiae is of necessity predicated
of the genus. The usefulness of this principle is found in
meeting those who assert the existence of Ideas : for if

25 absolute length exist, how will it be predicable of the genus
that it has breadth or that it lacks it ? For one assertion
or the other will have to be true of length universally, if
it is to be true of the genus at all : and this is contrary to
the fact : for there exist both lengths which have, and
lengths which have not, breadth. Hence the only people
against whom the rule can be employed are those who

30 assert that a genus is always l numerically one ; and this is
what is done by those who assert the real existence of the
Ideas ; for they allege that absolute length and absolute
animal are the genus.

It may be that in some cases the definer is obliged to
employ a negation as well, e. g. in defining privations. For

35 blind means a thing which cannot see when its nature is
to see. There is no difference between dividing the genus
by a negation, and dividing it by such an affirmation as is
i44 a bound to have a negation as its co-ordinate in a division,
e. g. supposing he had defined something as length
possessed of breadth ; for co-ordinate in the division with
that which is possessed of breadth is that which possesses
no breadth and that only, so that again the genus is divided
by a negation.

5 Again, see if he rendered the species as a differentia, as
do those who define contumely as insolence accompanied
by jeering ; for jeering is a kind of insolence, i. e. it is a
species and not a differentia.

Moreover, see if he has stated the genus as the differentia,

1 I43 b 30. Read TTOV yevos.

BOOK VI. 6 144*

e. g. Virtue is a good or noble state : for good is the 10
genus of virtue . Or possibly good here is not the
genus but the differentia, on the principle that the same
thing cannot be in two genera of which neither contains
the other: for good does not include state , nor vice
versa : for not every state is good nor every good a state .
Both, then, could not be genera, and consequently, if state 15
is the genus of virtue, clearly good cannot be its genus :
it must rather be the differentia. Moreover, a state in
dicates the essence of virtue, whereas good indicates not
the essence but a quality : and to indicate a quality is
generally held to be the function of the differentia.

See, further, whether the differentia rendered indicates ao
an individual rather than a quality : for the general view is
that the differentia always expresses a quality.

Look and see, further, whether the differentia belongs
only by accident to the object defined. For the differentia
is never an accidental attribute, any more than the genus 25
is : for the differentia of a thing cannot both belong and not
belong to it.

Moreover, if either the differentia or the species, or any
of the things which are under the species, is predicable of
the genus, then he could not have defined the term. For
none of the aforesaid can possibly be predicated of the 30
genus, seeing that the genus is the term with the widest
range of all. Again, see if the genus be predicated of the
differentia ; for the general view is that the genus is predi
cated, not of the differentia, but of the objects of which
the differentia is predicated. Animal (e. g.) is predicated
of man or ox or other walking animals, not of the 35
actual differentia itself which we predicate of the species.
For if animal is to be predicated of each of its differentiae,
then animal would be predicated of the species several
times over ; for the differentiae are predicates of the species. i44 b
Moreover, the differentiae will be all either species or indi
viduals, if they are animals ; for every animal is either
a species or an individual.

Likewise you must inquire also if the species or any of
the objects that come under it is predicated of the differen-

i44 b TOPICA

tia : for this is impossible, seeing that the differentia is a
term with a wider range than the various species. More
over, if any of the species be predicated of it, the result
will be that the differentia is a species : if, for instance,
man be predicated, the differentia is clearly the human
race. Again, see if the differentia fails to be prior to the

10 species : for the differentia ought to be posterior to the
genus, but prior to the species.

Look and see also if the differentia mentioned belongs
to a different genus, neither contained in nor containing the
genus in question. For the general view is that the same
differentia cannot be used of two non-subaltern genera.

15 Else the result will be that the same species as well will be
in two non-subaltern genera : for each of the differentiae
imports its own genus, e.g. walking and biped import
with them the genus animal . If, then, each of the
genera as well is true of that of which the differentia is
true, 1 it clearly follows that the species must be in two

ao non-subaltern genera. Or perhaps it is not impossible for
the same differentia to be used of two non-subaltern genera,
and we ought to add the words except they both be sub
ordinate members of the same genus . Thus walking
animal and flying animal are non-subaltern genera, and
biped is the differentia of both. The words except they

25 both be subordinate members of the same genus ought
therefore to be added ; for both these are subordinate to
animal . From this possibility, that the same differentia
may be used of two non-subaltern genera, it is clear also that
there is no necessity for the differentia to carry with it the
whole of the genus to which it belongs, but only the one
or the other of its limbs together with the genera that are
higher than this, as biped carries with it either flying

3 o or walking animal .

See, too, if he has rendered existence in something as
the differentia of a thing s essence : for the general view is
that locality cannot differentiate between one essence and
another. Hence, too, people condemn those who divide
animals by means of the terms walking and aquatic , on
1 I44 b 19. Read a comma only, not a full-stop, at t

BOOK VI. 6 H4 b

the ground that walking and aquatic indicate mere
locality. Or possibly in this case the censure is undeserved ;
for aquatic does not mean in anything ; nor does it 35
denote a locality, but a certain quality : for even if the
thing be on the dry land, still it is aquatic : and likewise a
land-animal, even though it be in the water, will still be
a land- and not an aquatic-animal. But all the same, if i45 a
ever the differentia does denote existence in something,
clearly he will have made a bad mistake.

Again, see if he has rendered an affection as the differen
tia : for every affection, if intensified, subverts the essence
of the thing, while the differentia is not of that kind : for
the differentia is generally considered rather to preserve 5
that which it differentiates ; and it is absolutely impossible
for a thing to exist without its own special differentia :
for if there be no walking , there will be no man .
In fact, we may lay down absolutely that a thing cannot
have as its differentia anything in respect of which it is
subject to alteration : for all things of that kind, if intensi
fied, destroy its essence. If, then, a man has rendered ro
any differentia of this kind, he has made a mistake : for
we undergo absolutely no alteration in respect of our
differentiae.

Again, see if he has failed to render the differentia of
a relative term relatively to something else ; for the
differentiae of relative terms are themselves relative, as in
the case also of knowledge. This is classed as speculative, 15
practical, and productive ; and each of these denotes a
relation : for it speculates upon something, and produces
something and does something.

Look and see also if the definer renders each relative
term relatively to its natural purpose : for while in some 20
cases the particular relative term can be used in relation to
its natural purpose only and to nothing else, some can be
used in relation to something else as well. Thus sight can
only be used for seeing, but a strigil can also be used to
dip up water. Still, if any one were to define a strigil as an
instrument for dipping water, he has made a mistake : for
that is not its natural function. The definition of a thing s 35

C46-26 K

i45 a TOPICA

natural function is that for which it would be used by the
prudent man, acting as such, and by the science that deals
specially with that thing .

Or see if, whenever a term happens to be used in a
number of relations, he has failed to introduce it in its
primary relation : e. g. by defining wisdom as the virtue

30 of man or of the soul , rather than of the reasoning
faculty : for wisdom is the virtue primarily of the
reasoning faculty : for it is in virtue of this that both the
man and his soul are said to be wise.

Moreover, if the thing of which the term defined has
been stated to be an affection or disposition, 1 or whatever
it may be, be unable to admit it, the definer has made
a mistake. For every disposition and every affection is

35 formed naturally in that of which it is an affection or dis
position, as knowledge, too, is formed in the soul, being a
disposition of soul. Sometimes, however, people make bad
mistakes in matters of this sort, e. g. all those who say that
i45 b sleep is a failure of sensation , or that perplexity is
a state of equality between contrary reasonings , or that
pain is a violent disruption of parts that are naturally
conjoined . For sleep is not an attribute of sensation,
whereas it ought to be, if it is a failure of sensation. Like-
5 wise, perplexity is not an attribute of opposite reasonings, nor
pain of parts naturally conjoined : for then inanimate things
will be in pain, since pain will be present in them. Similar
in character, too, is the definition of health , say, as a
balance of hot and cold elements : for then health will be
necessarily exhibited by the hot and cold elements : for a

10 balance of anything is an attribute inherent in those things
of which it is the balance, so that health would be an attribute
of them. Moreover, people who define in this way put effect
for cause, or cause for effect. For the disruption of parts
naturally conjoined is not pain, but only a cause of pain :
nor again is a failure of sensation sleep, but the one is the

15 cause of the other : for either we go to sleep 2 because sen
sation fails, or sensation fails because we go to sleep. Like
wise also an equality between contrary reasonings would be
1 I45 a 34. Read r) Sia&o-is. 2 I45 b 16. Read \nr

BOOK VI. 6 i45 b

generally considered to be a cause of perplexity : for it is
when we reflect on both sides of a question and find every
thing alike to be in keeping with either course that we are
perplexed which of the two we are to do. a

Moreover, with regard to all periods of time look and see
whether there be any discrepancy between the differentia and
the thing defined : e. g. supposing the immortal to be de
fined as a living thing immune at present from destruction .
For a living thing that is immune at present from destruc
tion will be immortal at present . Possibly, indeed, in this
case this result does not follow, owing to the ambiguity of
the words immune at present from destruction : for it
may mean either that the thing has not been destroyed at 25
present, or that it cannot be destroyed at present, or that
at present it is such that it never can be destroyed. When
ever, then, we say that a living thing is at present immune
from destruction, we mean that it is at present a living
thing of such a kind as never to be destroyed : and this is
equivalent to saying that it is immortal, so that it is not
meant that it is immortal only at present. Still, if ever it 3
does happen that what has been rendered according to the
definition belongs in the present only or past, whereas what
is meant by the word does not so belong, then the two
could not be the same. So, then, this commonplace rule
ought to be followed, as we have said.

7 You should look and see also whether the term being
defined is applied in consideration of something other
than the definition rendered. Suppose (e. g.) a definition of 35
justice as the ability to distribute what is equal . This
would not be right, for just describes rather the man who
chooses, than the man who is able, to distribute what is
equal : so that justice could not be an ability to distribute 146*
what is equal: for then also the most just man would be
the man with the most ability to distribute what is equal.

Moreover, see if the thing admits of degrees, whereas
what is rendered according to the definition does not, or,
vice versa, what is rendered according to the definition 5
admits of degrees while the thing does not. For either

K 2

6 a TOPICA

both must admit them or else neither, if indeed what is
rendered according to the definition is the same as the
thing. Moreover, see if, while both of them admit of
degrees, they yet do not both become greater together:
e. g. suppose sexual love to be the desire for intercourse :
for he who is more intensely in love has not a more intense
desire for intercourse, so that both do not become intensified
at once : they certainly should, however, had they been the
same thing.

Moreover, suppose two things to be before you, see
if the term to be defined applies more particularly to
the one to which the content of the definition is less
15 applicable. Take, for instance, the definition of fire as
the body that consists of the most rarefied particles .
For fire denotes flame rather than light, but flame l is less
the body that consists of the most rarefied particles than is
light : whereas both ought to be more applicable to the
same thing, if they had been the same. Again, see if the
one expression applies alike to both the objects before you,
20 while the other does not apply to both alike, but more
particularly to one of them.

Moreover, see if he renders the definition relative to two
things taken separately : thus, the beautiful is what is
pleasant to the eyes or to the ears 2 : or the real is what
is capable of being acted upon or of acting . For then the
same thing will be both beautiful and not beautiful, and
likewise will be both real and not real. For pleasant to
35 the ears will be the same as beautiful , so that not
pleasant to the ears will be the same as not beautiful :
for of identical things the opposites, too, are identical, and
the opposite of beautiful is not beautiful , while of
pleasant to the ears the opposite is not pleasant to the
ears : clearly, then, not pleasant to the ears is the same
thing as not beautiful . If, therefore, something be pleasant
30 to the eyes but not to the ears, it will be both beautiful and
not beautiful. In like manner we shall show also that the
same thing is both real and unreal.

Moreover, of both genera and differentiae and all the

1 146 17. Read 17 <Xo. 2 Cf. PI. Hipp. Mai. 297 E, 299 C.

BOOK VI. 7 146*

other terms rendered in definitions you should frame defini
tions in lieu of the terms, and then see if there be any 35
discrepancy between them.

8 If the term defined be relative, either in itself or in respect
of its genus, see whether the definition fails to mention that
to which the term, either in itself or in respect of its genus, i46 b
is relative, e. g. if he has defined knowledge as an
incontrovertible conception or wishing as painless
conation . For of everything relative the essence is rela
tive to something else, seeing that the being of every relative
term is identical with being in a certain relation to some
thing. He ought, therefore, to have said that knowledge is 5
conception of a knovvable and that wishing is conation
for a good . Likewise, also, if he has defined grammar
as knowledge of letters : whereas in the definition there
ought to be rendered either the thing to which the term
itself is relative, or that, whatever it is, to which its genus
is relative. Or see if a relative term has been described not
in relation to its end, the end in anything being whatever 10
is best in it or gives its purpose to the rest. Certainly it is
what is best or final that should be stated, e. g. that desire
is not for the pleasant but for pleasure : for this is our
purpose in choosing what is pleasant as well.

Look and see also if that in relation to which he has
rendered the term be a process or an activity : for nothing
of that kind is an end, for the completion of the activity or 15
process is the end rather than the process or activity itself.
Or perhaps this rule is not true in all cases, for almost
everybody prefers the present experience of pleasure to its
cessation, so that they would count the activity as the end
rather than its completion.

Again see in some cases if he has failed to distinguish 20
the quantity or quality or place or other differentiae of an
object; e.g. the quality and quantity of the honour the
striving for which makes a man ambitious : for all men
strive for honour, so that it is not enough to define the
ambitious man as him who strives for honour, but the
aforesaid differentiae must be added. Likewise, also, in

TOPICA

25 defining the covetous man the quantity of money he aims
at, or in the case of the incontinent man the quality of the
pleasures, should be stated. For it is not the man who
gives way to any sort of pleasure whatever who is called
incontinent, but only he who gives way to a certain kind of
pleasure. Or again, people sometimes define night as a
shadow on the earth , or an earthquake as a movement
of the earth , or a cloud as condensation of the air , or
a wind as a movement of the air ; whereas they ought to

30 specify as well quantity, quality, place, 1 and cause. Like
wise, also, in other cases of the kind : for by omitting any
differentiae whatever he fails to state the essence of the
term. One should always attack deficiency. For a move
ment of the earth does not constitute an earthquake, nor
a movement of the air a wind, irrespective of its manner

35 and the amount involved.

Moreover, in the case of conations, and in any other cases
where it applies, see if the word apparent is left out,
*47 a e. g. wishing is a conation after the good , or desire is
a conation after the pleasant instead of saying the
apparently good , or pleasant . For often those who
exhibit the conation do not perceive what is good or
pleasant, so that their aim need not be really good
or pleasant, but only apparently so. They ought, there-
5 fore, to have rendered the definition also accordingly. On
the other hand, any one who maintains the existence of
Ideas ought to be brought face to face with his Ideas, even
though he does render the word in question : for there can
be no Idea of anything merely apparent : the general view
is that an Idea is always spoken of in relation to an Idea :
thus absolute desire is for the absolutely pleasant, and
absolute wishing is for the absolutely good ; they therefore
cannot be for an apparently good or an apparently pleasant :

10 for the existence of an absolutely-apparently-good or
pleasant would be an absurdity.

Moreover, if the definition be of the state of anything, 9
look at what is in the state, while if it be of what is in the
Read KO.\ irov after KO.\ iroiov.

BOOK VI. 9 H7 a

state, look at the state : and likewise also in other cases
of the kind. Thus if the pleasant be identical with the
beneficial, then, too, the man who is pleased is benefited. 15
Speaking generally, in definitions of this sort it happens
that what the definer defines is in a sense more than one
thing : for in defining knowledge, a man in a sense defines
ignorance as well, and likewise also what has knowledge
and what lacks it, and what it is to know and to be
ignorant. For if the first be made clear, the others become 20
in a certain sense clear as well. We have, then, to be on
our guard in all such cases against discrepancy, using the
elementary principles drawn from consideration of contraries
and of co-ordinates.

Moreover, in the case of relative terms, see if the species
is rendered as relative to a species of that to which the
genus is rendered as relative, e. g. supposing belief to be
relative to some object of belief, see whether a particular 25
belief is made relative to some particular object of belief: 1
and, if a multiple be relative to a fraction, see whether a
particular multiple be made relative to a particular fraction.
For if it be not so rendered, clearly a mistake has been
made.

See, also, if the opposite of the term has the opposite
definition, whether (e.g.) the definition of half is the op- 30
posite of that of double : for if double is that which
exceeds another by an equal amount to that other , half
is that which is exceeded by an amount equal to itself .
In the same way, too, with contraries. For to the contrary
term will apply the definition that is contrary in some one
of the ways in which contraries are conjoined. Thus (e. g.)
if useful = productive of good , injurious = productive
of evil or destructive of good , for one or the other of 35
these is bound to be contrary to the term originally used. H7 b
Suppose, then, neither of these things to be the contrary of
the term originally used, then clearly neither of the defini
tions rendered later could be the definition of the contrary
of the term originally defined : and therefore the definition
originally rendered of the original term has not been rightly
1 147*25- Read npus TO T\ vT

H7 b TOPICA

rendered either. Seeing, moreover, that of contraries, the
5 one is sometimes a word formed to denote the privation of
the other, as (e. g.) inequality is generally held to be the
privation of equality (for unequal merely describes things
that are not equal ), it is therefore clear that l that contrary
whose form denotes the privation must of necessity be
defined through the other ; whereas the other cannot then
be defined through the one whose form denotes the priva
tion ; for else we should find that each is being interpreted

10 by the other. We must in the case of contrary terms keep
an eye on this mistake, e. g. supposing any one were to
define equality as the contrary of inequality : for then he
is defining it through the term which denotes privation
of it. Moreover, a man who so defines is bound to use in
his definition the very term he is defining ; and this becomes
clear, if for the word we substitute its definition. For to say

T 5 inequality is the same as to say privation of equality .
Therefore equality so defined will be the contrary of the
privation of equality , so that he would have used the very
word to be defined. Suppose, however, that neither of the
contraries be so formed as to denote privation, but yet the
definition of it be rendered in a manner like the above,
e. g. suppose good to be defined as the contrary of evil ,
then, since it is clear that evil too 2 will be the contrary
of good (for the definition of things that are contrary in

ao this way must be rendered in a like manner), 3 the result
again is that he uses the very term being defined : for
good is inherent in the definition of evil . If, then, good
be the contrary of evil, and evil be nothing other than the
contrary of good , then good will be the contrary of
the contrary of good . Clearly, then, he has used the very

25 word to be defined.

Moreover, see if in rendering a term formed to denote
privation, he has failed to render the term of which it is the
privation, e. g. the state, or contrary, or whatever it may be

1 I47 b 6. Read &q\ov oZv on.

2 I47 b * 9- Read dijXov yap on KCU KOKOV.

3 I47 b 20. For aTrodoTfos. wore read aTroSoreoy tort. The sentence
ra>v yap ovrms . . . anodortns fcrri is parenthetic, and may be enclosed in
brackets.

BOOK VI. 9 i 4 7 b

whose privation it is : also if he has omitted to add either
any term at all in which the privation is naturally formed,
or else that in which it is naturally formed primarily,
e. g. whether in defining ignorance as a privation he has 30
failed to say that it is the privation of knowledge ; or has
failed to add in what it is naturally formed, or, though he
has added this, has failed to render the thing in which it is
primarily formed, placing it (e. g.) in man or in the soul ,
and not in the reasoning faculty : for if in any of these
respects he fails, he has made a mistake. Likewise, also, if
he has failed to say that blindness is the privation of sight
in an eye : for a proper rendering of its essence must state 35
both of what it is the privation and what it is that is deprived. 148**

Examine further whether he has defined by the ex
pression a privation a term that is not used to denote
a privation : thus a mistake of this sort also would be
generally thought to be incurred in the case of error by 5
any one who is not using it as a merely negative term.
For what is generally thought to be in error is not that
which has no knowledge, but rather that which has been
deceived, and for this reason we do not talk of inanimate
things or of children as erring . Error , then, is not used
to denote a mere privation of knowledge.

10 Moreover, see whether the like inflexions in the definition
apply to the like l inflexions of the term ; e. g. if beneficial 10
means productive of health , does beneficially mean pro
ductively of health and a benefactor a producer of
health ?

Look too and see whether the definition given will apply
to the Idea as well. For in some cases it will not do so ;
e.g. in the Platonic definition where he adds the word 15
mortal in his definitions of living creatures : for the Idea
(e. g. the absolute Man) is not mortal, so that the definition
will not fit the Idea. So always wherever the words capable
of acting on or capable of being acted upon are added,
the definition and the Idea are absolutely bound to be
discrepant : for those who assert the existence of Ideas ao
1 148* 10. Read ei r! TU>V 6poiav.

i48 a TOPICA

hold that they are incapable of being acted upon, or of
motion. In dealing with these people even arguments of
this kind are useful.

Further, see if he has rendered a single common definition
of terms that are used ambiguously. For terms whose defini
tion corresponding to their common name is one and the

35 same, are synonymo^ls ; if, then, the definition applies in a
like manner to the whole range of the ambiguous term, it is
not true of any one of the objects described by the term.
This is, moreover, what happens to Dionysius definition of
life when stated as a movement of a creature sustained
by nutriment, congenitally present with it : for this is found
in plants as much as in animals, whereas life is generally

30 understood to mean not one kind of thing only, but to be
one thing in animals and another in plants. It is possible
to hold the view that life is a synonymous term and is
always used to describe one thing only, and therefore to
render the definition in this way on purpose: or it may
quite well happen that a man may see the ambiguous
character of the word, and wish to render the definition of

35 the one sense only, and yet fail to see that he has rendered
a definition common to both senses instead of one peculiar
to the sense he intends. In either case, whichever course
he pursues, he is equally at fault. Since ambiguous terms
sometimes pass unobserved, it is best in questioning to treat
i48 b such terms as though they were synonymous (for the defini
tion of the one sense will not apply to the other, so that the
answerer will be generally thought not to have defined it
correctly, for to a synonymous term the definition should
apply in its full range), whereas in answering you should
yourself distinguish between the senses. Further, as some
5 answerers call ambiguous what is really synonymous, when
ever the definition rendered fails to apply universally, and,
vice versa, call synonymous what is really ambiguous
supposing their definition applies to both senses of the term,
one should secure a preliminary admission on such points,
or else prove beforehand that so-and-so is ambiguous or
synonymous, as the case may be : for people are more ready
to agree when they do not foresee what the consequence

BOOK VI. 10 i48

will be. If, however, no admission has been made, and the 10
man asserts that what is really synonymous is ambiguous
because the definition he has rendered will not apply to the
second sense as well, see if the definition of this second
meaning applies also to the other meanings : for if so, this
meaning must clearly be synonymous with those others.
Otherwise, there will be more than one definition of those
other meanings, for there are applicable to them two distinct 15
definitions in explanation of the term, viz. the one previously
rendered and also the later one. Again, if any one were to
define a term used in several senses, and, finding that his
definition does not apply to them all, were to contend not
that the term is ambiguous, but that even the term does not
properly apply to all those senses, just because his definition
will not do so either, then one may retort to such a man
that though in some things one must not use the language 30
of the people, yet in a question of terminology one is bound
to employ the received and traditional usage and not to
upset matters of that sort.

II Suppose now that a definition has been rendered of some
complex term, take away the definition of one of the
elements in the complex, and see if also the rest of the 25
definition defines the rest of it : if not, it is clear that neither
does the whole definition define the whole complex. Suppose,
e. g., that some one has defined a finite straight line as the
limit of a finite plane, such that its centre is in a line with
its extremes ; if now the definition of a finite line be the
limit of a finite plane , the rest (viz. such that its centre 3
is in a line with its extremes ) ought to be a definition of
straight . But an infinite straight line has neither centre
nor extremes and yet is straight, so that this remainder
does not define the remainder of the term.

Moreover, if the term defined be a compound notion, see
if the definition rendered be equimembral with the term
defined. A definition is said to be equimembral with the
term defined when the number of the elements compounded 35
in the latter is the same as the number of nouns and verbs
in the definition. For the exchange in such cases is bound

i48 b TOPICA

to be merely one of term for term, 1 in the case of some if
I49 a not of all, seeing that there are no more terms used now
than formerly ; whereas in a definition terms ought to be
rendered by phrases, if possible in every case, or if not, in
the majority. For at that rate, simple objects too could
be defined by merely calling them by a different name,
e. g. cloak instead of doublet .

5 The mistake is even worse, if actually a less well known
term be substituted, e. g. pellucid mortal for white man :
for it is no definition, and moreover is less intelligible when
put in that form.

Look and see also whether, in the exchange of words,
the sense fails still to be the same. Take, for instance,
the explanation of speculative knowledge as speculative

10 conception : for conception is not the same as knowledge
as it certainly ought to be if the whole is to be the
same too : for though the word speculative is common to
both expressions, yet the remainder is different.

Moreover, see if in replacing one of the terms by something

15 else he has exchanged the genus and not the differentia, as
in the example just given : for speculative is a less familiar
term than knowledge ; for the one is the genus and the other
the differentia, and the genus is always the most familiar term
of all ; so that it is not this, but the differentia, that ought
to have been changed, seeing that it is the less familiar.

so It might be held that this criticism is ridiculous : because
there is no reason why the most familiar term should not
describe the differentia, and not the genus ; in which case,
clearly, the term to be altered would also be that denoting
the genus and not the differentia. If, however, a man is
substituting for a term not merely another term but a

25 phrase, clearly it is of the differentia rather than of the

genus that a definition should be rendered, seeing that

the object of rendering the definition is to make the subject

familiar ; for the differentia is less familiar than the genus.

2 If he has rendered the definition of the differentia, see

1 148^36. Read ai<Ta>i> TOJI> oj/o/ittTcoj .

2 149*29. Bekker follows the older editions in marking this as the
beginning of ch. 12.

BOOK VI. ii i49 a

whether the definition rendered is common to it and some- 3
thing else as well : e. g. whenever he says that an odd
number is a number with a middle , further definition is
required of how it has a middle : for the word number
is common to both expressions, and it is the word odd
for which the phrase has been substituted. Now both a line
and a body have a middle, yet they are not odd ; so that
this could not be a definition of odd . If, on the other 35
hand, the phrase with a middle be used in several senses,
the sense here intended requires to be defined. So that
this will either discredit the definition or prove that it is no
definition at all.

12 Again, see if the term of which he renders the definition
is a reality, whereas what is contained in the definition is
not. e. g. Suppose white to be defined as colour mingled i49 b
with fire : for what is bodiless cannot be mingled with body,
so that colour mingled with fire could not exist, whereas
white does exist.

Moreover, those who in the case of relative terms do
not distinguish to what the object is related, but have
described it only so as to include it among too large a 5
number of things, are wrong either wholly or in part ; e. g.
suppose some one to have defined medicine as a science
of Reality . For if medicine be not a science of any
thing that is real, the definition is clearly altogether false ;
while if it be a science of some real thing, but not of an
other, it is partly false ; for it ought to hold of all reality,
if it is said to be of Reality essentially and not accidentally ;
as is the case with other relative terms : for every object of 10
knowledge is a term relative to knowledge : likewise, also,
with other relative terms, inasmuch as all such are con
vertible. Moreover, if the right way to render account of
a thing be to render it as it is not in itself but accidentally,
then each and every relative term would be used in relation 15
not to one thing but to a number of things. For there is
no reason why the same thing should not be both real and
white and good, so that it would be a correct rendering to
render the object in relation to any one whatsoever of these,

i49 b TOPICA

if to render what it is accidentally be a correct way to
render it. It is, moreover, impossible that a definition of
this sort should be peculiar to the term rendered : for not

20 only medicine, but the majority of the other sciences too,
have for their object some real thing, so that each will be
a science of reality. Clearly, then, such a definition does
not define any science at all ; for a definition ought to be
peculiar to its own term, not general.

Sometimes, again, people define not the thing but only

35 the thing in a good or perfect condition. Such is the defini
tion of a rhetorician as one who can always see what will
persuade in the given circumstances, and omit nothing ;
or of a thief, as one who pilfers in secret : for clearly, if
they each do this, then the one will be a good rhetorician, and
the other a good thief: whereas it is not the actual pilfering

30 in secret, but the wish to do it, that constitutes the thief.
. Again, see if he has rendered what is desirable for its own
sake as desirable for what it produces or does, or as in any
way desirable because of something else, e. g. by saying that
justice is what preserves the laws or that wisdom is what
produces happiness ; for what produces or preserves some
thing else is one of the things desirable for something else.

35 It might be said that it is possible for what is desirable in
itself to be desirable for something else as well: but still to
define what is desirable in itself in such a way is none the
less wrong : for the essence contains par excellence what is
best in anything, and it is better for a thing to be desirable
in itself than to be desirable for something else, so that this
is rather what the definition too ought to have indicated.

i5Q a See also whether in defining anything a man has defined 13
it as an A and B , or as a product of A and B or as an
A + B . If he defines it as A and B , the definition will
be true of both and yet of neither of them ; suppose, e. g.,
justice to be defined as temperance and courage . For
5 if of two persons each has one of the two only, both and
yet neither will be just : for both together have justice, and
yet each singly fails to have it. Even if the situation here
described does not so far appear very absurd because of the

BOOK VI. 13 150

occurrence of this kind of thing in other cases also (for it is
quite possible for two men to have a mina between them,
though neither of them has it by himself), yet at least that
they should have contrary attributes surely seems quite 10
absurd ; and yet this will follow if the one be temperate
and yet a coward, and the other, though brave, be a profli
gate ; for then both will exhibit both justice and injustice :
for if justice be temperance and bravery, then injustice will
be cowardice and profligacy. In general, too, all the ways 15
of showing that the whole is not the same as the sum of its
parts are useful in meeting the type just described ; for
a man who defines in this way seems to assert that the
parts are the same as the whole. The arguments are par
ticularly appropriate in cases where the process of putting
the parts together is obvious, as in a house and other things
of that sort : for there, clearly, you may have the parts and 20
yet not have the whole, so that parts and whole cannot be
the same.

If, however, he has said that the term being defined is
not A and B but the product of A and B , look and see
in the first place if A and B cannot in the nature of things
have a single product : for some things are so related to
one another that nothing can come of them, e. g. a line and 25
a number. Moreover, see if the term that has been defined
is in the nature of things found primarily in some single
subject, whereas the things which he has said produce it
are not found primarily in any single subject, but each in
a separate one. If so, clearly that term could not be the
product of these things : for the whole is bound to be in
the same things wherein its parts are, so that the whole will
then be found primarily not in one subject only, but in a 30
number of them. If, on the other hand, both parts and
whole are found primarily in some single subject, see if that
medium is not the same, but one thing in the case of the
whole and another in that of the parts. Again, see whether
the parts perish together with the whole : for it ought to
happen, vice versa, that the whole perishes when the parts
perish ; when the whole perishes, there is no necessity that 35
the parts should perish too. Or again, see if the whole be

i5Q a TOPICA

good or evil, and the parts neither, or, vice versa, if the
parts be good or evil and the whole neither. For it is
impossible either for a neutral thing to produce something
I 5 b good or bad, or for things good or bad to produce a neutral
thing. Or again, see if the one thing is more distinctly
good than the other is evil, and yet the product be no more
good than evil, e. g. suppose shamelessness be defined as
the product of courage and false opinion : here the good-
5 ness of courage exceeds the evil of false opinion ; accordingly
the product of these ought to have corresponded to this
excess, and to be either good without qualification, or at
least more good than evil. Or it may be that this does not
necessarily follow, unless each be in itself good or bad ; for
many things that are productive are not good in themselves,
but only in combination ; or, per contra^ they are good taken

10 singly, and bad or neutral in combination. What has just
been said is most clearly illustrated in the case of things
that make for health or sickness; for some drugs are such
that each taken alone is good, but if they are both adminis
tered in a mixture, bad.

Again, see whether the whole, as produced from a better

15 and worse, fails to be worse than the better and better than
the worse element. This again, however, need not necessarily
be the case, unless the elements compounded be in them
selves good ; if they are not, the whole may very well not
be good, as in the cases just instanced.

Moreover, see if the whole be synonymous with one of
the elements : for it ought not to be, any more than in the

20 case of syllables : for the syllable is not synonymous with
any of the letters of which it is made up.

Moreover, see if he has failed to state the manner of their
composition : for the mere mention of its elements is not
enough to make the thing intelligible. For the essence of
any compound thing is not merely that it is a product of
so-and-so, but that it is a product of them compounded in

25 such and such a way, just as in the case of a house : for
here the materials do not make a house irrespective of the
way they are put together.

If a man has defined an object as A+ B , the first thing

BOOK VI. 13 i5o b

to be said is that A + B means the same either as A and B ,
or as the product of A and B . For honey + water means
either the honey and the water, or the drink made of honey
and water . If, then, he admits that A + B is the same as 30
either of these two things, the same criticisms will apply as
have already been given for meeting each of them. Moreover,
distinguish between the different senses in which one thing
may be said to be + another, and see if there is none of
them in which A could be said to exist + B . Thus e. g.
supposing the expression to mean that they exist either in 35
some identical thing capable of containing them (as e. g.
justice and courage are found in the soul), or else in the
same place or in the same time, and if this be in no way
true of the A and B in question, clearly the definition
rendered could not hold of anything, as there is no possible
way in which A can exist + B . If, however, among the 151*
various senses above distinguished, it be true that A and B
are each found in the same time as the other, look and see
if possibly the two are not used in the same relation. Thus
e. g. suppose courage to have been defined as daring with
right reasoning : here it is possible that the person exhibits
daring in robbery, and right reasoning in regard to the 5
means of health : but he may have the former quality + the
latter at the same time, and not as yet be courageous !
Moreover, even though both be used in the same relation
as well, e.g. in relation to medical treatment (for a man may
exhibit both daring and right reasoning in respect of medical
treatment), still, none the less, not even this combination of
the one + the other makes him courageous . For the two
must not relate to any casual object that is the same, any I0
more than each to a different object ; rather, they must
relate to the function of courage, e. g. meeting the perils of
war, or whatever is more properly speaking its function
than this.

Some definitions rendered in this form fail to come under
the aforesaid division at all, e.g. a definition of anger as 15
pain with a consciousness of being slighted . For what
this means to say is that it is because of a consciousness of
this sort that the pain occurs ; but to occur because of

645-26 L

i5i a TOPICA

a thing is not the same as to occur +a thing in any of its
aforesaid senses.

ao Again, if he have described the whole compounded as 14
the composition of these things (e. g. a living creature as
a composition of soul and body ), first of all see whether he
has omitted to state the kind of composition, as (e. g.) in
a definition of flesh or bone as the composition of fire,
earth, and air . For it is not enough to say it is a com
position, but you should also go on to define the kind of

25 composition : for these things do not form flesh irrespective
of the manner of their composition, but when compounded
in one way they form flesh, when in another, bone. It
appears, moreover, that neither of the aforesaid substances
is the same as a composition at all : for a composition
always has a decomposition as its contrary, whereas neither
of the aforesaid has any contrary. Moreover, if it is equally
probable that every compound is a composition or else that

30 none is, and every kind of living creature, though a com
pound, is never a composition, then no other compound
could be a composition either.

Again, if in the nature of a thing two contraries are
equally liable to occur, and the thing has been defined
through the one, clearly it has not been defined ; else there
will be more than one definition of the same thing ; for how

35 is it any more a definition to define it through this one than

through the other, seeing that both alike are naturally liable

i5i b to occur in it ? Such is the definition of the soul, if defined

as a substance capable of receiving knowledge : for it has

a like capacity for receiving ignorance.

Also, even when one cannot attack the definition as a
whole for lack of acquaintance with the whole, one should
5 attack some part of it, if one knows that part and sees it to
be incorrectly rendered : for if the part be demolished, so
too is the whole definition. Where, again, a definition is
obscure, one should first of all correct and reshape it in
order to make some part of it clear and get a handle for
attack, and then proceed to examine it. For the answerer

10 is bound either to accept the sense as taken by the questioner,

BOOK VI. 14 i5i b

or else himself to explain clearly whatever it is that his
definition means. Moreover, just as in the assemblies the
ordinary practice is to move an emendation of the existing
law and, if the emendation is better, they repeal the existing
law, so one ought to do in the case of definitions as well :
one ought oneself to propose a second definition : for if it is 15
seen to be better, and more indicative of the object defined,
clearly the definition already laid down will have been
demolished, on the principle that there cannot be more
than one definition of the same thing.

In combating definitions it is always one of the chief
elementary principles to take by oneself a happy shot at
a definition of the object before one, or to adopt some
correctly expressed definition. For one is bound, with the 20
model (as it were) before one s eyes, to discern both any
shortcoming in any features that the definition ought to
have, and also any superfluous addition, so that one is
better supplied with lines of attack.

As to definitions, then, let so much suffice.

L 2

BOOK VII

i5i b WHETHER two things are the same or different , in i
the most literal of the meanings ascribed to sameness
(and we said l that the same applies in the most literal
3 o sense to what is numerically one), may be examined in the
light of their inflexions and coordinates and opposites.
For if justice be the same as courage, then too the just man
is the same as the brave man, and justly is the same as
bravely . Likewise, too, in the case of their opposites:
for if two things be the same, their opposites also will
35 be the same, in any of the recognized forms of opposition.
For it is the same thing to take the opposite of the one or
that of the other, seeing that they are the same. Again it
may be examined in the light of those things which tend to

i52 a produce or to destroy the things in question, of their forma
tion and destruction, and in general of any thing that is
related in like manner to each. For where things are
absolutely the same, their formations and destructions also
are the same, and so are the things that tend to produce or
to destroy them.

5 Look and see also, in a case where one of two things
is said to be something or other in a superlative degree, it
the other of these alleged identical things can also be
described by a superlative in the same respect. Thus
Xenocrates argues that the happy life and the good life are
the same, seeing that of all forms of life the good life is the
most desirable and so also is the happy life : for the most
desirable and the greatest apply but to one thing. 2
10 Likewise also in other cases of the kind. Each, however,
of the two things termed greatest or most desirable
must be numerically one : otherwise no proof will have been
given that they are the same ; for it does not follow
because Peloponnesians and Spartans are the bravest of the

1 I03 a 23. * Fr. 82 Heinze.

BOOK VII. i 152

Greeks, that Peloponnesians are the same as Spartans,
seeing that Peloponnesian is not any one person nor yet 15
Spartan ; it only follows that the one must be included
under the other as Spartans are under Peloponnesians :
for otherwise, if the one class be not included under the
other, each will be better than the other. For then the
Peloponnesians are bound to be better than the Spartans, 20
seeing that the one class is not included under the other ;
for they are better than anybody else. Likewise also the
Spartans must perforce be better than the Peloponnesians ;
for they too are better than anybody else ; each then is better
than the other ! Clearly therefore what is styled best 25
and greatest must be a single thing, if it is to be proved
to be the same as another. This also is why Xenocrates
fails to prove his case : for the happy life is not numerically
single, nor yet the good life, so that it does not follow that,
because they are both the most desirable, they are therefore
the same, but only that the one falls under the other. 30

Again, look and see if, supposing the one to be the same
as something, the other also is the same as it : for if they
be not both the same as the same thing, clearly neither are
they the same as one another.

Moreover, examine them in the light of their accidents or
of the things of which they are accidents : for any accident
belonging to the one must belong also to the other, and if the 35
one belong to anything as an accident, so must the other
also. If in any of these respects there is a discrepancy,
clearly they are not the same.

See further whether, instead of both being found in one
class of predicates, the one signifies a quality and the other
a quantity or relation. Again, see if the genus of each be
not the same, the one being good and the other * evil , i5 a
or the one being virtue and the other knowledge : or
see if, though the genus is the same, the differentiae pre
dicted of either be not the same, the one (e.g.) being
distinguished as a speculative science, the other as a
practical science. Likewise also in other cases. 5

Moreover, from the point of view of degrees , see if
the one admits an increase of degree but not the other,

2 b TOPICA

or if though both admit it, they do not admit it at the
same time; just as it is not the case that a man desires inter
course more intensely, the more intensely he is in love,
so that love and the desire for intercourse are not the
same.

10 Moreover, examine them by means of an addition, and
see whether the addition of each to the same thing fails to
make the same whole ; or if the subtraction of the same
thing from each leaves a different remainder. Suppose
(e.g.) that he has declared double a half to be the same
as a multiple of a half: then, subtracting the words
a half from each, the remainders ought to have signified

J5 the same thing: but they do not; for double and a
multiple of do not signify the same thing.

Inquire also not only if some impossible consequence
results directly from the statement made, that A and B are
the same, but also whether it is possible for a supposition
to bring it about ; as happens to those who assert that

ao empty is the same as full of air : for clearly if the air be
exhausted, the vessel will not be less but more empty,
though it will no longer be full of air. So that by a
supposition, which may be true or may be false (it makes
no difference which), the one character is annulled and not
the other, showing that they are not the same.

25 Speaking generally, one ought to be on the look-out for
any discrepancy anywhere in any sort of predicate of each
term, and in the things of which they are predicated. For
all that is predicated of the one should be predicated also
of the other, and of whatever the one is a predicate, the
other should be a predicate of it as well.

30 Moreover, as sameness is a term used in many senses,
see whether things that are the same in one way are the
same also in a different way. For there is either no neces
sity or even no possibility that things that are the same
specifically or generically should be numerically the same,
and it is with the question whether they are or are not the
same in that sense that we are concerned.

Moreover, see whether the one can exist without the

35 other ; for, if so, they could not be the same.

BOOK VII. 2 i52 b

2 Such is the number of the commonplace rules that relate
to sameness . It is clear from what has been said that all
the destructive commonplaces relating to sameness are
useful also in questions of definition, as was said before : :
for if what is signified by the term and by the expression

be not the same, clearly the expression rendered could not 153*
be a definition. None of the constructive commonplaces,
on the other hand, helps in the matter of definition ; for it
is not enough to show the sameness of content between the
expression and the term, in order to establish that the
former is a definition, but a definition must have also all the
other characters already announced. 2 5

3 This then is the way, and these the arguments, whereby
the attempt to demolish a definition should always be made.
If, on the other hand, we desire to establish one, the first
thing to observe is that few if any who engage in discussion
arrive at a definition by reasoning : they always assume
something of v the kind as their starting point, both in 10
geometry and in arithmetic and the other studies of that
kind. In the second place, to say accurately what a defini
tion is, and how it should be given, belongs to another
inquiry. 3 At present it concerns us only so far as is
required for our present purpose, and accordingly we need
only make the bare statement that to reason to a thing s
definition and essence is quite possible. For if a definition 15
is an expression signifying the essence of the thing and the
predicates contained therein ought also to be the only ones
which are predicated of the thing in the category of essence ;
and genera and differentiae are so predicated in that cate
gory : it is obvious that if one were to get an admission
that so and so are the only 4 attributes predicated in that
category, the expression containing so and so would of 20
necessity be a definition ; for it is impossible that anything
else should be a definition, seeing that there is not anything
else predicated of the thing in the category of essence.

That a definition may thus be reached by a process of

1 io2 a ii. 2 139" 27- 35.

3 An. Post. ii. 3-13. 4 153*19. Read /xoVn.

i53 a TOPICA

reasoning is obvious. The means whereby it should be
established have been more precisely defined elsewhere, 1

25 but for the purposes of the inquiry now before us the same
commonplace rules serve. For we have to examine into
the contraries and other opposites of the thing, surveying
the expressions used both as wholes and in detail : for if the
opposite definition defines that opposite term, the definition
given must of necessity be that of the term before us.

30 Seeing, however, that contraries may be conjoined in more
than one way, we have to select from those contraries
the one whose contrary definition seems most obvious.
The expressions, then, have to be examined each as a
whole in the way we have said, and also in detail as follows.
First of all, see that the genus rendered is correctly rendered ;
for if the contrary thing be found in the contrary genus to
that stated in the definition, and the thing before you is

35 not in that same genus, then it would clearly be in the
contrary genus : for contraries must of necessity be either in
the same genus or in contrary genera. The differentiae,
too, that are predicated of contraries we expect to be con
trary, e. g. those of white and black, for the one tends to
i53 b pierce the vision, while the other tends to compress it. So
that if contrary differentiae to those in the definition are
predicated of the contrary term, then those rendered in the
definition would be predicated of the term before us. Seeing,
then, that both the genus and the differentiae have been
rightly rendered, clearly the expression given must be the
right definition. It might be replied that there is no necessity
5 why contrary differentiae should be predicated of contraries,
unless the contraries be found within the same genus :
of things whose genera are themselves contraries it may
very well be that the same differentia is used of both, e. g.
of justice and injustice ; for the one is a virtue and the
other a vice of the soul : of the soul , therefore, is the

10 differentia in both cases, seeing that the body as well has

its virtue and vice. But this much at least is true, that the

differentiae of contraries are either contrary or else the same.

If, then, the contrary differentia to that given be predicated

1 An. Post. ii. 13.

BOOK VII. 3 i53 b

of the contrary term and not of the one in hand, clearly the
differentia stated must be predicated of the latter. Speak
ing generally, seeing that the definition consists of genus
and differentiae, if the definition of the contrary term be 15
apparent, the definition of the term before you will be
apparent also : for since its contrary is found either in the
same genus or in the contrary genus, and likewise also the
differentiae predicated of opposites are either contrary to,
or the same as, each other, clearly of the term before you
there will be predicated either the same genus as of its
contrary, while, of its differentiae, either all are contrary to 2
those of its contrary, or at least some of them are so while
the rest remain the same ; or, vice versa, the differentiae
will be the same and the genera contrary ; or both genera
and differentiae will be contrary. And that is all ; for that
both should be the same is not possible ; else contraries
will have the same definition.

Moreover, look at it from the point of view of its inflexions 25
and coordinates. For genera and definitions are bound to
correspond in either case. Thus if forgetfulness be the loss
of knowledge, to forget is to lose knowledge, and to have
forgotten is to have lost knowledge. If, then, any one what
ever of these is agreed to, the others must of necessity be 30
agreed to as well. Likewise, also, if destruction is the de
composition of the thing s essence, then to be destroyed is to
have its essence decomposed, and destructively means in
such a way as to decompose its essence ; if again destruc
tive means apt to decompose something s essence , then
also destruction means the decomposition of its essence .
Likewise also with the rest : get an admission of any one
of them whatever, and all the rest are admitted too. 35

Moreover, look at it from the point of view of things
that stand in relations that are like each other. For if
healthy means productive of health , vigorous too will
mean productive of vigour , and useful will mean pro
ductive of good . For each of these things is related in
like manner to its own peculiar end, so that if one of them i54 a
is defined as productive of that end, this will also be the
definition of each of the rest as well.

i54 a TOPICA

Moreover, look at it from the point of view of greater and
like degrees, in all the ways in which it is possible to estab-
5 lish a result by comparing two and two together. Thus if
A defines a better than B defines (3, and B is a definition
of /?, so too is A of a. Further, if A s claim to define a is
like B s to define /?, and B defines (3, then A too defines a.
This examination from the point of view of greater degrees
is of no use when a single definition is compared with two
10 things, or two definitions with one thing ; for there cannot
possibly be one definition of two things or two of the same
thing.

The most handy of all the commonplace arguments are 4
those just mentioned and those from coordinates and
inflexions, and these therefore are those which it is most
important to master and to have ready to hand : for they
are the most useful on the greatest number of occasions.

15 Of the rest, too, the most important are those of most
general application : for these are the most effective, e. g.
that you should examine the individual cases, 1 and then
look to see in the case of their various species whether the
definition applies. For the species is synonymous with its
individuals. This sort of inquiry is of service against those
who assume the existence of Ideas, as has been said before. 2

ao Moreover see if a man has used a term metaphorically, or
predicated it of itself as though it were something different.
So too if any other of the commonplace rules is of general
application and effective, it should be employed.

That it is more difficult to establish than to overthrow 5
a definition, is obvious from considerations presently to be
35 urged. For to see for oneself, and to secure from those
whom one is questioning, an admission of premisses of this
sort is no simple matter, e. g. that of the elements of the
definition rendered the one is genus and the other differentia,
and that only the genus and differentiae are predicated in
the category of essence. Yet without these premisses it
is impossible to reason to a definition ; for if any other

1 154*17. Read ra KaP e*aora. 8 148*14

BOOK VII. 5 i54 a

things as well are predicated of the thing in the category of 3
essence, there is no telling whether the formula stated or
some other one is its definition, for a definition is an
expression indicating the essence of a thing. The point is
clear also from the following: It is easier to draw one
conclusion than many. Now in demolishing a definition it
is sufficient to argue against one point only l (for if we have
overthrown any single point whatsoever, we shall have
demolished the definition) ; whereas in establishing a defini- 35
tion, o ne is bound to bring people to the view that every
thing contained in the definition is attributable. Moreover,
in establishing a case, the reasoning brought forward must
be universal : for the definition put forward must be predi
cated of everything of which the term is predicated, and i54 b
must moreover be convertible, if the definition rendered is
to be peculiar to the subject. In overthrowing a view, on
the other hand, there is no longer any necessity to show
one s point universally : for it is enough to show that the
formula is untrue of any one of the things embraced under
the term. Further, even supposing it should be necessary 5
to overthrow something by a universal proposition, not even
so is there any need to prove the converse of the proposition
in the process of overthrowing the definition. For merely
to show that the definition fails to be predicated of every
one of the things of which 2 the term is predicated, is enough
to overthrow it universally : and there is no need to prove
the converse of this in order to show that 3 the term is
predicated of things of which the expression is not predi- i
cated. Moreover, even if it applies to everything embraced
under the term, but not to it alone, the definition is thereby
demolished.

The case stands likewise in regard to the property and
genus of a term also. For in both cases it is easier to
overthrow than to establish. As regards the property this *5
is clear from what has been said : for as a rule the property
is rendered in a complex phrase, so that to overthrow it, it
is only necessary to demolish one of the terms used, whereas

1 154*34. Read irpbs iv. 2 I54 b 7- Read Kara

8 iS4 b 9. Delete comma after 8iai.

i54 b TOPICA

to establish it it is necessary to reason to them all. Then,
too, nearly all the other rules that apply to the definition
will apply also to the property of a thing. For in estab-

20 lishing a property one has to show that it is true of every
thing included under the term in question, whereas to
overthrow one it is enough to show in a single case only
that it fails to belong : further, even if it belongs to every
thing falling under the term, but not to that only, it is over
thrown in this case as well, as was explained in the case of
the definition. 1 In regard to the genus, it is clear that you
are bound to establish it in one way only, viz. by showing

25 that it belongs in every case, while of overthrowing it there
are two ways : for if it has been shown that it belongs either
never or not in a certain case, the original statement has
been demolished. Moreover, in establishing a genus it is
not enough to show that it belongs, but also that it belongs
as genus has to be shown ; whereas in overthrowing it, it is
enough to show its failure to belong either in some particular

30 case or 2 in every case. It appears, in fact, as though, just
as in other things to destroy is easier than to create, so in
these matters too to overthrow is easier than to establish.

In the case of an accidental attribute the universal
proposition is easier to overthrow than to establish ; for to

35 establish it, one has to show that it belongs in every case,
whereas to overthrow it, it is enough to show that it does
not belong in one single case. The particular proposition
is, on the contrary, easier to establish than to overthrow :
for to establish it, it is enough to show that it belongs in
i55 a a particular instance, whereas to overthrow it, it has to be
shown that it never belongs at all.

It is clear also that the easiest thing of all is to overthrow

a definition. For on account of the number of statements

involved we are presented in the definition with the greatest

number of points for attack, and the more plentiful the

5 material, the quicker an argument comes : for there is more

likelihood of a mistake occurring in a large than in a small

number of things. Moreover, the other rules too may be

used as means for attacking a definition : for if either the

1 1. 10. 2 I54 b 29. Delete ^ at end of line.

BOOK VII. 5 i55 a

formula be not peculiar, or the genus rendered be the
wrong one, or something included in the formula fail to
belong, the definition is thereby demolished. On the other
hand, against the others we cannot bring all of the argu- 10
ments drawn from definitions, nor yet of the rest : for only
those relating to accidental attributes apply generally to
all the aforesaid kinds of attribute. For while each of
the aforesaid kinds of attribute must belong to the thing
in question, yet the genus may very well not belong as
a property without as yet being thereby demolished. Like
wise also the property need not belong as a genus, nor the 15
accident as a genus or property, so long as they do belong.
So that it is impossible to use one set as a basis of attack
upon the other except in the case of definition. Clearly,
then, it is the easiest of all things to demolish a definition,
while to establish one is the hardest. For there one both
has to establish all those other points by reasoning (i. e. that
the attributes stated belong, and that the genus rendered is 20
the true genus, and that the formula is peculiar to the
term), and moreover, besides this, that the formula indicates
the essence of the thing ; and this has to be done correctly.

Of the rest, the property is most nearly of this kind : for
it is easier to demolish, because as a rule it contains several
terms ; while it is the hardest to establish, both because of 25
the number of things that people must be brought to accept,
and, besides this, because it belongs to its subject alone and
is predicated convertibly with its subject.

The easiest thing of all to establish is an accidental
predicate : for in other cases one has to show not only that
the predicate belongs, but also that it belongs in such and
such a particular way : whereas in the case of the accident 30
it is enough to show merely that it belongs. On the other
hand, an accidental predicate is the hardest thing to over
throw, because it affords the least material : for in stating
an accident a man does not add how the predicate belongs ;
and accordingly, while in other cases it is possible to
demolish what is said in two ways, by showing either that
the predicate does not belong, or that it does not belong in
the particular way stated, in the case of an accidental predi- 35

i55 a TOPICA

cate the only way to demolish it is to show that it does not
belong at all.

The commonplace arguments through which we shall be
well supplied with lines of argument with regard to our
several problems have now been enumerated at about
sufficient length.

i55 b

BOOK VIII

NEXT there fall to be discussed the problems of arrange
ment and method in putting questions. Any one who
intends to frame questions must, first of all, select the
ground from which he should make his attack ; secondly, 5
he must frame them and arrange them one by one to him
self; thirdly and lastly, he must proceed actually to put
them to the other party. Now so far as the selection of his
ground is concerned the problem is one alike for the philo
sopher and the dialectician ; but how to go on to arrange
his points and frame his questions concerns the dialectician
only : for in every problem of that kind a reference to 10
another party is involved. Not so with the philosopher,
and the man who is investigating by himself: the premisses
of his reasoning, although true and familiar, may be refused
by the answerer because they lie too near the original state
ment and so he foresees what will follow if he grants them :
but for this the philosopher does not care. Nay, he may
possibly be even anxious to secure axioms as familiar and
as near to the question in hand as possible : for these are 15
the bases on which scientific reasonings are built up.

The sources from which one s commonplace arguments
should be drawn have already been described : l we have
now to discuss the arrangement and formation of questions
and first to distinguish the premisses, other than the necessary
premisses, which have to be adopted. By necessary pre
misses are meant those through which the actual reasoning 3 o
is constructed. Those which are secured other than these
are of four kinds ; they serve either inductively to secure the
universal premiss being granted, or to lend weight to the
argument, or to conceal the conclusion, or to render the argu
ment more clear. Beside these there is no other premiss
which need be secured : these are the ones whereby you 25

1 Top. ii-vii.

i55 b TOPICA

should try to multiply and formulate your questions. Those
which are used to conceal the conclusion serve a contro
versial purpose only; but inasmuch as an undertaking ot
this sort is always conducted against another person, we
are obliged to employ them as well.

The necessary premisses through which the reasoning is

30 effected, ought not to be propounded directly in so many
words. 1 Rather one should soar as far aloof from them as
possible. Thus if one desires to secure an admission that
the knowledge of contraries is one, one should ask him to
admit it not of contraries, but of opposites : for, if he grants
this, one will then argue that the knowledge of contraries is
also the same, seeing that contraries are opposites ; if he
does not, one should secure the admission by induction, by
formulating a proposition to that effect in the case of some

35 particular pair of contraries. For one must secure the
necessary premisses either by reasoning or by induction, or
else partly by one and partly by the other, although any
propositions which are too obvious to be denied may be
formulated in so many words. This is because the coming
i56 a conclusion is less easily discerned at the greater distance
and in the process of induction, while at the same time,
even if one cannot reach the required premisses in this way,
it is still open to one to formulate them in so many words.
The premisses, other than these, that were mentioned above, 2
must be secured with a view to the latter. The way to
employ them respectively is as follows : Induction should
5 proceed from individual cases to the universal and from the
known to the unknown ; and the objects of perception are
better known, to most people if not invariably. Conceal
ment of one s plan is obtained by securing through pro-
syllogisms the premisses through which the proof of the
original proposition is going to be constructed and as
many of them as possible. This is likely to be effected
by making syllogisms to prove not only the necessary

10 premisses but also some of those which are required to
establish them. Moreover, do not state the conclusions of

1 I 55 b 3- Read evdvs avras nporaTfov, with A, B, and Waitz.

2 I55 b 20-28.

BOOK VIII. i 156*

these premisses but draw them later one after another ; for
this is likely to keep the answerer at the greatest possible
distance from the original proposition. Speaking generally,
a man who desires to get information by a concealed method
should so put his questions that when he has put his whole
argument and has stated the conclusion, people still ask 15
Well, but why is that ? This result will be secured best
of all by the method above described : for if one states only
the final conclusion, it is unclear how it comes about ; for
the answerer does not foresee on what grounds it is based,
because the previous syllogisms have not been made articu
late to him : while the final syllogism, showing the con- ao
elusion, is likely to be kept least articulate if we lay down
not the secured propositions on which it is based, but only
the grounds on which we reason to them.

It is a useful rule, too, not to secure the admissions claimed
as the bases of the syllogisms in their proper order, but
alternately those that conduce to one conclusion and those
that conduce to another ; for, if those which go together 35
are set side by side, the conclusion that will result from
them is more obvious in advance.

One should also, wherever possible, secure the universal
premiss by a definition relating not to the precise terms
themselves but to their co-ordinates ; for people deceive
themselves, whenever the definition is taken in regard to
a co-ordinate, into thinking that they are not making the 30
admission universally. An instance would be, supposing
one had to secure the admission that the angry man desires
vengeance on account of an apparent slight, and were to
secure this, that anger is a desire for vengeance on account
of an apparent slight : for, clearly, if this were secured, we
should have universally what we intend. If, on the other
hand, people formulate propositions relating to the actual
terms themselves, they often find that the answerer refuses 35
to grant them because on the actual term itself he is readier
with his objection, e. g. that the angry man does not desire
vengeance, because we become angry with our parents, but
we do not desire vengeance on them. Very likely the
objection is not valid ; for upon some people it is vengeance

645-16 M

i56 b TOPICA

i56 b enough to cause them pain and make them sorry ; but still
it gives a certain plausibility and air of reasonableness to
the denial of the proposition. In the case, however, of the
definition of anger it is not so easy to find an objection.

Moreover, formulate your proposition as though you did
so not for its own sake, but in order to get at something
5 else : for people are shy of granting what an opponent s case
really requires. Speaking generally, a questioner should
leave it as far as possible doubtful whether he wishes to
secure an admission of his proposition or of its opposite : for
if it be uncertain what their opponent s argument requires,
people are more ready to say what they themselves think.

10 Moreover, try to secure admissions by means of likeness :
for such admissions are plausible, and the universal involved
is less patent ; e. g. make the other person admit that as
knowledge and ignorance of contraries is the same, so too
perception of contraries is the same ; or vice versa, that since
the perception is the same, so is the knowledge also. This
argument resembles induction, but is not the same thing;

15 for in induction it is the universal whose admission is secured
from the particulars, whereas in arguments from likeness,
what is secured is not the universal under which all the like
cases fall.

It is a good rule also, occasionally to bring an objection
against oneself: for answerers are put off their guard against

ao those who appear to be arguing impartially. It is useful
too, to add that So and so is generally held or commonly
said ; for people are shy of upsetting the received opinion
unless they have some positive objection to urge : and at
the same time they are cautious about upsetting such things
because they themselves too find them useful. Moreover,
do not be insistent, even though you really require the point :

25 for insistence always arouses the more opposition. Further,
formulate your premiss as though it were a mere illustration :
for people admit the more readily a proposition made to
serve some other purpose, and not required on its own
account. Moreover, do not formulate the very proposition
you need to secure, but rather something from which that
necessarily follows : for people are more willing to admit

BOOK VIII. i 156*

the latter, because it is not so clear from this what the result
will be, and if the one has been secured, the other has been
secured also. Again, one should put last the point which 3
one most wishes to have conceded ; for people are specially
inclined to deny the first questions put to them, because
most people in asking questions put first the points which
they are most eager to secure. On the other hand, in dealing
with some people propositions of this sort should be put
forward first : for ill-tempered men admit most readily what
comes first, unless the conclusion that will result actually 35
stares them in the face, while at the close of an argument
they show their ill-temper. Likewise also with those who
consider themselves smart at answering : for when they
have admitted most of what you want they finally talk
clap-trap to the effect that the conclusion does not follow
from their admissions : yet they say Yes readily, confident
in their own character, and imagining that they cannot suffer
any reverse. Moreover, it is well to expand the argument I57 a
and insert things that it does not require at all, as do those
who draw false geometrical figures : for in the multitude of
details the whereabouts of the fallacy is obscured. For
this reason also a questioner sometimes evades observation
as he adds in a corner what, if he formulated it by itself, 5
would not be granted.

For concealment, then, the rules which should be followed
are the above. Ornament is attained by induction and
distinction of things closely akin. What sort of process
induction is is obvious : as for distinction, an instance of the
kind of thing meant is the distinction of one form of
knowledge as better than another by being either more
accurate, or concerned with better objects ; or the distinction ro
of sciences into speculative, practical, and productive. For
everything of this kind lends additional ornament to the
argument, though there is no necessity to say them, so far
as the conclusion goes.

For clearness, examples and comparisons should be
adduced, and let the illustrations be relevant and drawn from 15
things that we know, as in Homer and not as in Choerilus ;
for then the proposition is likely to become clearer.

M 2,

i57 a TOPICA

In dialectics, syllogism should be employed in reasoning 2

20 against dialecticians rather than against the crowd: induction,
on the other hand, is most useful against the crowd. This
point 1 has been treated previously as well. 2 In induction,
it is possible in some cases to ask the question in its universal
form, but in others this is not easy, because there is no
established general term that covers all the resemblances :
in this case, when people need to secure the universal, they
use the phrase in all cases of this sort . But it is one of

25 the very hardest things to distinguish which of the things
adduced are of this sort , and which are not : and in this
connexion people often throw dust in each others eyes in
their discussion, the one party asserting the likeness of things
that are not alike, and the other disputing the likeness of
things that are. One ought, therefore, to try oneself to coin

3 o a word to cover all things of the given sort, so as to leave
no opportunity either to the answerer to dispute, and say
that the thing advanced does not answer to a like description,
or to the questioner to suggest falsely that it does answer to
a like description, for many things appear to answer to like
descriptions that do not really do so.

If one has made an induction on the strength of several
cases and yet the answerer refuses to grant the universal
35 proposition, then it is fair to demand his objection. But
until one has oneself stated in what cases it is so, it is not
fair to demand that he shall say in what cases it is not so :
for one should make the induction first, and then demand
the objection. One ought, moreover, to claim that the
objections should not be brought in reference to the actual
subject of the proposition, unless that subject happen to be
the one and only thing of the kind, as for instance two is
i57 b the one prime number among the even numbers : for,
unless he can say that this subject is unique of its kind, the
objector ought to make his objection in regard to some
other. People sometimes object to a universal proposition,
and bring their objection not in regard to the thing itself,
but in regard to some homonym of it : thus they argue

5 that a man can very well have a colour or a foot or a hand
1 I57 a 2i. Read iWp TGVTOV, with B, C, and Waitz. 2 io5 a 16.

BOOK VIII. 2 i57 b

other than his own, for a painter may have a colour that is
not his own, and a cook may have a foot that is not his
own. To meet them, therefore, you should draw the dis
tinction before putting your question in such cases : for so
long as the ambiguity remains undetected, so long will the
objection to the proposition be deemed valid. If, however,
he checks the series of questions by an objection in regard
not to some homonym, but to the actual thing asserted,
the questioner should withdraw the point objected to, and TO
form the remainder into a universal proposition, until he
secures what he requires ; e. g. in the case of forgetfulness
and having forgotten : for people refuse to admit that the
man who has lost his knowledge of a thing has forgotten it,
because if the thing alters, he has lost knowledge of it, but
he has not forgotten it. Accordingly the thing to do is to
withdraw the part objected to, and assert the remainder, 15
e. g. that if a person have lost knowledge of a thing while
it still remains, he then has forgotten it. One should
similarly treat those who object to the statement that the
greater the good, the greater the evil that is its opposite :
for they allege that health, which is a less good thing than
vigour, has a greater evil as its opposite : for disease is a
greater evil than debility. In this case too, therefore, we 20
have to withdraw the point objected to ; for when it has
been withdrawn, the man is more likely to admit the pro
position, e. g. that the greater good has the greater evil
as its opposite, unless the one good involves the other
as well , as vigour involves health. This should be done
not only when he formulates an objection, but also if,
without so doing, he refuses to admit the point because 25
he foresees something of the kind : for if the point ob
jected to be withdrawn, he will be forced to admit the
proposition because he cannot foresee in the rest of it
any case where it does not hold true : if he refuse to
admit it, then when asked for an objection he certainly will
be unable to render one. Propositions that are partly false
and partly true are of this type : for in the case of these it 30
is possible by withdrawing a part to leave the rest true.
If, however, you formulate the proposition on the strength

i57 b TOPICA

of many cases and he has no objection to bring, you may
claim that he shall admit it : for a premiss is valid in
dialectics which thus holds in several instances and to
which no objection is forthcoming.

Whenever it is possible to reason to the same conclusion
35 either through or without a reductio per impossibile, if one
is demonstrating and not arguing dialectically it makes no
difference which method of reasoning be adopted, but in
argument with another reasoning per impossibile should be
avoided. For where one has reasoned without the reductio
per impossibile, no dispute can arise ; if, on the other hand,
one does reason to an impossible conclusion, unless its
158* falsehood is too plainly manifest, people deny that it is
impossible, so that the questioners do not get what they
want.

One should put forward all propositions that hold true of

several cases, and to which either no objection whatever

appears or at least not any on the surface : for when people

5 cannot see any case in which it is not so, they admit it for

true.

The conclusion should not be put in the form of a
question ; if it be, and the man shakes his head, it looks as
if the reasoning had failed. For often, even if it be not put
as a question but advanced as a consequence, people deny
10 it, and then those who do not see that it follows * upon the
previous admissions do not realize that those who deny it
have been refuted : when, then, the one man merely asks it
as a question without even saying that it so follows, and
the other denies it, it looks altogether as if the reasoning
had failed.

Not every universal question can form a dialectical pro-
is position as ordinarily understood, e.g. What is man? or
How many meanings has " the good " ? For a dialectical
premiss must be of a form to which it is possible to reply
Yes or No , whereas to the aforesaid it is not possible.
For this reason questions of this kind are not dialectical
unless the questioner himself draws distinctions or divisions
before expressing them, e. g. Good means this, or this,
1 158*11. Read ori o-u/i/ScuWi with Waitz.

BOOK VIII. 2 158

does it not? For questions of this sort are easily answered 20
by a Yes or a No. Hence one should endeavour to
formulate propositions of this kind in this form. It is at the
same time also perhaps fair to ask the other man how many
meanings of the good there are, whenever you have your
self distinguished and formulated them, and he will not
admit them at all.

Any one who keeps on asking one thing for a long time 25
is a bad inquirer. For if he does so though the person
questioned keeps on answering the questions, clearly he
asks a large number of questions, or else asks the same
question a large number of times : in the one case he
merely babbles, in the other he fails to reason : for reason
ing always consists of a small number of premisses. If, on
the other hand, he does it because the person questioned
does not answer the questions, he is at fault in not taking
him to task or breaking off the discussion. 30

3 There are certain hypotheses upon which it is at once
difficult to bring, and easy to stand up to, an argument.
Such (e. g.) are those things which stand first and those
which stand last in the order of nature. For the former
require definition, while the latter have to be arrived at
through many steps if one wishes to secure a continuous
proof from first principles, or else all discussion about them 35
wears the air of mere sophistry : for to prove anything is
impossible unless one begins with the appropriate principles,
and connects inference with inference till the last are reached.
Now to define first principles is just what answerers do not
care to do, nor do they pay any attention if the questioner
makes a definition : and yet until it is clear what it is that
is proposed, it is not easy to discuss it. This sort of thing
happens particularly in the case of the first principles : for
while the other propositions are shown through these, these
cannot be shown through anything else : we [are obliged to
understand every item of that sort by a definition.

The inferences, too, that lie too close to the first principle 5
are hard to treat in argument : for it is not possible to bring
many arguments in regard to them, because of the small

TOPICA

number of those steps, between the conclusion and the
principle, whereby the succeeding propositions have to be
shown. The hardest, however, of all definitions to treat in
argument are those that employ terms about which, in the

10 first place, it is uncertain whether they are used in one
sense or several, and, further, whether they are used literally
or metaphorically by the definer. For because of their
obscurity, it is impossible to argue upon such terms ; and
because of the impossibility of saying whether this obscurity
is due to their being used metaphorically, it is impossible

15 to refute them.

In general, it is safe to suppose that, whenever any
problem proves intractable, it either needs definition or else
bears either several senses, or a metaphorical sense, or it is
not far removed from the first principles ; or else the reason
is that we have yet to discover in the first place just this

20 in which of the aforesaid directions the source of our
difficulty lies : when we have made this clear, then ob
viously our business must be either to define or to distin
guish, or to supply the intermediate premisses : for it is
through these that the final conclusions are shown.

It often happens that a difficulty is found in discussing

25 or arguing a given position because the definition has not
been correctly rendered : e. g. Has one thing one contrary
or many? : here when the term contraries has been
properly defined, it is easy to bring people to see whether
it is possible for the same thing to have several contraries
or not : in the same way also with other terms requiring
definition. It appears also in mathematics that the difficulty

30 in using a figure is sometimes due to a defect in definition ;
e. g. in proving that the line which cuts the plane parallel
to one side 1 divides similarly both the line which it cuts
and the area ; whereas if the definition be given, the fact
asserted becomes immediately clear: for the areas have
the same fraction subtracted from them as have the sides :

35 and this is the definition of the same ratio . The
most primary of the elementary principles are without
exception very easy to show, if the definitions involved,
1 St. of a parallelogram,

BOOK VIII. 3 i 5 8 b

e. g. the nature of a line or of a circle, be laid down ; only
the arguments that can be brought in regard to each of
them are not many, because there are not many intermediate
steps. If, on the other hand, the definition of the starting-
points be not laid down, to show them is difficult and may
even prove quite impossible. The case of the significance 159*
of verbal expressions is like that of these mathematical
conceptions.

One may be sure then, whenever a position is hard to
discuss, that one or other of the aforesaid things has
happened to it. Whenever, on the other hand, it is a
harder task to argue to the point claimed, i. e. the premiss, 5
than to the resulting position, a doubt may arise whether
such claims should be admitted or not : for if a man is
going to refuse to admit it and claim that you shall argue
to it as well, he will be giving the signal for a harder
undertaking than was originally proposed : if, on the other
hand, he grants it, he will be giving the original thesis
credence on the strength of what is less credible than
itself. If, then, it is essential not to enhance the difficulty
of the problem, he had better grant it ; if, on the other 10
hand, it be essential to reason through premisses that are
better assured, he had better refuse. In other words, in
serious inquiry he ought not to grant it, unless he be more
sure about it than about the conclusion ; whereas in a dia
lectical exercise he may do so if he is merely satisfied of its
truth. Clearly, then, the circumstances under which such
admissions should be claimed are different for a mere
questioner and for a serious teacher.

4 As to the formulation, then, and arrangement of one s 15
questions, about enough has been said.

With regard to the giving of answers, we must first
define what is the business of a good answerer, as of a good
questioner. The business of the questioner is so to develop
the argument as to make the answerer utter the most
extravagant paradoxes that necessarily follow because of ao
his position : while that of the answerer is to make it
appear that it is not he who is responsible for the absurdity

i59 a TOPICA

or paradox, but only his position : for one may, perhaps,
distinguish between the mistake of taking up a wrong
position to start with, and that of not maintaining it
properly, when once taken up.

35 Inasmuch as no rules are laid down for those who argue 5
for the sake of training and of examination: and the aim
of those engaged in teaching or learning is quite different
from that of those engaged in a competition ; as is the
latter from that of those who discuss things together in
the spirit of inquiry : for a learner should always state what
he thinks : for no one is even trying to teach him what is

3 false ; whereas in a competition the business of the questioner
is to appear by all means to produce an effect upon the other,
while that of the answerer is to appear unaffected by him ;
on the other hand, in an assembly of disputants discussing
in the spirit not of a competition but of an examination
and inquiry, there are as yet no articulate rules about what

35 the answerer should aim at, and what kind of things he
should and should not grant for the correct or incorrect
defence of his position : l inasmuch, then, as we have no
tradition bequeathed to us by others, let us try to say
something upon the matter for ourselves.

The thesis laid down by the answerer before facing the
questioner s argument is bound of necessity to be one
that is either generally accepted or generally rejected
or else is neither : and moreover is so accepted or re-
I 59 b jected either absolutely or else with a restriction, e. g. by
some given person, by the speaker or by some one else.
The manner, however, of its acceptance or rejection, what
ever it be, makes no difference : for the right way to answer,
i. e. to admit or to refuse to admit what has been asked,
will be the same in either case. If, then, the statement laid
down by the answerer be generally rejected, the conclusion
5 aimed at by the questioner is bound to be one generally
accepted, whereas if the former be generally accepted,
the latter is generally rejected : for the conclusion which

1 159*26-36. Put ov yap . . . rfjv Qioiv in brackets, followed by
a colon.

BOOK VIII. 5 i59 b

the questioner tries to draw is always the opposite of the
statement laid down. If, on the other hand, what is laid
down is generally neither rejected nor accepted, the conclu
sion will be of the same type as well. Now since a man
who reasons correctly demonstrates his proposed conclusion
from premisses that are more generally accepted, and more
familiar, it is clear that (i) where the view laid down by him
is one that generally is absolutely rejected, the answerer 10
ought not to grant either what is thus absolutely not
accepted at all, or what is accepted indeed, but accepted
less generally than the questioner s conclusion. For if the
statement laid down by the answerer be generally rejected,
the conclusion aimed at by the questioner will be one that
is generally accepted, so that the premisses secured by the
questioner should all be views generally accepted, and more
generally accepted than his proposed conclusion, if the less 15
familiar is to be inferred through the more familiar. Conse
quently, if any of the questions put to him be not of this
character, the answerer should not grant them. (2) If, on
the other hand, the statement laid down by the answerer be
generally accepted without qualification, clearly the conclu
sion sought by the questioner will be one generally rejected
without qualification. Accordingly, the answerer should admit
all views that are generally accepted and, of those that are
not generally accepted, all that are less generally rejected
than the conclusion sought by the questioner. For then he
will probably be thought to have argued sufficiently well.
(3) Likewise, too, if the statement laid down by the answerer 20
be neither rejected generally nor generally accepted; for then,
too, anything that appears to be true should be granted,
and, of the views not generally accepted, any that are more
generally accepted than the questioner s conclusion ; for in
that case the result will be that the arguments will be more
generally accepted. If, then, the view laid down by the
answerer be one that is generally accepted or rejected
without qualification, then the views that are accepted
absolutely must be taken as the standard of comparison : 25
whereas if the view laid down be one that is not generally
accepted or rejected, but only by the answerer, then the

i59 b TOPICA

standard whereby the latter must judge what is generally
accepted or not, and must grant or refuse to grant the point
asked, is himself. 1 If, again, the answerer be defending some
one else s opinion, then clearly it will be the latter s judge
ment to which he must have regard in granting or denying
the various points. This is why those, too, who introduce

30 other s opinions, e. g. that good and evil are the same thing ,
as Heraclitus says, 2 refuse to admit the impossibility of con
traries belonging at the same time to the same thing ; not
because they do not themselves 3 believe this, but because
on Heraclitus principles one has to say so. The same
thing is done also by those who take on the defence of

35 one another s positions ; their aim being to speak as would
the man who stated the position.

It is clear, then, what the aims of the answerer should be, 6
whether the position he lays down be a view generally
accepted without qualification or accepted by some definite
person. Now every question asked is bound to involve
some view that is either generally held or generally rejected
or neither, and is also bound to be either relevant to the
argument or irrelevant : if then it be a view generally
i6o a accepted and irrelevant, the answerer should grant it and
remark that it is the accepted view : if it be a view not
generally accepted and irrelevant, he should grant it but
add a comment that it is not generally accepted, in order
to avoid the appearance of being a simpleton. If it be
relevant and also be generally accepted, he should admit
that it is the view generally accepted but say that it lies too
5 close to the original proposition, and that if it be granted
the problem proposed collapses. If what is claimed by the
questioner be relevant but too generally rejected, the
answerer, while admitting that if it be granted the conclu
sion sought follows, should yet protest that the proposition
is too absurd to be admitted. Suppose, again, it be a view
that is neither rejected generally nor generally accepted,
then, if it be irrelevant to the argument, it may be granted
10 without restriction ; if, however, it be relevant, the answerer
1 I59 b 2y. Read avrov. 2 Frr. 58, icaDiels. 8 I59 b 32. Read avrols.

BOOK VIII. 6 i6o a

should add the comment that, if it be granted, the original
problem collapses. For then the answerer will not be held
to be personally accountable for what happens to him, if he
grants the several points with his eyes open, and also the
questioner will be able to draw his inference, seeing that all
the premisses that are more generally accepted than the
conclusion are granted him. Those who try to draw an
inference from premisses more generally rejected than the 15
conclusion clearly do not reason correctly : hence, when
men ask these things, they ought not to be granted.

7 The questioner should be met in a like manner also in
the case of terms used obscurely, i.e. in several senses.
For the answerer, if he does not understand, is always
permitted to say I do not understand : he is not compelled
to reply Yes or No to a question which may mean ao
different things. Clearly, then, in the first place, if what

is said be not clear, he ought not to hesitate to say that he
does not understand it ; for often people encounter some
difficulty from assenting to questions that are not clearly put.
If he understands the question and yet it covers many senses,
then supposing what it says to be universally true or false, 25
he should give it an unqualified assent or denial : if, on the
other hand, it be partly true and partly false, he should
add a comment that it bears different senses, and also
that in one it is true, in the other false : for if he leave
this distinction till later, it becomes uncertain whether
originally as well he perceived the ambiguity or not.
If he does not foresee the ambiguity, but assents to the
question having in view the one sense of the words, then, 30
if the questioner takes it in the other sense, he should say,
That was not what I had in view when I admitted it ;
I meant the other sense : for if a term or expression covers
more than one thing, it is easy to disagree. If, however,
the question is both clear and simple, he should answer
either Yes or No .

8 A premiss in reasoning always either is one of the con- 35
stituent elements in the reasoning, or else goes to establish

i6o a TOPICA

one of these : (*and you can always tell when it is secured in
order to establish something else by the fact of a number of
similar questions being put : for as a rule people secure their
universal by means either of induction or of likeness) :
accordingly the particular propositions should all be ad-
i6o b mitted, if they are true and generally held. On the other
hand, against the universal one should try to bring some
negative instance ; for to bring the argument to a standstill
without a negative instance, either real or apparent, shows
ill-temper. If, then, a man refuses to grant the universal
when supported 2 by many instances, although he has no
negative instance to show, he obviously shows ill-temper.
5 If, moreover, he cannot even attempt a counter-proof that
it is not true, far more likely is he to be thought ill-tempered
although even counter-proof is not enough : for we often
hear arguments that are contrary to common opinions, whose
solution is yet difficult, e. g. the argument of Zeno 3 that it
is impossible to move or to traverse the stadium ; but still,
this is no reason for omitting to assert the opposites of these
10 views. If, then, a man refuses to admit the proposition
without having either a negative instance or some counter
argument to bring against it, clearly he is ill-tempered : for
ill-temper in argument consists in answering in ways other
than the above, so as to wreck the reasoning.

Before maintaining either a thesis or a definition the 9
answerer should try his hand at attacking it by himself;

15 for clearly his business is to oppose those positions from
which questioners demolish what he has laid down.

He should beware of maintaining a hypothesis that is
generally rejected : and this it may be in two ways : for it
may be one which results in absurd statements, e. g. suppose
any one were to say that everything is in motion or that
nothing is ; and also there are all those which only a bad

so character would choose, and which are implicitly opposed to
men s wishes, e. g. that pleasure is the good, and that to do

1 160*36-7. Begin parenthesis at 8ij\ov . , . , and substitute colon for
bracket after e pwTav. 2 i6o b 3. Read (fraivopevov.

3 i6o b 8. Read xadaTrep TOV Zrjvuvos. Cf. Phys. 233* 21-31, 239 b 9~i4-

BOOK VIII. 9 i6o b

injustice is better than to suffer it. For people then hate
him, supposing him to maintain them not for the sake of
argument but because he really thinks them.

Of all arguments that reason to a false conclusion the
right solution is to demolish the point on which the fallacy
that occurs depends : for the demolition of any random
point l is no solution, even though the point demolished be 25
false. For the argument may contain many falsehoods,
e. g. suppose some one to secure the premisses, He who
sits, writes and Socrates is sitting : for from these it
follows that Socrates is writing . Now we may demolish
the proposition Socrates is sitting , and still be no nearer
a solution of the argument ; it may be true that the point
claimed is false ; but it is not on that that the fallacy of the 30
argument depends : for supposing that any one should
happen to be sitting and not writing, it would be impossible
in such a case to apply the same solution. Accordingly, it
is not this that needs to be demolished, but rather that
He who sits, writes : for he who sits does not always
write. He, then, who has demolished the point on which
the fallacy depends, has given the solution of the argument
completely. Any one who knows that it is on such and
such a point that the argument depends, knows the solution 35
of it, just as in the case of a figure falsely drawn. For it is
not enough to object, even if the point demolished be a
falsehood, but the reason of the fallacy should also be
proved : for then it would be clear whether the man makes
his objection with his eyes open or not.

There are four possible ways of preventing a man from i6i a
working his argument to a conclusion. It can be done either
by demolishing the point on which the falsehood that comes
about depends, or by stating an objection directed against
: the questioner : for often when a solution has not as a matter
; of fact been brought, yet the questioner is rendered thereby
r unable to pursue the argument any farther. Thirdly, one
may object to the questions asked : for it may happen that 5
what the questioner wants does not follow from the ques-
1 i6o b 24. Read 6 before t movv.

i6i a TOPICA

tions he has asked because he has asked them badly, whereas
if something additional be granted the conclusion comes
about. If, then, the questioner be unable to pursue his
argument farther, the objection l would properly be directed
against the questioner ; if he can do so, then it would be
against his questions. The fourth and worst kind of objec-

10 tion is that which is directed to the time allowed for dis
cussion : for some people bring objections of a kind which
would take longer to answer than the length of the discussion
in hand.

There are then, as we said, four ways of making objec
tions : but of them the first alone is a solution : the others

15 are just hindrances and stumbling-blocks to prevent the
conclusions.

Adverse criticism of an argument on its own merits, and n
of it when presented in the form of questions, are two
different things. For often the failure to carry through the
argument correctly in discussion is due to the person ques
tioned, because he will not grant the steps of which a correct
argument might have been made against his position : for it

20 is not in the power of the one side only to effect properly
a result that depends on both alike. Accordingly it some
times becomes necessary to attack the speaker and not his
position, when the answerer lies in wait for the points that
are contrary to the questioner and becomes abusive as well :
when people lose their tempers in this way, their argument
becomes a contest, not a discussion. Moreover, since argu-

25 ments of this kind are held not for the sake of instruction
but for purposes of practice and examination, clearly one
has to reason not only to true conclusions, but also to false
ones, and not always through true premisses, but sometimes
through false as well. For often, when a true proposition is
put forward, the dialectician is compelled to demolish it :
and then false propositions have to be formulated. Some-

30 times also when a false proposition is put forward, it has to
be demolished by means of false propositions : for it is
possible for a given man to believe what is not the fact

1 l6l a g. Read fj

BOOK VIII. ii i6i a

more firmly than the truth. Accordingly, if the argument
be made to depend on something that he holds, it will be
easier to persuade or help him. He, however, who would
rightly convert any one to a different opinion should do so
in a dialectical and not in a contentious manner, just as
a geometrician should reason geometrically, whether his 35
conclusion be false or true : what kind of syllogisms are
dialectical has already been said. 1 The principle that a
man who hinders the common business is a bad partner,
clearly applies to an argument as well ; for in arguments
as well there is a common aim in view, except with mere
contestants, for these cannot both reach the same goal ; for 40
more than one cannot possibly win. It makes no difference i6i b
whether he effects this as answerer or as questioner : for
both he who asks contentious questions is a bad dialectician,
and also he who in answering fails to grant the obvious
answer or to understand the point of the questioner s 5
inquiry. What has been said, then, makes it clear that
adverse criticism is not to be passed in a like strain upon
the argument on its own merits, and upon the questioner :
for it may very well be that the argument is bad, but that
the questioner has argued with the answerer in the best
possible way : for when men lose their tempers, it may
perhaps be impossible to make one s inferences straight
forwardly as one would wish : we have to do as we can. 10

Inasmuch as it is indeterminate when people are claiming
the admission of contrary things, and when they are claiming
what originally they set out to prove for often when they
are talking by themselves they say contrary things, and
admit afterwards what they have previously denied ; for
which reason they often assent, when questioned, to contrary
things and to what originally had to be proved the argu- 15
ment is sure to become vitiated. The responsibility, how
ever, for this rests with the answerer, because while refusing
to grant other points, he does grant points of that kind.
It is, then, clear that adverse criticism is not to be passed
in a like manner upon questioners and upon their argu
ments.

1 100*22.

646-16 N

i6i b TOPICA

In itself an argument is liable to five kinds of adverse
criticism :

20 (i) The first is when neither the proposed conclusion nor
indeed any conclusion at all is drawn from the questions
asked, and when most, if not all, of the premisses on which
the conclusion rests are false or generally rejected, when,
moreover, neither any withdrawals nor additions nor both
together can bring the conclusions about.

25 (a) The second is, supposing the reasoning, though con
structed from the premisses, and in the manner, described
above, were to be irrelevant to the original position.

(3) The third is, supposing certain additions would bring
an inference about but yet these additions were to be
weaker than those that were put as questions, and less
generally held than the conclusion.

(4) Again, supposing certain withdrawals could effect the
30 same : for sometimes people secure more premisses than

are necessary, so that it is not through them that the infer
ence comes about.

(5) Moreover, suppose the premisses be less generally held
and less credible than the conclusion, or if, though true, they
require more trouble to prove than the proposed view.

One must not claim that the reasoning to a proposed view
35 shall in every case equally be a view generally accepted and
convincing : for it is a direct result of the nature of things
that some subjects of inquiry shall be easier and some
harder, so that if a man brings people to accept his point
from opinions that are as generally received as the case
admits, he has argued his case correctly. Clearly, then,
not even the argument itself is open to the same adverse
criticism when taken in relation to the proposed conclusion
and when taken by itself. For there is nothing to prevent
40 the argument being open to reproach in itself, and yet com-
i62 a mendable in relation to the proposed conclusion, or again,
vice versa, being commendable in itself, and yet open to
reproach in relation to the proposed conclusion, whenever
there are many propositions both generally held and also
true whereby it could easily be proved. It is possible also
that an argument, even though brought to a conclusion,

BOOK VIII. ii i62 E

may sometimes be worse than one which is not so con- 5
eluded, whenever the premisses of the former are silly,
while its conclusion is not so ; whereas the latter, though
requiring certain additions, requires only such as are
generally held and true, and moreover does not rest as
an argument on these additions. With those which bring
about a true conclusion by means of false premisses, it is
not fair to find fault : for a false conclusion must of necessity
always be reached from a false premiss, but a true conclusion 10
may sometimes be drawn even from false premisses ; as is
clear from the Analytics. 1

Whenever by the argument stated something is demon
strated, but that something is other than what is wanted and
has no bearing whatever on the conclusion, then no inference
as to the latter 2 can be drawn from it : and if there appears
to be, it will be a sophism, not a proof. A philosopheme 15
is a demonstrative inference : an epichireme is a dialectical
inference : a sophism is a contentious inference : an aporeme
is an inference that reasons dialectically to a contradiction.

If something were to be shown from premisses, both of
which are views generally accepted, but not accepted with 20
like conviction, it may very well be that the conclusion shown
is something held more strongly than either. If, on the other
hand, general opinion be for the one and neither for nor
against the other, or if it be for the one and against the other,
then, if the pro and con be alike in the case of the premisses,
theywill be alike for the conclusion also: if,on the other hand,
the one preponderates, the conclusion too will follow suit.

It is also a fault in reasoning when a man shows some
thing through a long chain of steps, when he might employ 35
fewer steps and those already included in his argument :
suppose him to be showing (e.g.) that one opinion is more
properly so called than another, and suppose him to make
his postulates as follows : x-in-itself is more fully x than
anything else : there genuinely exists an object of opinion
in itself: therefore the objcct-of-opinion-in-itself is more
fully an object of opinion than the particular objects of
opinion . Now a relative term is more fully itself when
1 An. Pr. ii. 2. 2 162* 14. Read mpl Wi/ov.

N 2

i6a a TOPICA

its correlate is more fully itself : and there exists a genuine
30 opinion-in-itself, which will be " opinion " in a more accurate
sense than the particular opinions : and it has been postu
lated both that a genuine opinion-in-itself exists , and that
x-in-itself is more fully x than anything else : therefore
this will be opinion in a more accurate 1 sense . Wherein
lies the viciousness of the reasoning? Simply in that it
conceals the ground on which the argument depends.

35 An argument is clear in one, and that the most ordinary,
sense, if it be so brought to a conclusion as to make no
further questions necessary : in another sense, and this is
the type most usually advanced, when the propositions
i62 b secured are such as compel the conclusion, and the argument
is concluded 2 through premisses that are themselves con
clusions : moreover, it is so also if some step is omitted
that generally is firmly accepted.

An argument is called fallacious in four senses : (i) when
it appears to be brought to a conclusion, and is not really
5 so what is called contentious reasoning : (2) when it
comes to a conclusion but not to the conclusion proposed
which happens principally in the case of reductiones ad
impossibile : (3) when it comes to the proposed conclusion
but not according to the mode of inquiry appropriate to the
case, as happens when a non-medical argument is taken to
be a medical one, or one which is not geometrical for a

10 geometrical argument, or one which is not dialectical for
dialectical, whether the result reached be true or false:
(4) if the conclusion be reached through false premisses :
of this type the conclusion is sometimes false, sometimes
true : for while a false conclusion is always the result of
false premisses, a true conclusion may be drawn even from

15 premisses that are not true, as was said above as well. 3

Fallacy in argument is due to a mistake of the arguer
rather than of the argument : yet it is not always the fault
of the arguer either, but only when he is not aware of it :
for we often accept on its merits in preference to many true

1 l62 a 32. Read aur;; 8da aKpifteo-Tfpa eVriV, with best MSS.

2 l62 b 2. Read a-u/^Trenu/d/iei oy. 3 * IO.

BOOK VIII. 12 i62 b

ones an argument which demolishes some true proposition, 1
if it does so from premisses as far as possible generally ao
accepted. For an argument of that kind does demonstrate
other things that are true: for one of the premisses laid
down ought never to be there at all, and this will then be
demonstrated. If, however, a true conclusion were to be
reached through premisses that are false : and utterly
childish, the argument is worse than many arguments that
lead to a false conclusion, though an argument which
leads to a false conclusion may also be of this type. Clearly
then the first thing to ask in regard to the argument in 35
itself is, Has it a conclusion? ; the second, Is the conclu
sion true or false? ; the third, Of what kind of premisses
does it consist ? : for if the latter, though false, be generally
accepted, the argument is dialectical, whereas if, though
true, they be generally rejected, it is bad : if they be both
false and also entirely contrary to general opinion, clearly
it is bad, either altogether or else in relation to the particular
matter in hand. 3 o

13 Of the ways in which a questioner may beg the original
question and also beg contraries the true account has been
given in the Analytics : 2 but an account on the level of
general opinion must be given now.

People appear to beg their original question in five
ways : the first and most obvious being if any one begs 35
the actual point requiring to be shown : this is easily
detected when put in so many words ; but it is more apt to
escape detection in the case of different terms, or a term
and an expression, that mean the same thing. A second 163*
way occurs whenever any one begs universally something
which he has to demonstrate in a particular case : sup
pose (e. g.) he were trying to prove that the knowledge
of contraries is one and were to claim that the knowledge
of opposites in general is one : for then he is generally
thought to be begging, along with a number of other
things, that which he ought to have shown by itself. A
third way is if any one were to beg in particular cases 5
1 i.e. a reductio ad absurdum. J An. Pr. ii. 16.

i62 a TOPICA

its correlate is more fully itself : and there exists a genuine
30 opinion-in-itself, which will be " opinion " in a more accurate
sense than the particular opinions : and it has been postu
lated both that a genuine opinion-in-itself exists , and that
x-in-itself is more fully x than anything else : therefore
this will be opinion in a more accurate 1 sense . Wherein
lies the viciousness of the reasoning? Simply in that it
conceals the ground on which the argument depends.

35 An argument is clear in one, and that the most ordinary, 12
sense, if it be so brought to a conclusion as to make no
further questions necessary : in another sense, and this is
the type most usually advanced, when the propositions
i62 b secured are such as compel the conclusion, and the argument
is concluded 2 through premisses that are themselves con
clusions : moreover, it is so also if some step is omitted
that generally is firmly accepted.

An argument is called fallacious in four senses : (i) when
it appears to be brought to a conclusion, and is not really
5 so what is called contentious reasoning : (2) when it
comes to a conclusion but not to the conclusion proposed
which happens principally in the case of rcductiones ad
impossibile: (3) when it comes to the proposed conclusion
but not according to the mode of inquiry appropriate to the
case, as happens when a non-medical argument is taken to
be a medical one, or one which is not geometrical for a

10 geometrical argument, or one which is not dialectical for
dialectical, whether the result reached be true or false :
(4) if the conclusion be reached through false premisses :
of this type the conclusion is sometimes false, sometimes
true : for while a false conclusion is always the result of
false premisses, a true conclusion may be drawn even from

15 premisses that are not true, as was said above as well. 3

Fallacy in argument is due to a mistake of the arguer
rather than of the argument : yet it is not always the fault
of the arguer either, but only when he is not aware of it :
for we often accept on its merits in preference to many true

1 l62 a 32. Read avrrj Sda aKpiftfa-repa mV, with best MSS.

2 162 b 2. Read <rvnnfpaiv6fj.et>os. S a IO.

BOOK VIII. 12 i62 b

ones an argument which demolishes some true proposition, 1
if it does so from premisses as far as possible generally 20
accepted. For an argument of that kind does demonstrate
other things that arc true: for one of the premisses laid
down ought never to be there at all, and this will then be
demonstrated. If, however, a true conclusion were to be
reached through premisses that are false : and utterly
childish, the argument is worse than many arguments that
lead to a false conclusion, though an argument which
leads to a false conclusion may also be of this type. Clearly
then the first thing to ask in regard to the argument in 25
itself is, Has it a conclusion ? ; the second, Is the conclu
sion true or false? ; the third, Of what kind of premisses
does it consist ? : for if the latter, though false, be generally
accepted, the argument is dialectical, whereas if, though
true, they be generally rejected, it is bad : if they be both
false and also entirely contrary to general opinion, clearly
it is bad, either altogether or else in relation to the particular
matter in hand. 3 o

13 Of the ways in which a questioner may beg the original
question and also beg contraries the true account has been
given in the Analytics : 2 but an account on the level of
general opinion must be given now.

People appear to beg their original question in five
ways : the first and most obvious being if any one begs 35
the actual point requiring to be shown : this is easily
detected when put in so many words ; but it is more apt to
escape detection in the case of different terms, or a term
and an expression, that mean the same thing. A second 163*
way occurs whenever any one begs universally something
which he has to demonstrate in a particular case : sup
pose (e. g.) he were trying to prove that the knowledge
of contraries is one and were to claim that the knowledge
of opposites in general is one : for then he is generally
thought to be begging, along with a number of other
things, that which he ought to have shown by itself. A
third way is if any one were to beg in particular cases 5
1 i.e. a reductio ad absurdum. J An. Pr. ii. 1 6.

s a TOPICA

what he undertakes to show universally : e. g. if he under
took to show that the knowledge of contraries is always
one, and begged it of certain pairs of contraries: for he
also is generally considered to be begging independently
and by itself what, together with a number of other things,
he ought to have shown. Again, a man begs the question
if he begs his conclusion piecemeal : supposing e. g. that he
had to show that medicine is a science of what leads to

10 health and to disease, and were to claim first the one, then
the other ; or, fifthly, if he were to beg the one or the other
of a pair of statements that necessarily involve one other ;
e. g. if he had to show that the diagonal is incommensur
able with the side, and were to beg that the side is
incommensurable with the diagonal.

The ways in which people assume contraries are equal in
number to those in which they beg their original question.

15 For it would happen, firstly, if any one were to beg an
opposite affirmation and negation ; secondly, if he were to
beg the contrary terms of an antithesis, e. g. that the same
thing is good and evil ; thirdly, suppose any one were to
claim something universally and then proceed to beg its
contradictory in some particular case, e.g. if having secured
that the knowledge of contraries is one, he were to claim
that the knowledge of what makes for health or for disease is

ao different ; or, fourthly, suppose him, after postulating the
latter view, to try to secure universally the contradictory
statement. Again, fifthly, suppose a man begs the contrary
of the conclusion which necessarily comes about through the
premisses laid down ; and this would happen suppose, even
without begging the opposites in so many words, he were
to beg two premisses such that this contradictory statement
that is opposite to the first conclusion will follow from
them. The securing of contraries differs from begging

25 the original question in this way : in the latter case the
mistake lies in regard to the conclusion ; for it is by a
glance at the conclusion that we tell that the original
question has been begged : whereas contrary views lie in the
premisses, viz. in a certain relation which they bear to one
another.

BOOK VIII. 14 i6a a

14 The best way to secure training and practice in arguments
of this kind is in the first place to get into the habit of 3
converting the arguments. For in this way we shall be
better equipped for dealing with the proposition stated, and
after a few attempts we shall know several arguments by
heart. For by conversion of an argument is meant the
taking the reverse of the conclusion together with the
remaining propositions asked and so demolishing one of
those that were conceded : for it follows necessarily that
if the conclusion be untrue, some one of the premisses is 35
demolished, seeing that, given all the premisses, the conclu
sion was bound to follow. Always, in dealing with any
proposition, be on the look-out for a line of argument both
pro and con : and on discovering it at once set about looking i63 b
for the solution of it : for in this way you will soon find
that you have trained yourself at the same time in both
asking questions and answering them. If we cannot find
any one else to argue with, we should argue with ourselves.
Select, moreover, arguments relating to the same thesis 1
and range them side by side : for this produces a plentiful 5
supply of arguments for carrying a point by sheer force,
and in refutation also it is of great service, whenever one is
well stocked with arguments pro and con : for then you
find yourself on your guard against contrary statements to
the one you wish to secure. Moreover, as contributing to
knowledge and to philosophic wisdom the power of discern
ing and holding in one view the results of either of two 10
hypotheses is no mean instrument ; for it then only remains
to make a right choice of one of them. For a task of this
kind a certain natural ability is required : in fact real
natural ability just is the power rightly to choose the true
and shun the false. Men of natural ability can do this ; for 5
by a right liking or disliking for whatever is proposed to
them they rightly select what is best.

It is best to know by heart arguments upon those
questions which are of most frequent occurrence, and par
ticularly in regard to those propositions which are ultimate :
for in discussing these answerers frequently give up in despair.

1 163^4-5. Read eVcXtyoira npos rf}V airfjv dtffiv.

i6 3 b TOPICA

20 Moreover, get a good stock of definitions : and have those
of familiar and primary ideas at your fingers ends : for it is
through these that reasonings are effected. You should try,
moreover, to master the heads under which other arguments
mostly tend to fall. For just as in geometry it is useful to
be practised in the elements, and in arithmetic to have the

35 multiplication table up to ten at one s fingers ends and
indeed it makes a great * difference in one s knowledge of
the multiples of other numbers too likewise also in argu
ments it is a great advantage to be well up in regard to
first principles, and to have a thorough knowledge of
premisses at the tip of one s tongue. For just as in a
person with a trained memory, a memory of things them-

30 selves is immediately caused by the mere mention of their
loci, so these habits too will make a man readier in reason
ing, because he has his premisses classified before his mind s
eye, each under its number. It is better to commit to
memory a premiss of general application than an argument :
for it is difficult to be even moderately ready with a first
principle, or hypothesis.

Moreover, you should get into the habit of turning one

35 argument into several, and conceal your procedure as darkly
as you can : this kind of effect is best produced by keeping
as far as possible away from topics akin to the subject of
the argument. This can be done with arguments that are
i64 a entirely universal, e. g. the statement that there cannot be
one knowledge of more than one thing : for that is the case
with both relative terms and contraries and co-ordinates.

Records of discussions should be made in a universal
form, even though one has argued only some particular
5 case : for this will enable one to turn a single rule into
several. A like rule applies in Rhetoric as well to enthy-
memes. For yourself, however, you should as far as possible
avoid universalizing your reasonings. You should, more
over, always examine arguments to see whether they rest on
principles of general application : for all particular arguments
really reason universally, as well, i. e. a particular demonstra-

10 tion always contains a universal demonstration, because it
is impossible to reason at all without using universals. 2

1 163^25. Read e^eiv, KOI
a Read in 164* II TO>V

BOOK VIII. 14 i6 4

You should display your training in inductive reasoning
against a young man, in deductive against an expert. You
should try, moreover, to secure from those skilled in deduc
tion their premisses, from inductive reasoners their parallel 1 5
cases ; for this is the thing : in which they are respectively
trained. In general, too, from your exercises in argumenta
tion you should try to carry away either a syllogism on
some subject or a refutation or a proposition or an objection,
or whether some one put his question properly or improperly
(whether it was yourself or some one else) and the point
which made it the one or the other. For this is what gives i64
one ability, and the whole object of training is to acquire
ability, especially in regard to propositions and objections.
For it is the skilled propounder and objector who is, speak
ing generally, a dialectician. To formulate a proposition
is to form a number of things into one for the conclusion 5
to which the argument leads must be taken generally, as
a single thing 2 whereas to formulate an objection is to
make one thing into many : for the objector either distin
guishes or demolishes, partly granting, partly denying the
statements proposed.

Do not argue with every one, nor practise upon the man
in the street: for there are some people with whom any
argument is bound to degenerate. For against any one 10
who is ready to try all means in order to seem not to be
beaten, it is indeed fair to try all means of bringing about
one s conclusion : but it is not good form. Wherefore the
best rule is, not lightly to engage with casual acquaintances,
or bad argument is sure to result. For you see how in
practising together people cannot refrain from contentious
argument. *5

It is best also to have ready-made arguments relating to
those questions in which a very small stock will furnish
us with arguments serviceable on a very large number of
occasions. These are those that are universal, and those in
regard to which it is rather difficult to produce points for
ourselves from matters of everyday experience.

1 Read in 1 64* 1 5 tv TOITW.

2 164^5. Read tv o\u>s

DE SOPHISTICIS ELENCHIS

164*

I LET us now discuss sophistic refutations, i.e. what appear 20
to be refutations but are really fallacies instead. We will
begin in the natural order with the first.

That some reasonings are genuine, while others seem to
be so but are not, is evident. This happens with argu
ments, as also elsewhere, through a certain likeness between 25
the genuine and the sham. For physically some people are
in a vigorous condition, while others merely seem to be so by i64 b
blowing and rigging themselves out as the tribesmen do 20
their victims for sacrifice ; and some people are beautiful
thanks to their beauty, while others seem to be so, by dint of
embellishing themselves. So it is, too, with inanimate things;
for of these, too, some are really silver and others gold, while
others are not and merely seem to be such to our sense ; e. g.
things made of litharge and tin seem to be of silver, while
those made of yellow metal look golden. In the same way 25
both reasoning and refutation are sometimes genuine, some
times not, though inexperience may make them appear so :
for inexperienced people obtain only, as it were, a distant
view of these things. For reasoning rests on certain state- 165*
ments such that they involve necessarily the assertion of
something other than what has been stated, through what has
been stated : refutation is reasoning involving the contradic
tory of the given conclusion. Now some of them do not really
achieve this, though they seem to do so for a number of
reasons ; and of these the most prolific and usual domain is
the argument that turns upon names only. It is impossible 5
in a discussion to bring in the actual things discussed : we
use their names as symbols instead of them ; and therefore
we suppose that what follows in the names, follows in the
things as well, just as people who calculate suppose in
regard to their counters. But the two cases (names and 10
things) are not alike. For names are finite and so is the
sum-total of formulae, while things are infinite in number.

i6s a DE SOPHISTICIS ELENCHIS

Inevitably, then, the same formulae, and a single name, have
a number of meanings. Accordingly just as, in counting,
those who are not clever in manipulating their counters are

J 5 taken in by the experts, in the same way in arguments too
those who are not well acquainted with the force of names
misreason both in their own discussions and when they
listen to others. For this reason, then, and for others to be
mentioned later, there exists both reasoning and refutation
that is apparent but not real. Now for some people it is

20 better worth while to seem to be wise, than to be wise with
out seeming to be (for the art of the sophist is the sem
blance of wisdom without the reality, and the sophist is one
who makes money from an apparent but unreal wisdom) ;
for them, then, it is clearly essential also to seem to accom
plish the task of a wise man rather than to accomplish it
without seeming to do so. To reduce it to a single point

25 of contrast it is the business of one who knows a thing,
himself to avoid fallacies in the subjects which he knows
and to be able to show up the man who makes them ; and
of these accomplishments the one depends on the faculty to
render an answer, and the other upon the securing of one.
Those, then, who would be sophists are bound to study the
class of arguments aforesaid : for it is worth their while :

30 for a faculty of this kind will make a man seem to be wise,
and this is the purpose they happen to have in view.

Clearly, then, there exists a class of arguments of this
kind, and it is at this kind of ability that those aim whom
we call sophists. Let us now go on to discuss how many
kinds there are of sophistical arguments, and how many in

35 number are the elements of which this faculty is composed,
and how many branches there happen to be of this inquiry,
and the other factors that contribute to this art.

Of arguments in dialogue form there are four classes : 2

Didactic, Dialectical, Examination-arguments, and Con-

i6s b tentious arguments. Didactic arguments are those that

reason from the principles appropriate to each subject and

not from the opinions held by the answerer (for the learner

should take things on trust) : dialectical arguments are

CHAPTER II 165

those that reason from premisses generally accepted, to the
contradictory of a given thesis : examination-arguments
are those that reason from premisses which are accepted by 5
the answerer and which any one who pretends to possess
knowledge of the subject is bound to know in what
manner, has been defined in another treatise : l contentious
arguments are those that reason or appear to reason to a
conclusion from premisses that appear to be generally
accepted but are not so. The subject, then, of demonstra
tive arguments has been discussed in the Analytics^ while
that of dialectic arguments and examination-arguments has "
been discussed elsewhere : 2 let us now proceed to speak of
the arguments used in competitions and contests.

3 First we must grasp the number of aims entertained by
those who argue as competitors and rivals to the death.
These are five in number, refutation, fallacy, paradox, sole
cism, and fifthly to reduce the opponent in the discussion 15
to babbling i. e. to constrain him to repeat himself a
number of times : or it is to produce the appearance of
each of these things without the reality. For they choose if
possible plainly to refute the other party, or as the second
best to show that he is committing some fallacy, or as a
third best to lead him into paradox, or fourthly to reduce
him to solecism, i. e. to make the answerer, in consequence 20
of the argument, to use an ungrammatical expression ; or,
as a last resort, to make him repeat himself.

4 There are two styles of refutation : for some depend
on the language used, while some are independent of lan
guage. Those ways of producing the false appearance of an 25
argument which depend on language are six in number :
they are ambiguity, amphiboly, combination, division of
words, accent, form of expression. Of this we may assure
ourselves both by induction, and by syllogistic proof based
on this and it may be on other assumptions as well
that this is the number of ways in which we might fail
to mean the same thing by the same names or expressions.
Arguments such as the following depend upon ambiguity. 30

1 Top. viii. 5. 2 Top. i-viii.

i6s b DE SOPHISTICIS ELENCHIS

Those learn who know : for it is those who know their
letters who learn the letters dictated to them. For to
4 learn is ambiguous ; it signifies both to understand by
the use of knowledge, and also to acquire knowledge .
Again, Evils are good : for what needs to be is good, and
35 evils must needs be. For what needs to be has a double
meaning : it means what is inevitable, as often is the case
with evils, too (for evil of some kind is inevitable), while on
the other hand we say of good things as well that they
4 need to be . Moreover, The same man is both seated
and standing and he is both sick and in health : for it is he
who stood up who is standing, and he who is recovering
i66 a who is in health : but it is the seated man who stood up,
and the sick man who was recovering. For The sick
man does so and so , or has so and so done to him is
not single in meaning : sometimes it means the man who
is sick or is seated now , sometimes the man who was sick
formerly . Of course, the man who was recovering was
5 the sick man, who really was sick at the time : but the man
who is in health is not sick at the same time : he is the
sick man in the sense not that he is sick now, but that he
was sick formerly. Examples such as the following
depend upon amphiboly : I wish that you the enemy may
capture. Also the thesis, There must be knowledge of
what one knows : for it is possible by this phrase to mean
that knowledge belongs to both the knower and the known.
Also, There must be sight of what one sees : one sees the
10 pillar: ergo the pillar has sight . Also, What you pro
fess to-be, that you profess-to-be : you profess a stone to-be :
ergo you profess-to-be a stone. 1 Also, Speaking of the
silent is possible : for speaking of the silent also has
a double meaning : it may mean that the speaker is silent
or that the things of which he speaks are so. 1 There are
15 three varieties of these ambiguities and amphibolies: (i)
When either the expression or the name has strictly more
than one meaning, e. g. aero? and the dog ; (2) when by
custom we use them so ; (3) when words that have a simple
sense taken alone have more than one meaning in com-
1 Cf. PI. Euthyd. 300 B-C.

CHAPTER IV i66 a

bination ; e. g. knowing letters . For each word, both
knowing and letters , possibly has a single meaning : 20
but both together have more than one either that the
letters themselves have knowledge or that some one else has
it of them.

Amphiboly and ambiguity, then, depend on these modes
of speech. Upon the combination of words there depend
instances such as the following : A man can walk while
sitting, and can write while not writing . For the mean
ing is not the same if one divides the words and if one com- 25
bines them in saying that it is possible to walk-while-
sitting [and write while not writing]. 1 The same applies
to the latter phrase, too, if one combines the words to
write-while-not-writing : for then it means that he has the
power to write and not to write at once ; whereas if one
does not combine them, it means that when he is not writ
ing he has the power to write. Also, l He knows now if 3
he has learnt his letters. 2 Moreover, there is the saying
that One single thing if you can carry a crowd you can
carry too .

Upon division depend the propositions that 5 is 2 and 3,
and even and odd, and that the greater is equal : for it is that
amount and more besides. For the same phrase would not 35
be thought always to have the same meaning when divided
and when combined, e.g. I made thee a slave once a free
man , 3 and God-like Achilles left fifty a hundred men . 4

An argument depending upon accent it is not easy to
construct in unwritten discussion ; in written discussions and i66 b
in poetry it is easier. Thus (e. g.) some people emend Homer
against those who criticize as unnatural his expression TO yuei/
ov KararrvOfTai ofj./3pq>. 5 For they solve the difficulty by a
change of accent, pronouncing the ov with an acuter accent. 5
Also, in the passage about Agamemnon s dream, they say
that Zeus did not himself say We grant him the fulfilment

1 i66 a 267. The words K<J! p.!] ypdQovra yp<i<f>tiv should probably be
omitted : and read ro Kadrj^vov (26) and TO p.fj ypd(f>ovTa (27).

2 i66 a 3. Read fj.av6a.vti ivv ypafipara tlwtp fpavdavtv, omitting
n rirtorarat.

3 Source unknown, but cf. Terence, Andria, I. i. 10.

4 Source unknown. 6 Iliad, ^r. 328.

i66 b DE SOPHISTICIS ELENCHIS

of his prayer , 1 but that he bade the dream grant it.
Instances such as these, then, turn upon the accentuation.
10 Others come about owing to the form of expression used,
when what is really different is expressed in the same form,
e.g. a masculine thing by a feminine termination, or a
feminine thing by a masculine, or a neuter by either a
masculine or a feminine ; or, again, when a quality is
expressed by a termination proper to quantity or vice
versa, or what is active by a passive word, or a state by an
active word, and so forth with the other divisions pre-
15 viously 2 laid down. For it is possible to use an expres
sion to denote what does not belong to the class of actions
at all as though it did so belong. Thus (e. g.) flourish
ing is a word which in the form of its expression is like
cutting or building : yet the one denotes a certain quality
i. e. a certain condition while the other denotes a certain
action. In the same manner also in the other instances.
2 Refutations, then, that depend upon language are drawn
from these common-place rules. Of fallacies, on the other
hand, that are independent of language there are seven
kinds :

(1) that which depends upon Accident :

(2) the use of an expression absolutely or not absolutely
but with some qualification of respect, or place, or time, or
relation :

(3) that which depends upon ignorance of what ; refuta
tion is :

25 (4) that which depends upon the consequent :

(5) that which depends upon assuming the original con
clusion : 3

(6) stating as cause what is not the cause :

(7) the making of more than one question into one.

Fallacies, then, that depend on Accident occur whenever 5
any attribute is claimed to belong in a like manner to a
3o thing and to its accident. For since the same thing has

1 The words occur not in the passage referred to, Iliad, B. 1-35,
but in <J>. 297.

2 Top. i. 9.

;! Read, with Strache, -rrapa TO (TO) ( v apxfj An

CHAPTER V i66 l

many accidents there is no necessity that all the same attri
butes 1 should belong to all of a thing s predicates and to
their subject as well. Thus (e. g.), If Coriscus be different
from " man ", he is different from himself: for he is a man :
or If he be different from Socrates, and Socrates be a man,
then , they say, he has admitted that Coriscus is different 35
from a man, because it so happens (accidit) that the person
from whom he said that he (Coriscus) is different is a man .
Those that depend on whether an expression is used
absolutely or in a certain respect and not strictly, occur
whenever an expression used in a particular sense is taken
as though it were used absolutely, e. g. in the argument If 167**
what is not is the object of an opinion, then what is not is :
for it is not the same thing to be x and to be absolutely.
Or again, l What is, is not, if it is not a particular kind of
being, e. g. if it is not a man. For it is not the same thing
4 not to be x and not to be at all : it looks as if it were,
because of the closeness of the expression, i. e. because to 5
be x" is but little different from to be , and l not to be x
from not to be . Likewise also with any argument that
turns upon the point whether an expression is used in a
certain respect or used absolutely. Thus e. g. Suppose an
Indian to be black all over, but white in respect of his
teeth ; then he is both white and not white. Or if both
characters belong in a particular respect, then, they say,
contrary attributes belong at the same time . This kind ro
of thing is in some cases easily seen by any one, e. g. sup
pose a man were to secure the statement that the Ethiopian
is black, and were then to ask whether he is white in
respect of his teeth ; and then, if he be white in that
respect, were to suppose at the conclusion of his questions
that therefore he had proved dialectically that he was both
white and not white. But in some cases it often passes
undetected, viz. in all cases where, whenever a statement is
made of something in a certain respect, it would be gener- 15
ally thought that the absolute statement follows as well;
and also in all cases where it is not easy to see which of the
attributes ought to be rendered strictly. A situation of
1 i66 b 52. Read ralra.

645-26 O

i67 a DE SOPHISTICIS ELENCHIS

this kind arises, where both the opposite attributes belong
alike : for then there is general support for the view that
one must agree absolutely to the assertion of both, or of
neither : e. g. if a thing is half white and half black, is it

20 white or black ?

Other fallacies occur because the terms proof or refuta
tion have not been defined, and because something is left
out in their definition. For to refute is to contradict one
and the same attribute not merely the name, but the
reality and a name that is not merely synonymous but the

35 same name and to confute it from the propositions granted,
necessarily, without including in the reckoning the original
point to be proved, in the same respect and relation and
manner and time in which it was asserted. A false asser
tion about anything has to be defined in the same way.
Some people, however, omit some one of the said condi
tions and give a merely apparent refutation, showing (e. g.)
that the same thing is both double and not double : for two

30 is double of one, but not double of three. Or, it may be,
they show that it is both double and not double of the same
thing, but not that it is so in the same respect: for it is
double in length but not double in breadth. Or, it may be,
they show it to be both double and not double of the same
thing and in the same respect and manner, but not that it is so
at the same time : and therefore their refutation is merely

35 apparent. One might, with some violence, bring this
fallacy into the group of fallacies dependent on language
as well.

Those that depend on the assumption of the original point
to be proved, occur in the same way, and in as many ways,
as it is possible to beg the original point ; they appear to
refute because men lack the power to keep their eyes at
once upon what is the same and what is different.
j67 b The refutation which depends upon the consequent arises
because people suppose that the relation of consequence is
convertible. For whenever, suppose A is, B necessarily is,
they then suppose also that if B is, A necessarily is. This
5 is also the source of the deceptions that attend opinions
based on sense-perception. For people often suppose bile

CHAPTER V i6 7 b

to be honey because honey is attended by a yellow colour :
also, since after rain the ground is wet in consequence, we
suppose that if the ground is wet, it has been raining ;
whereas that does not necessarily follow. In rhetoric
proofs from signs are based on consequences. For when
rhetoricians wish to show that a man is an adulterer, they to
take hold of some consequence of an adulterous life, viz.
that the man is smartly dressed, or that he is observed to
wander about at night. There are, however, many people
of whom these things are true, while the charge in question
is untrue. It happens like this also in real reasoning ; e. g.
Melissus argument, that the universe is eternal, assumes
that the universe has not come to be (for from what is not
nothing could possibly come to be) and that what has come 15
to be has done so from a first beginning. If, therefore, the
universe has not come to be, it has no first beginning, and
is therefore eternal. But this does not necessarily follow :
for even if what has come to be always has a first beginning,
it does not also follow that what has a first beginning has
come to be ; any more than it follows that if a man in
a fever be hot, a man who is hot must be in a fever. 20

The refutation which depends upon treating as cause
what is not a cause, occurs whenever what is not a cause
is inserted in the argument, as though the refutation de
pended upon it. This kind of thing happens in arguments
that reason ad impossibile : for in these we are bound to
demolish one of the premisses. If, then, the false cause be
reckoned in among the questions that are necessary to 35
establish the resulting impossibility, it will often be thought
that the refutation depends upon it, e. g. in the proof that
the l soul and life are not the same : for if coming-to-be
be contrary to perishing, then a particular form of perishing
will have a particular form of coming-to-be as its contrary :
now death is a particular form of perishing and is contrary
to life : life, therefore, is a coming-to-be, and to live is to
come-to-be. But this is impossible : accordingly, the soul 30
and life ; are not the same. Now this is not proved : for
the impossibility results all the same, even if one does not
say that life is the same as the soul, but merely says that

o a

i67 b DE SOPHISTICIS ELENCHIS

life is contrary to death, which is a form of perishing, and
that perishing has coming-to-be as its contrary. Argu
ments of that kind, then, though not inconclusive absolutely,

35 are inconclusive in relation to the proposed conclusion.
Also even the questioners themselves often fail quite as
much to see a point of that kind.

Such, then, are the arguments that depend upon the con
sequent and upon false cause. Those that depend upon
the making of two questions into one occur whenever the
plurality is undetected and a single answer is returned as if
i68 a to a single question. Now, in some cases, it is easy to see that
there is more than one, and that an answer is not to be
given, e. g. Does the earth consist of sea, or the sky ?
But in some cases it is less easy, and then people treat the
question as one, and either confess their defeat by failing to
answer the question, or are exposed to an apparent refuta-
5 tion. Thus Is A and is B a man ? Yes. Then if
any one hits A and B, he will strike a man (singular), not
men (plural). Or again, where part is good and part bad,
is the whole good or bad ? For whichever he says, it is
possible that he might be thought to expose himself to an

10 apparent refutation or to make an apparently false state
ment : for to say that something is good which is not good,
or not good which is good, is to make a false statement.
Sometimes, however, additional premisses may actually give
rise to a genuine refutation ; e. g. suppose a man were to
grant that the descriptions white and naked and blind
apply to one thing and to a number of things in a like sense.
For if blind describes a thing that cannot see though nature
designed it to see, it will also describe things that cannot

15 see though nature designed them to do so. Whenever, then,
one thing can see while another cannot, they will either both
be able to see or else both be blind ; which is impossible.

The right way, then, is either to divide apparent proofs 6
and refutations as above, or else to refer them all to ignor
ance of what refutation is, and make that our starting-
point : for it is possible to analyse all the aforesaid modes
20 of fallacy into breaches of the definition of a refutation.

CHAPTER VI i68 a

In the first place, we may see if they are inconclusive: for
the conclusion ought to result from the premisses laid down,
so as to compel us necessarily to state it and not merely to
seem to compel us. Next we should also take the definition
bit by bit, and try the fallacy thereby. For of the fallacies
that consist in language, some depend upon a double
meaning, e. g. ambiguity of words and of phrases, and the
fallacy of like verbal forms (for we habitually speak of 25
everything as though it were a particular substance) while
fallacies of combination and division and accent arise because
the phrase in question or the term as altered l is not the
same as was intended. Even this, however, should be the
same, just as the thing signified should be as well, if a refu
tation or proof is to be effected ; e. g. if the point concerns
a doublet, then you should draw the conclusion of a doublet , 3
not of a cloak . For the former conclusion also would be
true, but it has not been proved ; we need a further question
to show that doublet means the same thing, in order to
satisfy any one who asks why you think your point proved.
Fallacies that depend on Accident are clear cases of
ignoratio elenchi when once proof has been defined.
For the same definition ought to hold good of refutation 35
too, except that a mention of the contradictory is here
added : for a refutation is a proof of the contradictory.
If, then, there is no proof as regards an accident of anything,
there is no refutation. For supposing, when A and B are,
C must necessarily be, and C is white, there is no necessity
for it to be white on account of the syllogism. So, if the 40
triangle has its angles equal to two right-angles, and it i68 b
happens to be a figure, or the simplest element or starting
point, it is not because it is a figure or a starting point or
simplest element that it has this character. For the demon
stration proves the point about it not q iia figure or qua
simplest element, but qua triangle. Likewise also in other
cases. If, then, refutation is a proof, an argument which
argued per accidens could not be a refutation. It is, how- 5
ever, just in this that the experts and men of science
generally suffer refutation at the hand of the unscientific :

1 l68 a 28. Read rowo/m TO ta<pot>.

i68 b DE SOPHISTICIS ELENCHIS

for the latter meet the scientists with reasonings constituted
per accidens ; and the scientists for lack of the power to
draw distinctions either say Yes to their questions, or

10 else people suppose them to have said Yes , although they
have not. 1

Those that depend upon whether something is said in
a certain respect only or said absolutely, are clear cases of
ignoratio elenchi because the affirmation and the denial
are not concerned with the same point For of white in
a certain respect the negation is not white in a certain
respect , while of white absolutely it is not white,
absolutely . If, then, a man treats the admission that
a thing is white in a certain respect as though it were

15 said to be white absolutely, he does not effect a refutation,
but merely appears to do so owing to ignorance of what
refutation is.

The clearest cases of all, however, are those that were
previously described 2 as depending upon the definition
of a refutation : and this is also why they were called
by that name. For the appearance of a refutation is
produced because of the omission in the definition, and

20 if we divide fallacies in the above manner, we ought to set
Defective definition as a common mark upon them all.

Those that depend upon the assumption of the original
point and upon stating as the cause what is not the cause,
are clearly shown to be cases of ignoratio elenchi through
the definition thereof. For the conclusion ought to come
about 3 because these things are so , 4 and this does not

25 happen where the premisses are not causes of it : and
again it should come about without taking into account the
original point, and this is not the case with those arguments
which depend upon begging the original point.

Those that depend upon the consequent are a branch of
Accident : for the consequent is an accident, only it differs
from the accident in this, that you may secure an admission
of the accident in the case of one thing only (e. g. the

30 identity of a yellow thing and honey and of a white thing

1 i68 b 9. Read Sovras. * 167*21-35.

3 i68 b 24 omitting ama roO. 4 Cf. An. Pr. A. i. 24 b 18.

CHAPTER VI i68 b

and swan), whereas the consequent always involves more
than one thing : for we claim that things that are the same
as one and the same thing are also the same as one another,
and this is the ground of a refutation dependent on the
consequent. It is, however, not always true, e. g. suppose
that A and B are the same as C per accidens * ; for both
snow and the swan are the same as something white .
Or again, as in Melissus argument, 2 a man assumes that to 35
1 have been generated and to have a beginning are the
same thing, or to become equal and to assume the same
magnitude . For because what has been generated has
a beginning, he claims also that what has a beginning has
been generated, and argues as though both what has been
generated and what is finite 3 were the same because each
has a beginning. Likewise also in the case of things that 40
are made equal he assumes that if things that assume one i6g a
and the same magnitude become equal, then also things
that become equal assume one magnitude : 4 i. e. he assumes
the consequent. Inasmuch, then, as a refutation depending
on accident consists in ignorance of what a refutation is,
clearly so also does a refutation depending on the conse
quent. We shall have further to examine this in another 5
way as well. 5

Those fallacies that depend upon the making of several
questions into one consist in our failure to dissect the defi
nition of proposition . For a proposition is a single state
ment about a single thing. For the same definition applies
to one single thing only and to the thing , simply, e. g.
to man and to one single man only ; and likewise also 10
in other cases. If, then, a single proposition be one which
claims a single thing of a single thing, a proposition ,
simply, will also be the putting of a question of that kind.
Now since a proof starts from propositions and refutation
is a proof, refutation, too, will start from propositions. If,
then, a proposition is a single statement about a single thing,

1 i68 1) 34- Omit Xeiocoj/ with A and B.

2 Cf. l67 b 13. * l68 b 4O. Read TO
4 i69 b 2. Read Aa^amv with A and B.

6 Chs. 24, 28.

6 169* 7. Omitting ^ /i?) Siaipeu/ with A and B.

i6 9 a DE SOPHISTICIS ELENCHIS

it is obvious that this fallacy too consists in ignorance of
15 what a refutation is : for in it what is not a proposition
appears to be one. If, then, the answerer has returned an
answer as though to a single question, there will be a refu
tation ; while if he has returned one not really but appar
ently, there will be an apparent refutation of his thesis. All
the types of fallacy, 1 then, fall under ignorance of what
a refutation is, some of them 2 because the 3 contradiction,
20 which is the distinctive mark of a refutation, is merely
apparent, and the rest failing to conform to the definition
of a proof.

The deception comes about in the case of arguments that 7
depend on ambiguity of words and of phrases because we
are unable to divide the ambiguous term (for some terms it
is not easy to divide, e. g. unity , being , and sameness ),

35 while in those that depend on combination and division, it is
because we suppose that it makes no difference whether the
phrase be combined or divided, as is indeed the case with
most phrases. Likewise also with those that depend on
accent : for the lowering or raising of the voice upon
a phrase is thought not to alter its meaning with any
phrase, or not with many. With those that depend on the

30 form of expression it is because of the likeness of expres
sion. For it is hard to distinguish what kind of things are
signified by the same and what by different kinds of expres
sion : for a man who can do this is practically next door to
the understanding of the truth. 4 A special reason why
a man is liable to be hurried into assent to the fallacy is that
we suppose every predicate of anything to be an individual
thing, and we understand it as being one with the thing :
and we therefore treat it as a substance : for it is to that

35 which is one with a thing or substance, as also to substance
itself, that individuality and being are deemed to belong
in the fullest sense. For this reason, too, this type of fallacy
is to be ranked among those that depend on language ; in

1 169*18. ReadrpoTroi.

2 i69 a 19 Trapa rrjv \eiv appears to be a gloss.

3 169* 20. Read c^aivo/jifvrj TJ avrifyaais (Wallies).

4 169*33. Read a full-stop at raXijtfes, Also, read e

CHAPTER VII i6g a

the first place, because the deception is effected the more
readily when we are inquiring into a problem in company
with others than when we do so by ourselves (for an inquiry
with another person is carried on by means of speech,
whereas an inquiry by oneself is carried on quite as much
by means of the object itself) ; secondly a man is liable to be 4
deceived, even when inquiring by himself, when he takes i6g b
speech as the basis of his inquiry : moreover the deception
arises out of the likeness (of two different things), and the
likeness arises out of the language. With those fallacies
that depend upon Accident, deception comes about 1 because
we cannot distinguish the sameness and otherness of terms,
i. e. their unity and multiplicity, or what kinds of predicate 5
have all the same accidents as their subject. Likewise also
with those that depend on the Consequent : for the conse
quent is a branch of Accident. Moreover, in many cases
appearances point to this and the claim is made that if
A is inseparable from S, so also is B from A. With those
that depend upon an imperfection in the definition of a 10
refutation, and with those that depend upon the difference
between a qualified and an absolute statement, the deception
consists in the smallness of the difference involved ; for we
treat the limitation to the particular thing or respect or
manner or time as adding nothing to the meaning, and so
grant the statement universally. Likewise also in the case
of those that assume the original point, and those of false
cause, and all that treat a number of questions as one : for
in all of them the deception lies in the smallness of the 15
difference : for our failure to be quite exact in our definition
of premiss and of proof is due to the aforesaid reason.

8 Since we know on how many points apparent syllogisms
depend, we know also on how many sophistical syllogisms
and refutations may depend. By a sophistical refutation 20
and syllogism I mean not only a syllogism or refutation
which appears to be valid but is not, but also one which,
though it is valid, only appears to be appropriate to the
thing in question. These are those which fail to refute and

1 l69 b 3 sc. T) avarr) yivtrai from 169*22, as also in l69 a 30.

i6g b DE SOPHISTICIS ELENCHIS

prove people to be ignorant according to the nature of the
thing in question, which was the function of the art of

25 examination. Now the art of examining is a branch of
dialectic: and this may prove a false conclusion because
of the ignorance of the answerer. Sophistic refutations on
the other hand, even though they prove the contradictory
of his thesis, do not make clear whether he is ignorant : for
sophists entangle the scientist as well with these arguments.

3 That we know them by the same line of inquiry is clear:
for the same considerations which make it appear to an
audience that the points required for the proof were asked
in the questions and that the conclusion was proved, would
make the answerer think so as well, so that false proof will
occur through all or some of these means : for what a man
has not been asked but thinks he has granted, he would

35 also grant if he were asked. Of course, in some cases the
moment we add the missing question, we also show up its
falsity, e. g. in fallacies that depend on language and on
solecism. If then, fallacious proofs of the contradictory of
a thesis depend on their appearing to refute, it is clear that
the considerations on which both proofs of false conclusions
and an apparent refutation depend must be the same in

4 o number. Now an apparent refutation depends upon the
iyo a elements involved in a genuine one : for the failure of one
or other of these must make the refutation merely apparent,
e. g. that which depends on the failure of the conclusion to
follow from the argument (the argument ad impossibile)
and that which treats two questions as one and so depends
upon a flaw in the premiss, and that which depends on the
substitution of an accident for an essential attribute, and
5 a branch of the last that which depends upon the conse
quent : moreover, the conclusion may follow not in fact but
only verbally : then, instead of proving the contradictory
universally and in the same respect and relation and
manner, the fallacy may be dependent on some limit of
extent or on one or other of these qualifications : more
over, there is the assumption of the original point J to be
proved, in violation of the clause without reckoning in the

1 170*9. Read TO (TO) eV apxfj Xapfidj ti.v.

CHAPTER VIII i7o

original point . Thus we should have the number of con
siderations on which the fallacious proofs depend : for they 10
could not depend on more, but all will depend on the
points aforesaid.

A sophistical refutation is a refutation not absolutely but
relatively to some one : and so is a proof, in the same way.
For unless that which depends upon ambiguity assumes
that the ambiguous term has a single meaning, and that
which depends on like verbal forms assumes that substance 15
is the only category, and the rest in the same way, there
will be neither refutations nor proofs, either absolutely or
relatively to the answerer : whereas if they do assume these
things, they will stand, relatively to the answerer ; but
absolutely they will not stand : for they have not secured a
statement that does have a single meaning, but only one
that appears to have, and that only from this particular man.

9 The number of considerations on which depend the ao
refutations of those who are refuted, we ought not to try to
grasp without a knowledge of everything that is. This,
however, is not the province of any special study : for
possibly the sciences are infinite in number, so that obviously
demonstrations may be infinite too. Now refutations may
be true as well as false: for whenever it is possible to
demonstrate something, it is also possible to refute the
man who maintains the contradictory of the truth; e.g. 25
if a man has stated that the diagonal is commensurate
with the side of the square, one might refute him by
demonstrating that it is incommensurate. Accordingly,
to exhaust all possible refutations we shall have to have
scientific knowledge of everything : for some refutations
depend upon the principles that rule in geometry and
the conclusions that follow from these, others upon those
that rule in medicine, and others upon those of the other
sciences. For the matter of that, the false refutations like- 30
wise belong to the number of the infinite : for according
to every art there is false proof, e. g. according to geo
metry there is false geometrical proof, and according
to medicine there is false medical proof. By according to

i 7 o a DE SOPHISTICIS ELENCHIS

the art . I mean according to the principles of it .
Clearly, then, it is not of all refutations, but only of those

35 that depend upon dialectic that we need to grasp the
common-place rules : for these stand in a common relation
to every art and faculty. And as regards the refutation
that is according to one or other of the particular sciences
it is the task of that particular scientist to examine whether
it is merely apparent without being real, and, if it be real,
what is the reason for it : whereas it is the business of
dialecticians so to examine the refutation that proceeds from
the common first principles that fall under no particular
special study. For if we grasp the starting-points of the

40 accepted proofs on any subject whatever we grasp those of
i7o b the refutations current on that subject. For a refutation is
the proof of the contradictory of a given thesis, so that either
one or two proofs of the contradictory constitute a refuta
tion. We grasp, then, the number of considerations on
which all such depend : if, however, we grasp this, we also
grasp their solutions as well ; for the objections to these
5 are the solutions of them. We also grasp the number of
considerations on which those refutations depend, that are
merely apparent apparent, I mean, not to everybody, but
to people of a certain stamp ; for it is an indefinite task if
one is to inquire how many are the considerations that
make them apparent to the man in the street. Accordingly
it is clear that the dialectician s business is to be able to
grasp on how many considerations depends the formation,
through the common first principles, of a refutation that

10 is either real or apparent, i. e. either dialectical or appar
ently dialectical, or suitable for an examination.

It is no true distinction between arguments which some 10
people draw when they say that some arguments are
directed against the expression, and others against the
thought expressed : for it is absurd to suppose that some
1 5 arguments are directed against the expression and others
against the thought, and that they are not the same. For
what is failure to direct an argument against the thought
except what occurs whenever a man does not in using the

CHAPTER X i 7 o b

expression think it to be used in his question in the same
sense in which the person questioned granted it ? And this
is the same thing" as to direct the argument against the
expression. On the other hand, it is directed against the
thought whenever a man uses the expression in the same
sense which the answerer had in mind when he granted it.
If now any one (i. e. both the questioner and the person 20
questioned), in dealing with an expression with more than
one meaning, were to suppose it to have one meaning as
e. g. it may be that Being and One have many meanings,
and yet both the answerer answers and the questioner 1
puts his question supposing it to be one, and the argu
ment is to the effect that All things are one will this
discussion be directed any more against the expression
than against the thought of the person questioned ? If, on 25
the other hand, one of them 2 supposes the expression to
have many meanings, it is clear that such a discussion will not
be directed against the thought. Such being the meanings
of the phrases in question, they clearly cannot describe two
separate classes of argument. For, in the first place, it is
possible for any such argument as bears more than one
meaning to be directed against the expression and against
the thought, and next it is possible for any argument
whatsoever ; for the fact of being directed against the
thought consists not in the nature of the argument, but in
the special attitude of the answerer towards the points he 30
concedes. Next, all of them may be directed to the expres
sion. For to be directed against the expression means in
this doctrine not to be directed against the thought . For
if not all are directed against either expression or thought,
there will be certain other arguments directed neither
against the expression nor against the thought, whereas
they say that all must be one or the other, and divide them
all as directed either against the expression or against the
thought, while others (they say) there are none. But in 35
point of fact those that depend on mere expression are only
a branch of those syllogisms that depend on a multiplicity

1 iyo b 23. Omit Zfjvwv obviously a gloss.

2 170^ 25. Read fitfiXey^eVoy; d 8 ertpos . . ..

i7o b DE SOPHISTICIS ELENCHIS

of meanings. For the absurd statement has actually been
made that the description dependent on mere expression
describes all the arguments that depend on language :
whereas some of these are fallacies not because the answerer
adopts a particular attitude towards them, but because the

40 argument itself involves the asking of a question such as

bears more than one meaning.

171* It is, too, altogether absurd to discuss Refutation with
out first discussing Proof: for a refutation is a proof, so
that one ought to discuss proof as well before describing
false refutation : for a refutation of that kind is a merely

5 apparent proof of the contradictory of a thesis. Accord
ingly, the reason of the falsity will be either in the proof or
in the contradiction (for mention of the contradiction
must be added), while sometimes it is in both, if the refuta
tion be merely apparent. In the argument that speaking of
the silent is possible it lies in the contradiction, not in the
proof; in the argument that one can give what one does

10 not possess, it lies in both ; in the proof that Homer s poem is
a figure through its being a cycle it lies in the proof. An
argument that does not fail in either respect is a true proof.
But, to return to the point whence our argument
digressed, 1 are mathematical reasonings directed against
the thought, or not ? And if any one thinks triangle to
be a word with many meanings, and granted it in some

15 different sense from the figure which was proved to con
tain two right angles, has the questioner here directed his
argument against the thought of the former or not ?

Moreover, if the expression bears many senses, while the
answerer does not understand or suppose it to have them,
surely the questioner here has directed his argument
against his thought ! Or how else ought he to put his
question except by suggesting a distinction suppose one s
question to be Is speaking of the silent possible or not ?

20 as follows, Is 2 the answer "No" in one sense, but

" Yes " in another ? If, then, any one were to answer that

it was not possible in any sense and the other were to argue

that it was, has not his argument been directed against the

1 I7o b 40. 2 171* 19. Read a y e /jcor^a-fie, and ^ in line 20.

CHAPTER X 171*

thought of the answerer ? Yet his argument is supposed
to be one of those that depend on the expression. There is
not, then, any definite kind of arguments that is directed
against the thought. Some arguments are, indeed, directed
against the expression : but these l are not all even appar
ent refutations, let alone all refutations. For there are also 25
apparent refutations which do not depend upon language,
e. g. those that depend upon accident, and others.

If, however, any one claims that one should actually draw
the distinction, and say, By " speaking of the silent " I
mean, in one sense this and in the other sense that , surely
to claim this is in the first place absurd (for sometimes the 30
questioner does not see the ambiguity of his question, and
he cannot possibly draw a distinction which he does not
think to be there) : in the second place, what else but this
will didactic argument be ? For it will make manifest the
state of the case to one who has never considered, and does
not know or suppose that there is any other meaning but
one. For what is there to prevent the same thing also
happening to us in cases where there is no double meaning ?
Are the units in four equal to the twos ? Observe that the 35
twos are contained in four in one sense in this way, in
another sense in that. Also, Is the knowledge of con
traries one or not? Observe that some contraries are
known, while others are unknown. Thus the man who
makes this claim seems to be unaware of the difference
between didactic and dialectical argument, and of the fact \^
that while he who argues didactically should not ask ques
tions but make things clear himself, the other should
merely ask questions.

II Moreover, to claim a Yes or No answer is the busi
ness not of a man who is showing something, but of one
who is holding an examination. For the art of examining
is a branch of dialectic and has in view not the man who has 5
knowledge, but the ignorant pretender. He, then, is a
dialectician who regards the common principles with their
application to the particular matter in hand, while he who

1 171*24. Read KmVot ovTot.

i 7 i b DE SOPHISTICIS ELENCHIS

only appears to do this is a sophist. Now for contentious
and sophistical reasoning: (i) one such is a merely appar
ent reasoning, on subjects on which dialectical reasoning is
the proper method of examination, even though its conclu-

10 sion be true: for it misleads us in regard to the cause:
also (2) there are those misreasonings which do not conform
to the line of inquiry proper to the particular subject, but
are generally thought to conform to the art in question.
For false diagrams of geometrical figures are not conten
tious (for the resulting fallacies conform to the subject of
the art) any more than is any false diagram that may be

15 offered in proof of a truth e.g. Hippocrates figure or
the squaring of the circle by means of the lunules. But
Bryson s method of squaring the circle, 1 even if the circle is
thereby squared, is still sophistical because it does not con
form to the subject in hand. 2 So, then, any merely appar
ent reasoning about these things is a contentious argument,
and any reasoning that merely appears to conform to the

30 subject in hand, even though it be genuine reasoning, is
a contentious argument : for it is merely apparent in its con
formity to the subject-matter, so that it is deceptive and
plays foul. For just as a foul in a race is a definite type of
fault, and is a kind of foul fighting, so the art of conten
tious reasoning is foul fighting in disputation : for in the
former case those who are resolved to win at all costs
snatch at everything, and so in the latter case do conten
tious reasoners. Those, then, who do this in order to win

25 the mere victory are generally considered to be contentious
and quarrelsome persons, while those who do it to win
a reputation with a view to making money are sophistical.
For the art of sophistry is, as we said, 3 a kind of art of
money-making from a merely apparent wisdom, and this is
why they aim at a merely apparent demonstration : and

30 quarrelsome persons and sophists both employ the same
arguments, but not with the same motives : and the same
argument will be sophistical and contentious, but not in the

1 On the various methods of attempting to square the circle, here
and below (i;2 a 2-7), see Poste, Soph. EL, Appendix F.

2 Cf. 172*2-7 below. 3 i6s a 22.

CHAPTER XI i 7 i b

same respect ; rather, it will be contentious in so far as
its aim is an apparent victory, while in so far as its aim is
an apparent wisdom, it will be sophistical : for the art of
sophistry is a certain appearance of wisdom without the
reality. The contentious argument stands in somewhat the 35
same relation to the dialectical as the drawer of false dia
grams to the geometrician ; for it beguiles by misreasoning
from the same principles as dialectic uses, just as the drawer
of a false diagram beguiles the geometrician. But whereas
the latter is not a contentious reasoner, because he bases
his false diagram on the principles and conclusions that
fall under the art of geometry, the argument which is 172*
subordinate to the principles of dialectic will yet clearly be
contentious as regards other subjects. Thus, e. g., though
the squaring of the circle by means of the lunules is not
contentious, Bryson s solution is contentious : and the
former argument cannot be adapted to any subject except
geometry, because it proceeds from principles that are 5
peculiar to geometry, whereas the latter can be adapted as
an argument against all the number of people who do not
know what is or is not possible in each particular context :
for it will apply to them all. Or there is the method
whereby Antiphon squared the circle. Or again, an argu
ment which denied that it was better to take a walk after
dinner, because of Zeno s argument, would not be a proper
argument for a doctor, because Zeno s argument is of
general application. If, then, the relation of the conten
tious argument to the dialectical were exactly like that of I0
the drawer of false diagrams to the geometrician, a conten
tious argument upon the aforesaid subjects could not have
existed. But, as it is, the dialectical argument is not con
cerned with any definite kind of being, nor does it show
anything, nor is it even an argument such as we find in the
general philosophy of being. For all beings are not con
tained in any one kind, nor, if they were, could they
possibly fall under the same principles. Accordingly, no 15
art that is a method of showing the nature of anything
proceeds by asking questions : for it does not permit a man
to grant whichever he likes of the two alternatives in the

172* DE SOPHISTICIS ELENCHIS

question : for they will not both of them yield a proof.
Dialectic, on the other hand, does proceed by questioning,
wnereas if it were concerned to show things, it would have
refrained from putting questions, even if not about every
thing, at least about the first principles and the special prin
ciples that apply to the particular subject in hand. For

20 suppose the answerer not to grant these, 1 it would then no
longer have had any grounds from which to argue any
longer against the objection. Dialectic is at the same
time a mode of examination as well. For neither is the
art of examination an accomplishment of the same kind as
geometry, but one which a man may possess, even though
he has not knowledge. For it is possible even for one
without knowledge to hold an examination of one who is
without knowledge, if also the latter grants him points

25 taken not from things that he knows or from the special
principles of the subject under discussion but from all that
range of consequences attaching to the subject which a man
may indeed know without knowing the theory of the sub
ject, but which if he do not know, he is bound to be ignor
ant of the theory. So then clearly the art of examining
does not consist in knowledge of any definite subject. For
this reason, too, it deals with everything: for every
theory of anything employs also certain common prin-

30 ciples. Hence everybody, including even amateurs, makes
use in a way of dialectic and the practice of examining :
for all undertake to some extent a rough trial of those who
profess to know things. What serves them here is the
general principles : for they know these of themselves just
as well as the scientist, even if in what they say they seem to
the latter to go wildly astray from them. All, then, are
engaged in refutation ; for they take a hand as amateurs in

35 the same task with which dialectic is concerned profession
ally ; and he is a dialectician who examines by the help of
a theory of reasoning. Now there are many identical
principles which are true of everything, 2 though they are
not such as to constitute a particular nature, i. e. a particular

1 I72 a 20. Read 8i86vros.

2 172*36. Read ravra Kara Traj/rwv (BC have rnvrd and AB have no Kai).

CHAPTER XI i 7 2 a

kind of being, but are like negative terms, while other
principles are not of this kind but are special to particular
subjects ; accordingly it is possible from these general
principles to hold an examination on everything, and that
there should be a definite art of so doing, and, moreover, an 172
art which is not of the same kind as those which demon
strate. 1 This is why the contentious reasoner does not
stand in the same condition in all respects as the drawer of
a false diagram : for the contentious reasoner will not be
given to misreasoning from any definite class of principles,
but will deal with every class.

These, then, are the types of sophistical refutations : and 5
that it belongs to the dialectician to study these, and to be
able to effect them, is not difficult to see : for the investiga
tion of premisses comprises the whole of this study.

12 So much, then, for apparent refutations. As for show
ing that the answerer is committing some fallacy, and 10
drawing his argument into paradox for this was the
second item of the sophist s programme 2 in the first place,
then, this is best brought about by a certain manner of
questioning and through the question. For to put the
question without framing it with reference to any definite
subject is a good bait for these purposes: for people are
more inclined to make mistakes when they talk at large,
and they talk at large when they have no definite subject 15
before them. Also the putting of several questions, even
though the position against which one is arguing be quite
definite, and the claim that he shall say only what he thinks,
create abundant opportunity for drawing him into paradox
or fallacy, and also, whether to any of these questions he
replies Yes or replies No , of leading him on to state
ments against which one is well off for a line of attack.
Nowadays, however, men are less able 3 to play foul by ao
these means than they were formerly : for people rejoin
with the question, What has that to do with the original
subject ? It is, too, an elementary rule for eliciting some

I72 b I. Read

i65 b ig. 3 i72 b ig. Read

P 2

i72 b DE SOPHISTICIS ELENCHIS

fallacy or paradox that one should never put a contro
versial question straightaway, but say that one puts it from
the wish for information : for the process of inquiry thus
invited gives room for an attack.

25 A rule specially appropriate for showing up a fallacy is
the sophistic rule, that one should draw the answerer on to
the kind of statements against which one is well supplied
with arguments: this can 1 be done both properly and
improperly, as was said before. 2

Again, to draw a paradoxical statement, look and see to
what school of philosophers the person arguing with you

30 belongs, and then question him as to some point wherein
their doctrine is paradoxical to most people : for with every
school there is some point of that kind. It is an elemen
tary rule in these matters to have a collection of the special
* theses of the various schools among your propositions.
The solution recommended as appropriate here, too, is to
point out that the paradox does not come about because of
the argument : whereas this is what his opponent always

35 really wants.

Moreover, argue from men s wishes and their professed
opinions. For people do not wish the same things as they
say they wish : they say what will look best, whereas they
wish what appears to be to their interest : e. g. they say that
a man ought to die nobly rather than to live in pleasure,
i73 a and to live in honest poverty rather than in dishonourable
riches ; but they wish the opposite. Accordingly, a man
who speaks according to his wishes must be led into stating
the professed opinions of people, while he who speaks
according to these must be led into admitting those that
5 people keep hidden away : for in either case they are
bound to introduce a paradox ; for they will speak con
trary either to men s professed or to their hidden opinions.
The widest range of common-place argument for leading
men into paradoxical statement is that which depends on
the standards of Nature and of the Law : it is so that both
Callicles is drawn as arguing in the Gorgias? and that all
the men of old supposed the result to come about : for
1 I72 b 26. Read eo-rt. 2 Top. ii. 5. 3 482 E.

CHAPTER XII i73 a

nature (they said) and law are opposites, and justice is a fine 10
thing- by a legal standard, but not by that of nature.
Accordingly, they said, the man whose statement agrees
with the standard of nature you should meet by the stan
dard of the law, but the man who agrees with the law by
leading him to the facts of nature : for in both ways para
doxical statements may be committed. In their view the
standard of nature was the truth, while that of the law was 15
the opinion held by the majority. So that it is clear that
they, too, used to try either to refute the answerer or to
make him make paradoxical statements, just as the men of
to-day do as well.

Some questions are such that in both forms the answer
is paradoxical ; e. g. Ought one to obey the wise or one s 20
father ? and Ought one to do what is expedient or what
is just ? and Is it preferable to suffer injustice or to do an
injury ? You should lead people, then, into views oppo
site to the majority and to the philosophers ; if any one
speaks as do the expert reasoners, lead him into opposition
to the majority, while if he speaks as do the majority, then
into opposition to the reasoners. For some say that of 25
necessity the happy man is just, whereas it is paradoxical to
the many that a king should not be happy. To lead a man
into paradoxes of this sort is the same as to lead him into
the opposition of the standards of nature and law :. for the
law represents the opinion of the majority, whereas philo
sophers speak according to the standard of nature and 30
the truth.

13 Paradoxes, then, you should seek to elicit by means of
these common -place rules. Now as for making any one
babble, we have already said what we mean by to babble . 1
This is the object in view in all arguments of the following
kind : If it is all the same to state a term and to state its
definition, the double and double of half are the same : 35
if then double be the double of half, it will be the
double of half of half . And if, instead of double , double
of half be again put, then the same expression will be

1 I6s b i6.

i73 a DE SOPHIST1CIS ELENCHIS

repeated three times, double of half of half of half. Also
desire is of the pleasant, isn t it ? But desire is conation
for the pleasant : accordingly, desire is conation for the

40 pleasant for the pleasant .

i73 b All arguments of this kind occur in dealing (i) with any
relative terms which not only have relative genera, but are
also themselves relative, and are rendered in relation to one
and the same thing, as e. g. conation is conation for some
thing, and desire is desire of something, and double is
5 double of something, i. e. double of half: also in dealing (2)
with any terms which, though they be not relative terms at
all, yet have their substance, viz. the things of which they
are the states or affections or what not, indicated as well in
their definition, they being predicated of these things. Thus
e. g. odd is a 4 number containing a middle : but there is
an odd number : therefore there is a number-containing-a-

10 middle number . Also, if snub-ness be a concavity of the
nose, and there be a snub nose, there is therefore a l con
cave-nose nose .

People sometimes appear to produce this result, without
really producing it, because they do not add the question
whether the expression double , just by itself, has any
meaning or no, and if so, whether it has the same meaning,
or a different one ; but they draw their conclusion straight

15 away. Still it seems, inasmuch as the word is the same, to
have the same meaning as well.

We have said before what kind of thing solecism is. 1 14
It is possible both to commit it, and to seem to do so with
out doing so, and to do so without seeming to do so. Sup
pose, as Protagoras used to say, that /z^m ( wrath ) and
20 irfarjg ( helmet ) are masculine : according to him a man
who calls wrath a destructress (ouAo/zei/T/y) commits a sole
cism, though he does not seem to do so to other people,
whereas he who calls it a destructor (ovXa^vov} commits
no solecism though he seems to do so. It is clear, then,
that any one could produce this effect by art as well : and

1 i6s b 2o

CHAPTER XIV r/3 b

for this reason many arguments seem to lead to solecism
which do not really do so, as happens in the case of refuta
tions. 25

Almost all apparent solecisms depend upon the word
this (TO&), and upon occasions when the inflection
denotes neither a masculine nor a feminine object but a
neuter. For l he (ouro?) signifies a masculine, and she
(ai/rT; ) a feminine; but this (rotJro), though meant to
signify a neuter, often also signifies one or other of the
former : e. g. What is this ? It is Calliope ; it is a 3
log ; it is Coriscus . Now in the masculine and feminine
the inflections are all different, whereas in the neuter some
are and some are not. Often, then, when this (TOVTO) has
been granted, people reason as if him (TOVTOV) had been
said: and likewise also they substitute one inflection for
another. The fallacy comes about because this (TOVTO)
is a common form of several inflections : for this signi- 35
fies sometimes he (ouroy) and sometimes him (TOVTOV).
It should signify them alternately ; when combined with
is (e<m) it should be he , while with being it should be
him : e. g. Coriscus (Kopiovcoy) is , but being Coriscus
(KopicrKov). It happens in the same way in the case of
feminine nouns as well, and in the case of the so-called
chattels that have feminine or masculine designations. 40
For only those names which end in -o and v, have the 174**
designation proper to a chattel, e. g. v\ov ( log ), cryoiviov
( rope ) ; those which do not end so have that of a mascu
line or feminine object, though some of them we apply to
chattels : e. g. ao-Ko? ( wine-skin ) is a masculine noun, and
K\IV 77 ( bed ) a feminine. For this reason in cases of this
kind as well there will be a difference of the same sort
between a construction with is (eon) or with being (TO 5
tlvai). Also, Solecism resembles in a certain way those
refutations which are said to depend on the like expression
of unlike things. For, just as there we come upon a
material solecism, so here we come upon a verbal : for
man is both a matter for expression and also a word :
and so is white .

1 i;3 b 28. Read TO p< v ydp.

i74 a DE SOPHISTICIS ELENCHIS

10 It is clear, then, that for solecisms we must try to con
struct our argument out of the aforesaid inflections.

These, then, are the types of contentious arguments, and
the subdivisions of those types, and the methods for con
ducting them aforesaid. But it makes no little difference if
the materials for putting the question be arranged in a
certain manner with a view to concealment, as in the case of

15 dialectics. Following then upon what we have said, this
must be discussed first.

With a view then to refutation, one resource is length 15
for it is difficult to keep several things in view at once ; and
to secure length the elementary rules that have been stated
before 1 should be employed. One resource, on the other
hand, is speed ; for when people are left behind they look

20 ahead less. Moreover, there is anger and contentiousness,
for when agitated everybody is less able to take care of
himself. Elementary rules for producing anger are to make
a show of the wish to play foul, and to be altogether shame
less. Moreover, there is the putting of one s questions
alternately, whether one has more than one argument lead
ing to the same conclusion, or whether one has arguments

35 to show both that something is so, and that it is not so : for
the result is that he has to be on his guard at the same time
either against more than one line, or against contrary lines,
of argument. In general, all the methods described before 2
of producing concealment are useful also for purposes of
contentious argument : for the object of concealment is to
avoid detection, and the object of this is to deceive.

30 To counter those who refuse to grant whatever they
suppose to help one s argument, one should put the question
negatively, as though desirous of the opposite answer, or at
any rate as though one put the question without prejudice ;
for when it is obscure what answer one wants to secure,
people are less refractory. Also when, in dealing with
particulars, a man grants the individual case, when the
induction is done 3 you should often not put the universal

174*34. Read eVaya-yoWa.

CHAPTER XV i 74 a

as a question, but take it for granted and use it : for some- 35
times people themselves suppose that they have granted it,
and also appear to the audience to have done so, for they
remember the induction and assume that the questions could
not have been put for nothing. In cases where there is no
term to indicate the universal, still you should avail yourself
of the resemblance of the particulars to suit your purpose ;
for resemblance often escapes detection. Also, with a view
to obtaining your premiss, you ought to put it in your 40
question side by side with its contrary. E. g. if it were 174**
necessary to secure the admission that A man should obey
his father in everything , ask Should a man obey his
parents in everything, or disobey them in everything ? ; and
to secure that A number multiplied by a large number is
a large number , ask Should one agree that it is a large
number or a small one ? For then, if compelled to choose,
one will be more inclined to think it a large one : for the 5
placing of their contraries close beside them makes things
look big to men, both relatively and absolutely, and worse
and better.

A strong appearance of having been refuted is often
produced by the most highly sophistical of all the unfair
tricks of questioners, when without proving anything,
instead of putting their final proposition as a question, they 10
state it as a conclusion, as though they had proved that
Therefore so-and-so is not true .

It is also a sophistical trick, when a paradox has been
laid down, first to propose at the start some 1 view that is
generally accepted, and then claim that the answerer shall
answer what he thinks about it, and to put one s question
on matters of that kind in the form Do you think that . . . ?
For then, if the question be taken as one of the premisses 15
of one s argument, either a refutation or a paradox is bound
to result ; if he grants the view, a refutation ; if he refuses
to grant it or even to admit it as the received opinion,
a paradox ; if he refuses to grant it, but admits that it is
the received opinion, something very like a refutation,
results.

1 I74 b 13. Read rov (= TIVOS) for TOV.

i 7 4 b DE SOPHISTICIS ELENCHIS

Moreover, just as in rhetorical discourses, so also in those

20 aimed at refutation, you should examine the discrepancies
of the answerer s position either with his own statements,
or with those of persons whom he admits to say and do
aright, moreover with those of people who are generally
supposed to bear that kind of character, or who are like
them, or with those of the majority or of all men. Also
just as answerers, too, often, when they are in process of
being confuted, draw a distinction, if their confutation is

25 just about to take place, so questioners also should resort to
this from time to time to counter objectors, pointing out,
supposing that against one sense of the words the objection
holds, but not against the other, that they have taken it in
the latter sense, as e.g. Cleophon does in the Mandrobulus^
They should also break off their argument and cut down
their other lines of attack, while in answering, 2 if a man
perceives this being done beforehand, he should put in

30 his objection and have his say first. One should also
lead attacks sometimes against positions other than the
one stated, on the understood condition that 3 one cannot
find lines of attack against the view laid down, as
Lycophron did when ordered to deliver a eulogy upon the
lyre. To counter those who demand Against what are
you directing your effort ? 4 , since one is generally thought
bound to state the charge made, while, on the other hand,

35 some ways of stating it make the defence too easy, 5 you
should state as your aim only the general result that always
happens in refutations, 6 namely the contradiction of his
thesis viz. that your effort is to deny what he has affirmed, 7
or to affirm what he denied : don t say that you are trying
to show that the knowledge of contraries is, or is not, the
same. One must not ask one s conclusion in the form of

1 Probably a dialogue by Speusippus ; cf. I. Bywater in Journal of
Philology, xii. 21-30, and P. Lang, De Speusippi Academid Scriptis,
39-41,52.

1 I74 b 2g. Omit rov.

3 Or perhaps, and interpret the latter so, if one cannot &c.

4 I74 b 34- Read rrpoy TI em^fipets ;

8 I74 b 35, Read a comma after fixpuXaKTorepov.

6 I74 b 36. Read a comma after Xeyeiv, none after

7 I74 b 36. Read on 6 e

CHAPTER XV i 74 b

a premiss, while some conclusions should not even be put as
questions at all ; l one should take and use it as granted. 40

16 We have now therefore dealt with the sources of questions, 175*
and the methods of questioning in contentious disputations :
next we have to speak of answering, and of how solutions
should be made, and of what requires them, and of what use
is served by arguments of this kind.

The use of them, then, is, for philosophy, two-fold. For 5
in the first place, since for the most part they depend upon
the expression, they put us in a better condition for seeing
in how many senses any term is used, and what kind of
resemblances and what kind of differences occur between
things and between their names. In the second place they
are useful for one s own personal researches ; for the man who 10
is easily committed to a fallacy by some one else, and does not
perceive it, is likely to incur this fate of himself also on many
occasions. Thirdly and lastly, they further contribute to
one s reputation, viz. the reputation of being well trained in
everything, and not inexperienced in anything : for that a
party to arguments should find fault with them, if he cannot
definitely point out their weakness, creates a suspicion, TS
making it seem as though it were not the truth of the matter
but merely inexperience that put him out of temper.

Answerers may clearly see how to meet arguments of
this kind, if our previous account was right of the sources
whence fallacies came, and also our distinctions adequate of
the forms of dishonesty in putting questions. 2 But it is not 20
the same thing to take an argument in one s hand and then
to see and solve its faults, as it is to be able to meet it
quickly while being subjected to questions: for what we
know, we often do not know in a different context. More
over, just as in other things speed 3 is enhanced by training,
so it is with arguments too, so that supposing we are un- 25
practised, even though a point be clear to us, we are often
too late for the right moment. Sometimes too it happens
as with diagrams ; for there we can sometimes analyse the
figure, but not construct it again : so too in refutations,

1 I74 b 39- Read evia 5 ovfi eparrjTfov as parenthetical.

2 Chs. 4-11, 15. s 175*24. Omitting Kal ro ftpadurfpov.

i 7 5 a DE SOPHISTICIS ELENCHIS

though we know the thing on which the connexion of
3 the argument depends, we still are at^a loss to split the
argument apart.

First then, just as we say that we ought sometimes to 17
choose to prove something in the general estimation rather
than in truth, so also we have sometimes to solve arguments
rather in the general estimation than according to the truth.
For it is a general rule in fighting contentious persons, to
treat them not as refuting, but as merely appearing to

35 refute : for we say that they don t really prove their case,
so that our object in correcting them must be to dispel the
appearance of it. For if refutation be an unambiguous
contradiction arrived at from certain views, there could be
no need to draw distinctions against amphiboly and ambi
guity : for they do not effect a proof. The only motive for
drawing further distinctions is that the conclusion reached

40 looks like a refutation. What, then, we have to beware of,
is not being refuted, but seeming to be, because of course
the asking of amphibolies and of questions that turn upon
i7g b ambiguity, and all the other tricks of that kind, conceal
even a genuine refutation, and make it uncertain who is
refuted and who is not. For since one has the right at the
end, when the conclusion is drawn, to say that the only
5 denial made of one s statement is ambiguous, no matter
how precisely he may have addressed his argument to the
very same point as oneself, it is not clear whether one has
been refuted : for it is not clear whether at the moment one
is speaking the truth. If, on the other hand, one had drawn
a distinction, and questioned him on the ambiguous term or
the amphiboly, the refutation would not have been a matter
of uncertainty. Also what is incidentally the object of
contentious arguers, though less so nowadays than formerly,
would have been fulfilled, namely that the person questioned

10 should answer either Yes or No : whereas nowadays the
improper forms in which questioners put their questions
compel the party questioned to add something to his answer
in correction of the faultiness of the proposition as put:
for certainly, if the questioner distinguishes his meaning

CHAPTER XVII i 75 b

adequately, the answerer is bound to reply either Yes
or No .

If any one is going to suppose that an argument which 15
turns upon ambiguity is a refutation, it will be impossible
for an answerer to escape being refuted in a sense : for in
the case of visible objects one is bound of necessity to deny
the term one has asserted, and to assert what one has
denied. For the remedy which some people have for this
is quite unavailing. They say, not that Coriscus is both
musical and unmusical, but that this Coriscus is musical 20
and this Coriscus unmusical. But this will not do, for to
say this Coriscus * is unmusical , or musical , 2 and to say
this Coriscus is so, is to use the same expression : and
this he is both affirming and denying at once. But perhaps
they do not mean the same. Well, nor did the simple
name in the former case : so where is the difference ? 3 If,
however, he is to ascribe to the one person the simple 25
title Coriscus , while to the other he is to add the prefix
4 one or this , he commits an absurdity : for the latter is
no more applicable to the one than to the other : for to
whichever he adds it, it makes no difference.

All the same, since if a man does not distinguish the senses
of an amphiboly, it is not clear w r hether he has been confuted
or has not been confuted, and since in arguments the right
to distinguish them is granted, it is evident that to grant 30
the question simply without drawing any distinction is
a mistake, so that, even if not the man himself, at any rate
his argument looks as though it had been refuted. It often
happens, however, that, though they see the amphiboly,
people hesitate to draw such distinctions, because of the
dense crowd of persons who propose questions of the kind,
in order that they may not be thought to be obstructionists 35
at every turn : then, though they would never have sup
posed that that was the point on which the argument
turned, they often find themselves faced by a paradox.
Accordingly, since the right of drawing the distinction

1 I75 b 21. Read . . Xo -yor TO TOVTOV TOV K.

2 I75 b 22. Read apovo-ov emu (TJ povainov).
8 I75 b 24. Read coo-Tf TI Sia^e pfi;

i 7 5 b DE SOPHISTICIS ELENCHIS

is granted, one should not hesitate, as has been said
before. 1

If people never made 2 two questions into one question,

40 the fallacy that turns upon ambiguity and amphiboly would
not have existed either, but either genuine refutation or
none. For what is the difference between asking Are
176* Callias and Themistocles musical ? and what one might
have asked if they, being different, had had one name ?
For if the term applied means more than one thing, he has
asked more than one question. If then it be not right to
demand simply to be given a single answer to two questions,
it is evident that it is not proper to give a simple answer to
5 any ambiguous question, not even if the predicate be true
of all the subjects, as some claim that one should. For this
is exactly as though he had asked Are Coriscus and
Callias at home or not at home ? , supposing them to be
both in or both out : for in both cases there is a number of
propositions : for though the simple answer be true, that

10 does not make the question one. For it is possible for it to
be true to answer even countless different questions when
put to one, all together with either a Yes or a No : but
still one should not answer them with a single answer : for
that is the death of discussion. Rather, the case is like as
though different things had actually had the same name
applied to them. If then, one should not give a single

15 answer to two questions, it is evident that we should not
say simply Yes or No in the case of ambiguous terms
either : for the remark is simply a remark, not an answer
at all, although among disputants such remarks are loosely
deemed to be answers, because they do not see what the
consequence is.

As we said, 3 then, inasmuch as certain refutations are

ao generally taken for such, though not such really, in the
same way also certain solutions will be generally taken for
solutions, though not really such. Now these, we say,
must sometimes be advanced rather than the true solutions
in contentious reasonings and in the encounter with ambi-

1 i6o a 23ff. 2 I75 b 39. Read

CHAPTER XVII i 7 6 a

guity. The proper answer in saying what one thinks is to
say Granted ; for in that way the likelihood of being
refuted on a side issue is minimized. If, on the other hand, 25
one is compelled to say something paradoxical, one should
then be most careful to add that it seems so : for in that
way one avoids the impression of being either refuted or
paradoxical. Since it is clear what is meant by begging
the original question , and people think that they must at
all costs overthrow the premisses l that lie near the con
clusion, and plead in excuse for refusing to grant him some
of them that he is begging the original question, so when
ever any one claims from us a point such 2 as is bound to 30
follow as a consequence from our thesis, but is false or
paradoxical, we must plead the same : for the necessary
consequences are generally held to be a part of the thesis
itself. 3 Moreover, whenever the universal has been secured
not under a definite name, but by a comparison of instances,
one should say that the questioner assumes it not in the
sense in which it was granted nor in which he proposed it
in the premiss : for this too is a point upon which a refuta- 35
tion often depends.

If one is debarred from these defences one must pass to
the argument that the conclusion has not been properly
shown, approaching it in the light of the aforesaid distinction
between the different kinds of fallacy. 4

In the case, then, of names that are used literally one is
bound to answer either simply or by drawing a distinction:
the tacit understandings implied in our statements, e. g. in
answer to questions that are not put clearly but elliptically 40
it is upon this that the consequent refutation depends. i76 b
For example, Is what belongs to Athenians the property
of Athenians ? Yes. And so it is likewise in other
cases. But observe ; man belongs to the animal kingdom,
doesn t he ? Yes. Then man is the property of
the animal kingdom. But this is a fallacy : for we say
that man belongs to the animal kingdom because he is

1 176* 28. Read ndvruf, av [= a ai>] . . .

2 176*30. Read TiroiouToi .

3 176*32. Read avTijs fivai 8K(l Trjs 6f(T((as.

4 Cf. ch. 6.

i76 b DE SOPHISTICIS ELENCHIS

5 an animal, just as we say that Lysander belongs to the
Spartans, because he is a Spartan. It is evident, then, that
where the premiss put forward is not clear, one must not
grant it simply.

Whenever of two things it is generally thought that if
the one is true the other is true of necessity, whereas, if the
other is true, the first is not true of necessity, one should,

10 if asked which of them is true, 1 grant the smaller one : for
the larger the number of premisses, the harder it is to draw
a conclusion from them. If, again, the sophist tries to
secure that A has a contrary while B has not, 2 suppose
what he says is true, you should say that each has a con
trary, only for the one there is no established name.

Since, again, in regard to some of the views they express,

1 5 most people would say that any one who did not admit
them was telling a falsehood, while they would not say this
in regard to some, e. g. to any matters whereon opinion is
divided (for most people have no distinct view whether the
soul of animals is destructible or immortal), accordingly (i)
wherever it is uncertain in which of two senses the premiss
proposed is usually meant whether as maxims are (for
people call by the name of maxims both true opinions and

20 general assertions), or like the doctrine the diagonal of
a square is incommensurate with its side : 3 and moreover
(2) whenever opinions are divided as to the truth, we then
have subjects of which it is very easy to change the
terminology undetected. For because of the uncertainty in
which of the two senses the premiss contains the truth, one
will not be thought to be playing any trick, while because of
the division of opinion, one will not be thought to be telling
a falsehood. Change the terminology therefore, for the

25 change 4 will make the position irrefutable.

Moreover, whenever one foresees any question coming,
one should put in one s objection and have one s say before
hand : for by doing so one is likely to embarrass the ques
tioner most effectually.

1 I76 b IO. Read iro-repov (sc. ecrri).

2 Cf. io6 a 36, I23 b 3i.

3 iy6 b 20. Read a comma, instead of a full-stop, after a

4 176^24. Read rj yap jJifTatyopa..

CHAPTER XVIII I?6 b

xg Inasmuch as a proper solution is an exposure of false
reasoning-, showing on what kind of question the falsity 3 o
depends, and whereas false reasoning has a double mean
ing for it is used either if a false conclusion has been
proved, or if there is only an apparent proof and no real
one there must be both the kind of solution just described, 1
and also the correction of a merely apparent proof, so as to
show upon which of the questions the appearance depends.
Thus it comes about that one solves arguments that are 35
properly reasoned by demolishing them, whereas one
solves merely apparent arguments by drawing distinctions.
Again, inasmuch as of arguments that are properly reasoned
some have a true and others a false conclusion, those that
are false in respect of their conclusion it is possible to solve
in two ways ; for it is possible both by demolishing one of
the premisses asked, and by showing that the conclusion is 40
not the real state of the case : those, on the other hand, that 177*
are false in respect of their premisses can be solved only by
a demolition of one of them ; for the conclusion is true. So
that those who wish to solve an argument should in the
first place look and see if it is properly reasoned, or is
unreasoned ; and next, whether the conclusion be true or
false, in order that we may effect the solution either by
drawing some distinction or by demolishing something, and 5
demolishing it either in this way or in that, as was laid down
before. 2 There is a very great deal of difference between
solving an argument when being subjected to questions and
when not : for to foresee traps is difficult, whereas to see
them at one s leisure is easier.

19 Of the refutations, then, that depend upon ambiguity and
amphiboly some contain some question with more than one 10
meaning, while others contain a conclusion bearing a
number of senses : e. g. in the proof that speaking of the
silent is possible, the conclusion has a double meaning,
while in the proof that he who knows does not understand
what he knows one of the questions contains an amphiboly.
Also the double-edged saying is true in one context but

1 Ch. 17. - i?6 b 36-i77 a 2.

645-26 Q

i 7 7 a DE SOPHISTICIS ELENCHIS

15 not in another : it means something that is and something
that is not.

Whenever, then, the many senses lie in the conclusion no
refutation takes place unless the sophist secures as well the
contradiction of the conclusion he means to prove ; e. g. in
the proof that seeing of the blind is possible : for without
the contradiction there was no refutation. Whenever,
on the other hand, the many senses lie in the questions,
there is no necessity to begin by denying the double-edged
premiss : for this was not the goal of the argument but

20 only its support. At the start, then, one should reply with
regard to an ambiguity, whether of a term or of a phrase, in
this manner, that in one sense it is so, and in another not
so , as e. g. that speaking of the silent is in one sense
possible but in another not possible : also that in one sense
one should do what must needs be done , but not in
another : for what must needs be bears a number of
senses. If, however, the ambiguity escapes one, one should

25 correct it at the end by making an addition to the ques
tion : Is speaking of the silent possible ? No, but to
speak of A while he is silent is possible. Also, in cases
which contain the ambiguity in their premisses, one should
reply in like manner : Do people then not understand
what they know ? l Yes, but not those who know it in
the manner described : for it is not the same thing to say
that those who know cannot understand what they know ,
and to say that those who know something in this particu-

3 lar manner cannot do so . In general, too, even though he
draws his conclusion in a quite unambiguous manner, one
should contend that what he has negated is not the fact
which one has asserted but only its name; and that therefore
there is no refutation.

It is evident also how one should solve those refutations 2C

that depend upon the division and combination of words :

for if the expression means something different when

35 divided and when combined, as soon as one s opponent

draws his conclusion one should take the expression in the

1 177*28. Read o e

CHAPTER XX i 77 a

contrary way. All such expressions as the following
depend upon the combination or division of the words :
1 Was X being beaten with that with which you saw him
being beaten ? and Did you see him being beaten with
that with which he was being beaten ? This fallacy has
also in it an element of amphiboly in the questions, but it \ii
really depends upon combination. For the meaning that
depends upon the division of the words is not really
a double meaning (for the expression when divided is not
the same), 1 unless also the word that is pronounced, accord
ing to its breathing, as opoy and 6 po? is a case of double
meaning. (In writing, indeed, a word is the same when
ever it is written of the same letters and in the same manner 5
and even there people nowadays put marks at the side
to show the pronunciation but the spoken words are not
the same.) Accordingly an expression that depends upon
division is not an ambiguous one. It is evident also that
not all refutations depend upon ambiguity as some people
say they do.

The answerer, then, must divide the expression: for I- 10
saw-a-man-being-beaten with my eyes is not the same as
to say I saw a man being-beaten-with-my-eyes . Also
there is the argument of Euthydemus proving Then you
know now in Sicily that there are triremes in Piraeus : 2
and again, Can a good man who is a cobbler be bad ?
No. But a good man may be a bad cobbler : therefore
a good cobbler will be bad. Again, Things the know- ^5
ledge of which is good, are good things to learn, aren t
they ? Yes. The knowledge, however, of evil is good : 3
therefore evil is a good thing to know. Yes. But, you
see, evil is both evil and a thing-to-learn, so that evil is an
evil-thing-to-learn, although the knowledge of evils is good.
Again, Is it true to say in the present moment that you 20
are born ? Yes. l Then you are born in the present
moment. No ; the expression as divided has a different

1 I77 b 2 ov yap . . . diaipovntvos is parenthetic.

2 I77 b i2-i3. Read "Ap ot8ay( 1 2) and a colon instead of a question-
mark after eV SixeX/a >v.

3 J 77 b 17 o-TTovfiatoi/ TO uddrjua probably a slip for cnrovSaia 17 firtaTrjut],
which the argument requires. The translation assumes the latter.

Q2

i 7 7 b DE SOPHISTICIS ELENCHIS

meaning : for it is true to say-in-the-present-moment that
"you are born", but not "You are born-in-the-present-
moment ". Again, Could you do what you can, and as you
can ? Yes. But when not harping, you have the power
to harp : and therefore you could harp when not harping.

2 5 No : he has not the power to harp-while-not-harping ;
merely, when he is not doing it, he has the power to do it. 1
Some people solve this last refutation in another way
as well. For, they say, if he has granted that he can do
anything in the way he can, still it does not follow that
he can harp when not harping : for it has not been granted
that he will do anything in every way in which he can ; and

30 it is not the same thing to do a thing in the way he can
and to do it in every way in which he can . But evidently
they do not solve it properly : for of arguments that depend
upon the same point the solution is the same, w r hereas this
will not fit all cases of the kind nor yet all ways of putting
the questions : it is valid against the questioner, but not
against his argument.

35 Accentuation gives rise to no fallacious arguments, either 21
as written or as spoken, except perhaps some few that
might be made up ; e. g. the following argument. Is ov
KaraXveis a house ? Yes. Is then ov KaraXveis the
I78 a negation of KaraXveis ? Yes. But you said that ov
KaraXveis is a house : therefore the house is a negation.
How one should solve this, is clear : for the word does not
mean the same when spoken with an acuter and when
spoken with a graver accent.

It is clear also how one must meet those fallacies that 22
5 depend on the identical expression of things that are not
identical, seeing that we are in possession of the kinds of
predications. For the one man, say, has granted, when
asked, that a term denoting a substance does not belong as
an attribute, while the other has shown that some attribute
belongs which is in the Category of Relation or of Quantity,
but is usually thought to denote a substance because of its
expression ; e. g. in the following argument : Is it possible
to be doing and to have done the same thing at the same

CHAPTER XXII I7 8

time? No. But, you see, it is surely possible to be :o
seeing and to have seen the same thing at the same time,
and in the same aspect. Again, Is any mode of passivity
a mode of activity ? No. Then " he is cut ", " he is
burnt ", " he is struck by some sensible object " are alike in
expression and all denote some form of passivity, while
again " to say ", " to run ", " to see " are like one another in
expression : but, you see, " to see " is surely a form of being 15
struck by a sensible object ; therefore it is at the same time
a form of passivity and of activity. Suppose, however,
that in that case any one, after granting that it is not
possible to do and to have done the same thing in the same
time, were to say that it is possible to see and to have
seen it, still he has not yet been refuted, suppose him to say
that to see is not a form of doing (activity) but of
1 passivity : for this question is required as well, though
he is supposed by the listener to have already granted it, 20
when he granted that to cut is a form of present, and to
have cut a form of past, activity, and so on with the other
things that have a like expression. For the listener adds
the rest by himself, thinking the meaning to be alike:
whereas really the meaning is not alike, though it appears
to be so because of the expression. The same thing
happens here as happens in cases of ambiguity : for in 2 5
dealing with ambiguous expressions the tyro in argument
supposes the sophist to have negated the fact which he (the
tyro) affirmed, and not merely the name : whereas there still
wants the question whether in using the ambiguous term
he had a single meaning in view : for if he grants that that
was so, the refutation will be effected.

Like the above are also the following arguments. It is
asked if a man has lost what he once had and afterwards 30
has not : for a man will no longer have ten dice even though
he has only lost one die. No : rather it is that he has lost
what he had before and has not now ; but there is no
necessity for him to have lost as nmch or as many things
as he has not now. So then, he asks the questions as to
what he has, and draws the conclusion as to the whole
number that he has : for ten is a number. If then he had

i?8 a DE SOPHISTICIS ELENCHIS

asked to begin with, whether a man no longer having the
35 number of things he once had has lost the whole number,
no one would have granted it, but would have said Either
the whole number or one of them . Also there is the
argument that a man may give what he has not got : for
he has not got only one die. No : rather it is that he has
given, not what he had not got, but in a manner in which
he had not got it, viz. just the one. For the word only
does not signify a particular substance or quality or number,
i78 b but a manner of relation, e. g. that it is not coupled with
any other. It is therefore just as if he had asked Could
a man give what he has not got ? and, on being given the
answer No , were to ask if a man could give a thing
quickly when he had not got it quickly, and, on this being
granted, were to conclude that a man could give what he
had not got . It is quite evident that he has not proved
5 his point : for to give quickly is not to give a thing, but
to give in a certain manner ; and a man could certainly give
a thing in a manner in which he has not got it, e. g. he
might have got it with pleasure and give it with pain.

Like these are also all arguments of the following kind :
Could a man strike a blow with a hand which he has not
got, or see with an eye which he has not got ? For he has
10 not got only one eye. Some people solve this case, where
a man has more than one eye, or more than one of any
thing else, by saying also that he has only one. Others
also solve it as they solve the refutation of the view that
what a man has, he has received : for A gave only one
vote ; and certainly B, they say, has only one vote from A.
Others, again, proceed by demolishing straight away the
proposition asked, and admitting that it is quite possible
to have what one has not received ; e. g. to have received
15 sweet wine, but then, owing to its going bad in the course
of receipt, to have it sour. But, as was said also above, 1
all these persons direct their solutions against the man, not
against his argument. For if this were a genuine solution,
then, suppose any one to grant the opposite, he could find
no solution, just as happens in other cases; e.g. suppose

CHAPTER XXII I?8 t

the true solution to be So-and-so is partly true and partly
not V then, if the anwerer grants the expression without 20
any qualification, the sophist s conclusion follows. If, on
the other hand, the conclusion does not follow, then that
could not be the true solution : and what we say in regard
to the foregoing examples is that, even if all the sophist s
premisses be granted, still no proof is effected.

Moreover, the following too belong to this group of
arguments. If something be in writing did some one write 25
it ? Yes. But it is now in writing that you are seated
a false statement, though it was true at the time when it was
written : therefore the statement that was written is at the
same time false and true. But this is fallacious, for the
falsity or truth of a statement or opinion indicates not a
substance but a quality : for the same account applies to the
case of an opinion as well. Again, Is what a learner
learns what he learns ? Yes. But suppose some one 30
learns " slow " quick . Then his (the sophist s) words
denote not what the learner learns but how he learns it.
Also, Does a man tread upon what he walks through ?
Yes. But X walks through a whole day. No, rather
the words denote not what he walks through, but when he
walks ; just as when any one uses the words to drink the
cup he denotes not what he drinks, but the vessel o^lt of
which he drinks. Also, Is it either by learning or by dis
covery that a man knows what he knows ? Yes. But
suppose that of a pair of things he has discovered one and 35
learned the other, the pair is not known to him by either
method. No : what he knows, means every single
thing he knows, individually; but this does not 2 mean
all the things he knows, collectively. Again, there is the
proof that there is a third man distinct from Man and
from individual men. But that is a fallacy, for Man , and
indeed every general predicate, denotes not an individual
substance, but a particular quality, or the being related to
something in a particular manner :! , or something of that sort.
Likewise also in the case of Coriscus and Coriscus the 179

1 I78 b 19-20. Read olov d tori /uii> o, eWi 8 6 ou 17 Autrir (sc. fWi).
- I78 b 36. Read TO 8 oix anavra. 3 I78 a 38-9. Read f) npos ri nw.

i 79 a DE SOPHISTICIS ELENCHIS

musician there is the problem, Are they the same or
different ? For the one denotes an individual substance
and the other a quality, so that it cannot be isolated ; though
it is not the isolation which creates the third man , but the
admission that it is an individual substance. For Man can-
5 not be an individual substance, as Callias is. 1 Nor is the case
improved one whit even if one were to call the element he
has isolated not an individual substance but a quality : for
there will still be the one beside the many, just as Man
was. It is evident then that one must not grant that what
is a common predicate applying to a class universally is an
individual substance, but must say that it denotes either a
10 quality, or a relation, or a quantity, or something of that kind.

It is a general rule in dealing with arguments that depend 23
on language that the solution always follows the opposite of
the point on which the argument turns : e. g. if the argu
ment depends upon combination, then the solution consists
in division ; if upon division, then in combination. Again,
if it depends on an acute accent, the solution is a grave

15 accent ; if on a grave accent, it is an acute. If it depends on
ambiguity, one can solve it by using the opposite term ;
e.g. if you find yourself calling something inanimate, 2
despite your previous denial that it was so, show in what
sense it is alive : if, on the other hand, one has declared it
to be inanimate and the sophist has proved it to be animate,
say how it is inanimate. Likewise also in a case of amphi-

20 boly. If the argument depends on likeness of expression,
the opposite will be the solution. Could a man give what
he has not got ? No, not what he has not got ; but he
could give it in a way in which he has not got it, e. g. one
die by itself. Does a man know either by learning or by
discovery each thing that he knows, singly ? Yes, but not
the things that he knows, collectively. Also a man treads,
perhaps, on any thing he walks through, but not on the
time he walks through. Likewise also in the case of the

25 other examples.

1 179*5. Read a comma after KaXXiay.

2 I79 a 17. Read ityv^ov for t/x^v^oi/.

CHAPTER XXIV i 79

2 4 In dealing with arguments that depend on Accident, one
and the same solution meets all cases. For since it is
indeterminate when an attribute should be ascribed to a
thing, in cases where it belongs to the accident of the thing,
and since in some cases it is generally agreed and people
admit that it belongs, while in others they deny that it need
belong, we should therefore, as soon as the conclusion has 30
been drawn, 1 say in answer to them all alike, that there is
no need for such an attribute to belong. One must, how
ever, be prepared to adduce an example of the kind of
attribute meant. All arguments such as the following
depend upon Accident. Do you know what I am going
to ask you ? Do you know the man who is approaching ,
or the man in the mask ? Is the statue your work of
art ? or Is the dog your father ? 2 Is the product of a 35
small number with a small number a small number ? For
it is evident in all these cases that there is no necessity for
the attribute which is true of the thing s accident to be true
of the thing as well. For only to things that are indis
tinguishable and one in essence is it generally agreed that
all the same attributes belong ; whereas in the case of a
good thing, to be good is not the same as to be going to
be the subject of a question ; nor in the case of a man i7Q b
approaching, or wearing a mask, is to be approaching the
same thing as to be Coriscus , so that suppose I know
Coriscus, but do not know the man who is approaching, it
still isn t the case that I both know and do not know the
same man ; nor, again, if this is mine and is also a work of
art, is it therefore my work of art, but my property or thing 5
or something else. (The solution is after the same manner
in the other cases as well.)

Some solve these refutations by demolishing the original
proposition asked : for they say that it is possible to know
and not to know the same thing, only not in the same
respect : accordingly, when they don t know the man who is
coming towards them, but do know Coriscus, they assert
that they do know and don t know the same object, but not 10

1 I79 a 3O. Read (ru/i3<,3a(r^eVro?.

2 Cf. PI. Euthyd. 298 E.

i79 b DE SOPHISTICIS ELENCHIS

in the same respect. Yet, as we have already remarked, 1
the correction of arguments that depend upon the same
point ought to be the same, whereas this one will not stand
if one adopts the same principle in regard not to knowing
something, but to being, or to being in a certain state, e. g.

15 suppose that X is a father, and is also yours : for if in some
cases this is true and it is possible to know and not to know
the same thing, yet with that case the solution stated has
nothing to do. Certainly there is nothing 2 to prevent the
same argument from having a number of flaws ; but it is
not the exposition of any and every fault that constitutes a
solution : for it is possible for a man to show that a false con
clusion has been proved, but not to show on what it depends,
e. g. in the case of Zeno s argument to prove that motion is

20 impossible. So that even if any one were to try to establish
that this doctrine is an impossible one, he still is mistaken,
and even if he proved his case ten thousand times over, still
this is no :! solution of Zeno s argument : for the solution
was all along an exposition of false reasoning, showing on
what its falsity depends. If then he has not proved his case,
or is trying to establish even a true proposition, or a false

25 one, in a false manner, 4 to point this out is a true solution.
Possibly, indeed, the present suggestion may very well
apply in some cases : but in these cases, at any rate, not
even this would be generally agreed : for he knows both
that Coriscus is Coriscus and that the approaching figure is
approaching. To know and not to know the same thing is
generally thought to be possible, when e. g. one knows that

30 X is white, but does not realize that he is musical : for in
that way he does know and not know the same thing,
though not in the same respect. But as to the approach
ing figure and Coriscus he knows both that it is approaching
and that he is Coriscus.

A like mistake to that of those whom we have mentioned
is that of those who solve the proof that every number is

1 I77 b 3i. 2 I79 b iy. Read oi,8ev &?.

3 I79 b 22. Omitting , and reading dXX OVK fa-nv, with a comma after

2 4~5 f Read TI KOI a\T)Oes fj \l/ev8os {\|/fu5ws) fVt^etpei trvvdytU

CHAPTER XXIV 179"

a small number : for if, when the conclusion is not proved, 35
they pass this over and say that a conclusion has been
proved and is true, on the ground that every number is
both great and small, they make a mistake.

Some people also use the principle of ambiguity to solve
the aforesaid reasonings, e. g. the proof that X is your
father , or son , or slave . Yet it is evident that if the
appearance of a proof depends upon a plurality of mean- i8o a
ings, the term, or the expression in question, ought to bear
a number of literal senses, whereas no one speaks of A as
being 4 !?<$, child in the literal sense, if B is the child s
master, but the combination depends upon Accident. Is
A yours ? 4 Yes. And is A a child ? Yes. Then 5
the child A is yours, l because he happens to be both yours
and a child ; but he is not * your child .

There is also the proof that something " of evils " is
good 1 ; for wisdom is a knowledge " of evils " . But the
expression that this is of so-and-so ( = so-and-so s ) has
not a number of meanings : it means that it is so-and-so s 10
property . We may suppose of course, on the other hand,
that it has a number of meanings for we also say that man
is of the animals , though not their property ; and also
that any term related to evils in a way expressed by a
genitive case is on that account a so-and-so of evils ,
though it is not one of the evils 2 but in that case the
apparently different meanings seem to depend on whether
the term is used relatively or absolutely. Yet it is con
ceivably possible to find a real ambiguity in the phrase
"Something of evils is good". Perhaps, but not with 15
regard to the phrase in question. It would occur more
nearly, suppose that A servant is good of the wicked ;
though perhaps it is not quite found even there : for a thing
may be good and be X s without being at the same time
1 JTs good . Nor is the saying that Man is of the animals
a phrase with a number of meanings : for a phrase does not
become possessed of a number of meanings merely suppose a
we express it elliptically : for we express Give me the

1 l8o a 5. Read a-ov <"pa TOVTO TO reKi/of.

8 Extend the parenthesis to after the second KUKUV in 1. 13.

i8o a DE SOPHISTICIS ELENCHIS

Iliad by quoting half a line of it, e. g. Give me " Sing,
goddess, of the wrath ..."

Those arguments which depend upon an expression that 25
is valid of a particular thing, or in a particular respect, or
place, or manner, or relation, and not valid absolutely,
should be solved by considering the conclusion in relation

25 to its contradictory, to see if any of these things can possibly
have happened to it. For it is impossible for contraries
and opposites and an affirmative and a negative to belong
to the same thing absolutely ; there is, however, nothing to
prevent each from belonging in a particular respect or rela
tion or manner, or to prevent one of them from belonging
in a particular respect and the other absolutely. So that if
this one belongs absolutely and that one in a particular

3 respect, there is as yet no refutation. This is a feature one
has to find in the conclusion by examining it in comparison
with its contradictory.

All arguments of the following kind have this feature :
( Is it possible for what is-not to be ? No. But, you
see, it zs something, despite its not being 1 Likewise also,
Being will not be ; for it will not be some particular form of

35 being. Is it possible for the same man at the same time to
be a keeper and a breaker of his oath ? Can the same
man at the same time both obey and disobey the same
man ? Or isn t it the case that being something in particu
lar and Being are not the same ? On the other hand, Not-
being, even if it be something, need not also have absolute
being as well. Nor if a man keeps his oath in this
particular instance or in this particular respect, is he bound
also to be a keeper of oaths absolutely, but he who swears
i8o b that he will break his oath, and then breaks it, keeps this
particular oath only ; he is not a keeper of his oath : nor is
the disobedient man obedient , though he obeys one
particular command. The argument is similar, also, as
regards the problem whether the same man can at the same
time say what is both false and true : but it appears to be
a troublesome question because it is not easy to see in which

1 Cf. l67 a I supra.

CHAPTER XXV iS

of the two connexions the word absolutely is to be ren
dered 5 with true or with false . There is, however, 5
nothing to prevent it from being false absolutely, though true
in some particular respect or relation, i. e. being true in some
things, though not true absolutely. Likewise also in cases
of some particular relation and place and time. For all
arguments of the following kind depend upon this. Is
health, or wealth, a good thing ? Yes. But to the fool
who does not use it aright it is not a good thing : therefore 10
it is both good and not good. Is health, or political
power, a good thing ? Yes. But sometimes it is not
particularly good : therefore the same thing is both good
and not good to the same man. Or rather there is nothing
to prevent a thing, though good absolutely, being not good
to a particular man, or being good to a particular man, and
yet not good now or here. Is that which the prudent man 15
would not wish, an evil ? Yes. But to get rid of, he
would not wish the good : therefore the good is an evil.
But that is a mistake ; for it is not the same thing to say
The good is an evil and to get rid of the good is an
evil . Likewise also the argument of the thief is mistaken.
For it is not the case that if the thief is an evil thing, acquir
ing things is also evil : what he wishes, therefore, is not
what is evil but what is good ; for to acquire something 20
good is good. Also, disease is an evil thing, but not to get
rid of disease. Is the just preferable to the unjust, and
what takes place justly to what takes place unjustly ?
1 Yes. But to be put to death unjustly is preferable. Is
it just that each should have his own ? Yes. But what
ever decisions a man comes to on the strength of his
personal opinion, even if it be a false opinion, 2 are valid in 25
law: therefore the same result is both just and unjust.
Also, should one decide in favour of him who says what
is just, or of him who says what is unjust ? 3 The former.
But, you see, it is just for the injured party also to say
fully the things he has suffered ; and these were unjust.

1 l8o b 4. Read a comma after (JTrXco?. 2 lSo b 25. Read tyevdrjs.
3 Or read TU S<*a V i*av in i8o b 27= should one judge him ... or
him ... to be the winner ? (cf. 1. 38).

i8o b DE SOPHISTICIS ELENCHIS

But these are fallacies. For because to suffer a thing
unjustly is preferable, unjust ways are not therefore prefer-
3 o able to just ; but, absolutely, just ways are preferable,
though in this particular case the unjust may very well be
better than the just. Also, to have one s own is just, while
to have what is another s is not just: all the same, the
decision in question may very well be a just decision, what
ever it be that the opinion of the man who gave the decision
supports : for because it is just in this particular case or in
this particular manner, it is not also just absolutely. Like
wise also, though things are unjust, there is nothing to pre-
35 vent the speaking of them being just : for because to
speak of things is just, there is no necessity that the things
should be just, any more than because to speak of things
be of use, the things need be of use. Likewise also in the
case of what is just. So that it is not the case that because
the things spoken of are unjust, the victory goes to him
who speaks unjust things : for he speaks of things that are
just to speak of, though absolutely, i. e. to suffer, they are
unjust.

i8i a Refutations that depend on the definition of a refutation 26
must, according to the plan sketched above, 1 be met by
comparing together the conclusion with its contradictory,
and seeing that it shall involve the same attribute in the
same respect and relation and manner and time. If this
5 additional question be put at the start, you should not
admit that it is impossible for the same thing to be both
double and not double, but grant that it is possible, only
not in such a way as was agreed to constitute a refutation
of your case. All the following arguments depend upon
a point of that kind. Does a man who knows A to be A,
know the thing called A ? and in the same way, is one
who is ignorant that A is A ignorant of the thing called A ?
10 Yes. But one who knows that Coriscus is Coriscus
might be ignorant of the fact that he is musical, so that he
both knows and is ignorant of the same thing. Is a thing
four cubits long greater than a thing three cubits long ?

1 167*21.

CHAPTER XXVI i8i 8

Yes. But a thing might grow from three to four cubits
in length ; now what is greater is greater than a less" :
accordingly the thing in question will be both greater and
less than itself in the same respect. 1

27 As to refutations that depend on begging and assuming 15
the original point to be proved, suppose the nature of the
question to be obvious, 2 one should not grant it, even
though it be a view generally held, but should tell him the
truth. Suppose, however, that it escapes one, then, thanks
to the badness of arguments of that kind, one should make
one s error recoil upon the questioner, and say that he has
brought no argument : for a refutation must be proved
independently of the original point. Secondly, one should
say that the point was granted under the impression that he
intended not to use it as a premiss, but to reason against it, 3 20
in the opposite way from that adopted in refutations on side
issues.

28 Also, those refutations that bring one to their conclusion
through the consequent you should show up in the course
of the argument itself. The mode in which consequences
follow is two-fold. For the argument either is that as the
universal follows on its particular as (e.g.) animal
follows from man so does the particular on its
universal: for the claim is made that if A is always found 25
with B, then B also is always found with A. Or else it
proceeds by way of the opposites of the terms involved :
for if A follows B, it is claimed that A s opposite will
follow It s opposite. On this latter claim the argument of
Melissus also depends : for he claims that because that
which has come to be has a beginning, that which has not
come to be has none, so that if the heaven has not come to
be, it is also eternal. But that is not so ; for the sequence

is vice versa. 3

29 In the case of any refutations whose reasoning depends
on some addition, look and see if upon its subtraction the

1 l8l a 14. Read Kara TOVTO after CIVTOV.

2 i8l a 16. Read iruvdavopewp, av ^.tv 17 8rj\ov,

3 l8l a 21. Read a comma after avXXoymrfifvov, not after rovvavriuv.

i8i a DE SOPHISTICIS ELENCHIS

absurdity follows none the less : and then if so, the answerer
should point this out, and say that he granted the addition
not because he really thought it, but for the sake of the
argument, whereas the questioner has not used it for the
35 purpose of his argument at all.

To meet those refutations which make several questions 30
into one, one should draw a distinction between them
straight away at the start. For a question must be single
to which there is a single answer, so that one must not
affirm or deny several things of one thing, nor one thing
of many, but one of one. But just as in the case of
ambiguous terms, an attribute belongs to a term sometimes
i8i b in both its senses, and sometimes in neither, so that a
simple answer does one, as it happens, no harm despite
the fact that the question is not simple, so it is in these
cases of double questions too. Whenever, then, the several
attributes belong to the one subject, or the one to the many,
5 the man who gives a simple answer encounters no obstacle
even though he has committed this mistake : but when
ever an attribute belongs to one subject but not to the
other, or there is a question of a number of attributes
belonging to a number of subjects and in one sense both
belong to both, while in another sense, again, they do not,
then there is trouble, so that one must beware of this.
Thus (e. g.) in the following arguments : Supposing A to
10 be good and B evil, you w r ill, if you give a single answer
about both, be compelled to say that it is true to call these
good, and that it is true to call them evil and likewise to
call them neither good nor evil (for each of them has not
each character), so that the same thing will be both good
and evil and neither good nor evil. Also, since everything
is the same as itself and different from anything else, 1
inasmuch as 2 the man who answers double questions simply
can be made to say that several things are the same not
as other things but as themselves, and also that they are
different from themselves, it follows that the same things must

1 l8l b 13. Read a comma after erepoi>.

2 l8l b 14. Read erreiSq for end 8\

CHAPTER XXX i8i b

be both the same as and different from themselves. 1 More- 15
over, if what is good becomes evil while what is evil is
good, 2 then they must both become two. So of two unequal
things each being equal to itself, it will follow that they are
both equal and unequal to themselves.

Now these refutations fall into the province of other
solutions as well : for both and all have more than one 20
meaning, so that the resulting affirmation and denial of the
same thing does not occur, except verbally : and this is not
what we meant by a refutation. But it is clear that if there
be not put a single question on a number of points, but the
answerer has affirmed or denied one attribute only of one
subject only, the absurdity will not come to pass.

31 With regard to those who draw one into repeating the 25
same thing 3 a number of times, it is clear that one must not
grant that predications of relative terms have any meaning
in abstraction by themselves, e. g. that double is a signifi
cant term apart from the whole phrase double of half
merely on the ground that it figures in it. For ten figures
in ten minus one and do in not do , and generally the 3
affirmation in the negation ; but for all that, suppose any
one were to say, This is not white , he does not say that it
is white. The bare word double , one may perhaps say,
has not even any meaning at all, any more than has the in
the half : and even if it has a meaning, yet it has not the
same meaning as in the combination. Nor is knowledge
the same thing in a specific branch of it (suppose it, e. g., to
be medical knowledge ) as it is in general : for in general 35
it was the knowledge of the knowable . In the case of
terms that are predicated of the terms through which they
are defined, you should say the same thing, 4 that the term
defined is not the same in abstraction as it is in the whole
phrase. For concave has a general meaning which is the

1 i8l b 14-15 fTfpa avrwv . . . eavrois trtpn. The Greek idiom must
here be kept, to bring about the contradiction: the English idiom
different from one another 1 avoids it.

2 i8i b 15-16 ft TO nw . . . iiyaduv earn , sc. as happens if you answer
a double question about them together simply.

3 l8l b 25 Read (Is (TO) TO avro.

4 lSl b 36 Read TCIVTO for TOVTO.

i8i b DE SOPHISTICIS ELENCHIS

same in the case of a snub nose, and of a bandy leg, but

when added to either substantive nothing- prevents it from

differentiating its meaning; in fact it bears one sense 1 as

i82 ;l applied to the nose, and another as applied to the leg : for

in the former connexion it means snub and in the latter

bandy-shaped ; i. e. it makes no difference whether you

say a snub nose or a concave nose . Moreover, the

expression must not be granted in the nominative case : for

it is a falsehood. For snubness is not a concave nose but

something (e. g. an affection) belonging to a nose : hence,

5 there is no absurdity in supposing that the snub nose is

a nose possessing the concavity that belongs to a nose.

With regard to solecisms, we have previously said 2 what 32
it is that appears to bring them about ; the method of their
solution will be clear in the course of the arguments them
selves. Solecism is the result aimed at in all arguments of

10 the following kind : Is a thing truly that which you truly
call it ? Yes. But, speaking of a stone, you call him real 3 :
therefore of a stone it follows that " him is real ". No : rather,
talking of a stone means not saying which but whom ,
and not that but him . If, then, any one were to ask, Is
a stone him whom you truly call him ? he would be
generally thought not to be speaking good Greek, any more
than if he were to ask, Is he what you call her ? Speak in

15 this way 4 of a stick or any neuter word, and the difference
does not break out. For this reason, also, no solecism is
incurred, suppose any one asks, Is a thing what you say it
to be ? Yes. But, speaking of a stick, you call it real :
therefore, of a stick it follows that it is real. Stone ,
however, and he have masculine designations. Now
suppose some one were to ask, Can " he " be a " she " (a
female) ? , and then again, Well, but is not he Coriscus ?

1 i82 a i Read cr^aiVet. 2 i65 b 2of.

3 182* ii. Stone (Xi $oy) being masculine in Greek. It has been
necessary to deal rather freely with this passage, because stone
is not inflected in English. Literally, the Greek says, You declare
something to be a stone (ace.) : something therefore is a stone (still
ace., though the change to oratio recta requires a change to the nom.).

* l82 a 15 Read (l-ntlv ouraiy.

CHAPTER XXXII : 8a a

and then were to say, Then he is a " she " , he has not ao
proved the solecism, even if the name Coriscus does
signify a she , if, on the other hand, the answerer does
not grant this: this point must be put as an additional
question : while if neither is it the fact nor does he grant it,
then the sophist has not proved his case either in fact or as
against the person he has been questioning. In like manner,
then, in the above instance as well it must be definitely put 25
that he means the stone. If, however, this neither is so
nor is granted, the conclusion must not be stated : though
it follows apparently, because the case (the accusative), that
is really unlike, appears to be like the nominative. Is it
true to say that this object is what you call it by name ?
Yes. But you call it by the name of a shield : this object
therefore is " of a shield ". No: not necessarily, because
the meaning of this object is not l of a shield but a 30
shield : of a shield would be the meaning of l this
object s . Nor again if He is what you call him by name ,
while the name you call him by is Cleon s , is he therefore
1 Cleon s : for he is not Cleon s , for what was said was
that He, not his^ is what I call him by name . For the
question, if put in the latter way, would not even be Greek.
Do you know this ? Yes. But this is he : therefore you 35
know he . 2 No : rather this has not the same meaning
in Do you know this ? as in This is a stone ; in the first
it stands for an accusative, in the second for a nominative
case. When you have understanding " of anything, do you
understand it ? Yes. But you have understanding of
a stone : therefore you understand of a stone. No : the one
phrase is in the genitive, of a stone , while the other is in
the accusative, a stone 4 : and what was granted was that i82 b

1 182*29-30 avTt] acrniSa, 3! raiTrjv, 32 KXeWrr, 33 TOVTOV. Posses-
sive cases are here substituted for the Greek accusative, as the
English accusative is not inflected.

2 i82 a 35 \idos: lit. a stone : but he has been substituted,
because stone does not inflect in English.

3 i8z a 38 f nio-Twrjv, eWraovu : lit. knowledge , know : but
understanding , understand have been substituted because the
phrase know of a stone has a meaning in English, and therefore fails
to bring out the solecism of the Greek conclusion.

4 l82 a 39- b l Read r\ TO fj.fi> TOVTOV (\idov) Xeyeif, TO 8f TOVTOV (M0oi>).

R 2

i82 b DE SOPHISTICIS ELENCHIS

you understand that, not of that, of which you have under
standing , so that you understand not of a stone , but the
stone .

Thus that arguments of this kind do not prove solecism
but merely appear to do so, and both why they so appear
5 and how you should meet them, is clear from what has
been said.

We must also observe that of all the arguments aforesaid 33
it is easier with some to see why and where the reasoning
leads the hearer astray, while with others it is more difficult,
though often they are the same arguments as the former.
For we must call an argument the same if it depends upon
the same point ; but the same argument is apt to be thought

10 by some to depend on diction, by others on accident, and
by others on something else, because each of them, when
worked with different terms, is not so clear as it was.
Accordingly, just as in fallacies that depend on ambiguity,
which are generally thought to be the silliest form of

15 fallacy, some are clear even to the man in the street (for
humorous phrases nearly all depend on diction ; e. g. The
man got the cart down from the stand 1 ; and Where are
you bound ? To the yard arm ; and Which cow will
calve afore ? Neither, but both behind ; and Is the
North wind clear ? No, indeed ; for it has murdered the

20 beggar and the merchant. Is he a Goodenough-King?
No, indeed ; a Rob-son : and so with the great majority of
the rest as well), 2 while others appear to elude the most
expert ;i (and it is a symptom of this that they often fight
about their terms, e. g. whether the meaning of Being
and One is the same in all their applications or different ;

25 for some think that Being and One mean the same;

1 An obscure joke : the phrase fapfa-Oai Kara K\ip.aKos Stypov probably
contains a double pun, (i) to get the body of a car (dtypos) taken off its
chassis (K\lfj.a^ the notched support on top of the axle, on which
the car rested), (2) to come a sitter (8i(ppos = a seat) off a ladder
(\r/ia).

2 i82 b 22 Close the bracket, and read a comma instead of a full-stop

after rr\e tcrrot.

3 1 82^ 22 (Trjuelov ... 27 TO ov is parenthetic (like 15 <a\ yap-22 7rXi-
a-roi), and should be likewise enclosed in brackets, followed by a comma,
the colon after \av6aveiv (1. 22) being removed.

CHAPTER XXXIII i8 2 b

while others solve the argument of Zeno and Parmenides
by asserting that One and Being are used in a
number of senses), likewise also as regards fallacies of
Accident and each of the other types, some of the argu
ments will be easier to see while others are more difficult ;
also to grasp to which class a fallacy belongs, and whether 30
it is a refutation or not a refutation, is not equally easy in
all cases.

An incisive argument is one which produces the greatest
perplexity : for this is the one with the sharpest fang. Now
perplexity is two-fold, one which occurs in reasoned argu
ments, respecting which of the propositions asked one is to
demolish, and the other in contentious arguments, respect- 35
ing the manner in which one is to assent to what is pro
pounded. Therefore it is in syllogistic arguments that the
more incisive ones produce the keenest heart-searching.
Now a syllogistic argument is most incisive if from premisses
that are as generally accepted as possible it demolishes a
conclusion that is accepted as generally as possible. For
the one argument, if the contradictory is changed about,
makes all the resulting syllogisms alike in character : for i83 a
always from premisses that are generally accepted it will
prove a conclusion, negative or positive as the case may be,
that is just as generally accepted ; and therefore one is
bound to feel perplexed. 1 An argument, then, of this kind
is the most incisive, viz. the one that puts its conclusion on
all fours with the propositions asked ; and second comes
the one that argues from premisses, all of which are equally
convincing : for this will produce an equal perplexity as to 5
what kind of premiss, of those asked, one should demolish.

1 i82 b 37-183* 2. The nature of the syllogisms which produce this
most incisive and perplexing form of argument by changing about
the contradictory (of the first conclusion established) may be illus
trated by Pacius example. Suppose the thesis maintained to be the
exceedingly probable view that Medea did not love her children , the
dialectician then argues

I. All mothers love their children (exceedingly probable).

Medea was a mother (exceedingly probable).

. . Medea loved her children (just as probable as, but utterly sub
versive of, the exceedingly probable thesis).

Next, he constructs two syllogisms in which the contradictory of
this conclusion (i. e. the original, and exceedingly probable, thesis) is

i8 3 a DE SOPHISTICIS ELENCHIS

Herein is a difficulty : for one must demolish something,
but what one must demolish is uncertain. Of contentious
arguments, on the other hand, the most incisive is the one
which, in the first place, is characterized by an initial
uncertainty whether it has been properly reasoned or not ;
and also whether the solution depends on a false premiss
or on the drawing of a distinction ; while, of the rest, the

ro second place is held by that whose solution clearly depends
upon a distinction or a demolition, and yet it does not
reveal clearly which it is of the premisses asked, whose
demolition, or the drawing of a distinction within it, will
bring the solution about, but even leaves it vague whether
it is on the conclusion or on one of the premisses that the
deception l depends.

Now sometimes an argument which has not been properly

15 reasoned is silly, supposing the assumptions required to be
extremely contrary to the general view or false ; but some
times it ought not to be held in contempt. For whenever
some question is left out, of the kind that concerns both the
subject and the nerve of the argument, the reasoning that
has both failed to secure this as well, and also failed to
reason properly, is silly ; but when what is omitted is some
extraneous question, then it is by no means to be lightly

o despised, but the argument is quite respectable, though the
questioner has not put his questions well.
Just as it is possible to bring a solution sometimes

used in a changed position with each of the two original premisses in
turn, to subvert the other : thus

II. All mothers love their children (exceedingly probable).

Medea did not love her children (exceedingly probable).
. . Medea was not a mother (just as probable as, but subversive of,

the exceedingly probable minor premiss of Syllogism I).
III. Medea did not love her children (exceedingly probable).

Medea was a mother (exceedingly probable).
. . Some mothers do not love their children (as probable as, but
subversive of, the exceedingly probable major premiss of Syllo
gism I).

All three syllogisms are alike , in that each overthrows an
exceedingly probable view by means of a conclusion based on exceed
ingly probable premisses, and therefore itself exceedingly probable. To
gether they produce the maximum of perplexity because, as a result,
of each of three exceedingly probable propositions the contradictory
has also been shown to be exceedingly probable.

1 i83 a 12 Read ?) ima-m for ntJrq (v. Pseudo-Alexander).

CHAPTER XXXIII i8 3 a

against the argument, at others against the questioner and
his mode of questioning, and at others against neither of
these, likewise also it is possible to marshal one s questions
and reasoning both against the thesis, and against the
answerer and against the time, whenever the solution 25
requires a longer time to examine than the period available. 1

34. As to the number, then, and kind of sources whence
fallacies arise in discussion, and how we are to show that
our opponent is committing a fallacy and make him utter
paradoxes ; moreover, by the use of what materials solecism
is brought about, and how to question and what is the way 30
to arrange the questions ; moreover, as to the question
what use is served by all arguments of this kind, and con
cerning the answerer s part, both as a whole in general, and
in particular how to solve arguments and solecisms 2 on
all these things let the foregoing discussion suffice. It
remains to recall our original proposal and to bring our 35
discussion to a close \vith a few words upon it.

Our programme was, then, to discover some faculty of
reasoning about any theme put before us from the most
generally accepted premisses that there are. For that is
the essential task of the art of discussion (dialectic) and
of examination (peirastic). Inasmuch, however, as it is 183
annexed to it, on account of the near presence of the art
of sophistry (sophistic), not only to be able to conduct
an examination dialectically but also with a show of
knowledge, we therefore proposed for our treatise not
only the aforesaid aim of being able to exact an account
of any view, but also the aim of ensuring that in standing 5
up to an argument we shall defend our thesis in the same
manner by means of views as generally held as possible.
The reason of this we have explained ; a for this, too, was
why Socrates used to ask questions and not to answer
them ; for he used to confess that he did not know.

1 I8s a 26 Omit toaXt^wu ir,ws r<> Ximi clearly a marginal
gloss on ij \vais (25).

2 183*30 o-uXXoyio-^or, 33 irvX^oyiarfiovs : Read aoXonturpos and o-o-
XOIKHT^OVS (cf. i65 b i9, 20).

8 165* 19-27.

i8 3 b DE SOPHISTICIS ELENCHIS

We have made clear, in the course of what precedes, the
number both of the points with reference to which, and of
the materials from which, this will be accomplished, and

10 also from what sources we can become well supplied with
these : we have shown, moreover, how to question or
arrange the questioning as a whole, and the problems
concerning the answers and solutions to be used against
the reasonings of the questioner. We have also cleared up
the problems concerning all other matters that belong to the
same inquiry into arguments. In addition to this we have

15 been through the subject of Fallacies, as we have already
stated above. 1

That our programme, then, has been adequately com
pleted is clear. But we must not omit to notice what has
happened in regard to this inquiry. For in the case of all
discoveries the results of previous labours that have been
handed down from others have been advanced bit by bit
by those who have taken them on, whereas the original

20 discoveries generally make an advance that is small at
first though much more useful than the development which
later springs out of them. For it may be that in every
thing, as the saying is, the first start is the main part :
and for this reason also it is the most difficult ; for in propor
tion as it is most potent in its influence, so it is smallest in

25 its compass and therefore most difficult to see : whereas
when this is once discovered, it is easier to add and develop
the remainder in connexion with it. This is in fact what
has happened in regard to rhetorical speeches and to prac
tically all the other arts : for those who discovered the
beginnings of them advanced them in all only a little way,

30 whereas the celebrities of to-day are the heirs (so to speak) of
a long succession of men who have advanced them bit by
bit, and so have developed them to their present form, Tisias
coming next after the first founders, then Thrasymachus
after Tisias, and Theodorus next to him, while several
people have made their several contributions to it : and
therefore it is not to be wondered at that the art has attained
considerable dimensions. Of this inquiry, on the other

1 183*27.

CHAPTER XXXIV i8 3 b

hand, it was not the case that part of the work had been 35
thoroughly done before, while part had not. Nothing
existed at all. For the training given by the paid pro
fessors of contentious arguments was like the treatment of
the matter by Gorgias. For they used to hand out speeches
to be learned by heart, some rhetorical, others in the form
of question and answer, each side supposing that their
arguments on either side generally fall among them. And i84 a
therefore the teaching they gave their pupils was ready but
rough. For they used to suppose that they trained people
by imparting to them not the art but its products, as though
any one professing that he would impart a form of know
ledge to obviate any pain in the feet, were then not to 5
teach a man the art of shoe-making or the sources whence
he can acquire anything of the kind, but were to present
him with several kinds of shoes of all sorts : for he has
helped him to meet his need, but has not imparted an art
to him. Moreover, on the subject of Rhetoric there exists
much that has been said long ago, whereas on the subject 184
of reasoning we had nothing else of an earlier date to speak
of at all, but were kept at work for a long time in experi
mental researches. If, then, it seems to you after inspec
tion that, such being the situation as it existed at the start,
our investigation is in a satisfactory condition compared
with the other inquiries that have been developed by tradi- 5
tion, there must remain for all of you, or for our students,
the task of extending us your pardon for the shortcomings
of the inquiry, and for the discoveries thereof your warm
thanks.

INDEX

Absolute attributes : to belong
absolutely def., Ii5 b 29-35.

A. belongs absolutely, if in
greater or less degrees, i I5 b 3 ;
not vice versa, Ii5*32-3, b 8-io:
or if in a certain respect, time
or place, H5 b u : objections to
positive use of this principle,
Il5 b l4, 17, 19, 26; reply to
some of them, H5 b 24, 27.

Good absolutely better than
good for X , I i6 b 8 (cf. a 21-2) :
if A is better absolutely than
B, best ex. of A is better than
best ex. of B, and vice versa,
H7 b 33. That A is absolutely
good or desirable or objection
able can be shown by same
argts. which show it to be more
so than B, ii9 a 2-9. Absolute
predication of Properties, 134*
32, I35 a 2.

Fallacy of Absolute and quali
fied use of expression (dictum
simpliciter and secunduin quid),
one of 7 fallacious refutations not
dependent on diction, i66 b 22~3:
illustrated, i66 b 37-167* 20: its
solution, Soph. El., ch. 25 ; a
form of ign. elenchi,\6& > 1 1-16 :
why deceptive, i69 b 10-12.

Accent(npo(Tu>&ia), Fallacy of : one
of 6 fallacious refutations de
pendent on diction, l65 b 27;
illustrated, i66 b l-9: its solu
tion, Soph. EL, ch. 21 and 179*
14-15 ; a form of ign. elenchi,
1 68* 27 foil. : why deceptive,
169* 27-29. (Cf. Breathing.}

Accident: ioi b 18,25: def. nega
tively, I02 b 4, and (better) affir
matively, !O2 b 6-l4.

Commonplace tests of acci
dent: Bk. II passim.

Comparisons of things based
on accidents, io2 b 14 : common
place tests of, Bk. \\\ passim.

Tests of a., alone apply to all
other predicables, 155* 11-12.
Tests common to genus and a.,
I20 b i5~i7, I24 b 7~8 (from con

tradictories), I25 b 10 and 126*
14 (from consideration of sub
jects wherein S and P inhere):
to property and a., 129*32-4,
I 33 a 3 2 ~4: to definition and a.,
I02 b 27, I39 a 36- b 3.

A. may = temporary or relative
property, io2 b 21 (cf. I2g a 32-4),
but never = property absolutely,
I02 b 25: cf. 131*27-37, b 5~i8.
No a. of X can be X s genus,
I2o b 21, 30-35; or differentia,
144*23-7.
A., as test of sameness, 152*

33-7-

)( essential attribute (xad
ain-o), no b 2i foil., 116*31-3,
b 2-7, 143*3-4, I49 b 9, 13, 170*
4. Universal affirmation of a.
easier to disprove than to prove,
l$4* 33! particular do., easier
to prove than to disprove, I54 b
36: proof of a. the easiest task
in dialectic, 155*28-31 ; disproof
of do. very difficult, 155*31-36.

A., alone of predicables, may
belong in part only, and /. ad
mit only precariously of conver
sion (i.e. of transition from P
belongs to S to S is P ), 109*
10-26. Sophistical difficulty
whether an attribute of S be
longs to S qualified by some a.,
133^15-24, 31-36 (cf. 178 39-
179* I). If both variable, S and
its a. should vary together, 115*
4-6.

Immortality an accident

(rn^ifirco/uri) of life, I26 36, 39.

Fallacy of Accident : one of 7
fallacious refutations not depen
dent on diction, i66 b 22 : illus
trated, i66 b 28-36: its solution,
Soph. EL, ch. 24 ; why decep
tive, l69 b 3-6 : a form of ign.
elenchi, 168*34- 5, 169*3-4.
Usual fallacy whereby amateurs
entrap scientists, i68 b 6-lo.
Fallacy of Consequent, a branch
of F. of A., l68 b 27 foil.
Achilles : ii7 b 14-15, 24 : i66 :l 38.

INDEX

Activity ( i ) = noie iv : a category
)( passivity, 103^3.

Capacity for a. and p. not a
property of Being-, 139*4-8;
nor its defn., 146*22-3, 31-2,
I48 a 18-21.

Movement rather a form of
a. or p. in soul than the soul s
genus, I2o b 26-7.

Verbal terminations proper to
a. )( those proper to passivity or
quality; their confusion a source
of fallacy of form of expres
sion , i66 b l3-8, I78 a 11-24.

(2) = evepyeia : considered as
genus of building , I24 a 21 ; of
using , i24 a 33 : genus of mo
tion , I25 b i7; of memory ,
I25 b i9. )( State (efw), 125*
15. Regarded (like yeveais) as
aiming at further end, in which
it ceases ; contr. pleasure , re
garded as an a. which is also an
end in itself, I46 b 13-19. Kiss
ing a physical activity , io6 b
2-3-.

Affection (naffos) : cannot have as
its genus the thing affected (TO
TTfirovdos), I26 b 34-I27 a 2; nor
yet its subject, S (ov eVrl iniOos),
127*3 ; unless the affection can
be called an S , 127* 9-19.

Must be inherent in the thing
whose affection it is, I45 a 35- b
II. = an accident (o-i^Tmopi),
I26 b 36, 39.

Agamemnon, his dream, i66 b 6~7.
Air: not its property to be
breathable , for ( i ) this, though
true of particular portions of air,
is not true of the air as a whole,
I 35 a 33- b i: (2) it is merely po
tential and presupposes an ani
mal capable of breathing, which
may not exist, I38 b 30-37.

Not the genus of wind ,
I27 a 4. Full of air )( empty ,
152*19-34,

Windlessness : air = calm :
sea, io8 a 11-12, b 24-6.
Ajax, more like Achilles, and . . a
better man, than Odysseus,
Ii7 b i3, 1 6, 24.

Alteration (aAXoi coo-iy), a species
of motion , 121*32: pleasure
not an a., ib.
Ambiguity, inevitable because

things infinite, names finite, in
no., i65 a 6-i3. Importance of
detecting, io8 a 18 foil. : rules
for, Bk. I, ch. 15.

As source of tests of accidents,
lio a 23- b 15. To be avoided in
rendering Genus, 123*27-29,
33-7, I27 b 5-7 ; in rendering a
Property correctly (/aiAou), I2g b
30 foil., or its subject, 130* 15
foil. ; in Definition, I39 b 19 foil.,
I48 a 23~ b 23. One of most gene
ral and effective tests, 154* 18,
20. A. of term (6 j/o^ia), as opp. a.
of whole phrase (o\os 6 \6yos),
!29 a 30-2. [Cf. lio b 16-17 and
see Amphiboly^

Fallacy of Ambiguity, one of 6
fallacious refutations dependent
on diction, l65 b 26: illustrated,
I65 b 30-l66 a 6, 14-21 : rules for
its solution, Soph. El., ch. 19 and
I79 a 15-19: why deceptive,
l69 a 22-5. Not all sophistical
refutations depend on ambiguity,
!77 b 7-9 (cf. I79 b 38-i8o*7);
only amphiboly and fallacy of
form of expression , i68 a 23-5 ;
resemblance between fallacies
of a. and form of expression,
178*24-28. Depends on latent
double question , I75 b 39-41,
176*14-15. Silliest type of
fallacy, i82 b 13-14 : humorous
exx. of, i82 b 15-21.

A. in questions renders even
genuine refutation disputable,
175* 4o- b 14, 28-30 : leads into
paradox, I75 b 33~7.
Ambiguous terms (v. esp. Bk. I,
ch. 15) : same , 103*7, 25-39,
l69 a 25: good , 106*4, 107*5
foil. : sharp , 106* 13, 32, 107*
13, b i4, 23: papv, 106*18;
fine (KaAoj/), ic6* 20 ; clear
(\VKOV) and obscure (/ifXoi>),
of sounds and colours, 106*25,
b 5, 107*12, b 14, 35 ; dull
(/ij3Avy), 1 06* 32 : pleasure ,
1 06* 37 : to love ($iXeti/), io6 b
2-4 : see OXeVeii/), io6 b 15 :
have sense (alo-ddvfo-dai), lo6 b
23, cf. I29 b 33-4 : just , io6 b
29: healthy , io6 b 34, cf.
I07 b 8-l2: donkey (6W),
107*19,29: to be commensur-
ably related to health

INDEX

fierpus fX flv ni><is vyeiuv), IO7 b
8: colour , 107 28 : desir
able (aiperov), Ii8 b 27: pas
sage into . . . (dycoyi; fly . . .),
I39 b 2i : balance (o-u/x/uerpui),
I39 b 21 : unsupplantable (ane-
TOTrrcoTos), nurse (nOr^r/), har
mony (o-u/zcpamV), I39 b 33:
life (in plants and animals),
148*23 foil. (esp. 27 foil.):
what needs to be (uvayKnlov,
8eoy), i65 b 35-8; eroy and
KVU>V, i66 a i6: Being and
One , i69 a 24, I70 b 21-2 (but
cf. i82 b 24-7).

Ambitious man : def. = one who
strives for honour inadequate,

Amphiboly : as test of Accident,
lio b i6-in a 7 (no technical
name used : described as an
ambiguity pi) naff 6ncavvp.ini ,
dXAu KIIT ii\\ov TpoTrov). To be
avoided in rendering Property,
I29 b 30 (again no technical
name : described as ambiguity
of the whole phrase ). Exx.,
the science of many things is
one , no b i7: immune at
present from destruction (de
scribed as (ifj.(f)ij3o\oi>}, I45 b 24.

Fallacy of Amphiboly : one of
6 fallacious refutations depen
dent on diction, i65 b 26 : illus
trated, 166*6-23: its solution,
Soph. El., ch. 19 and I79 a is-
20 : really depends on ambi
guity , i68 a 2 3 -5, !75 a 36-8:
on concealed double question ,
I75 b 39-41 : renders even genu
ine refutation disputable, I75 a
4l- b S, 28-30.

Analytics, the (Prior], i62 a ii
(II. 2); i62 b 32 (II. 16) : (Pos
terior ), 153* ii n. (II. 3-13) ;
153*24 n. (II. 13) ; l65 b 9.

Anger (opy/) : def. = desire for
vengeance on account of an ap
parent slight , ii;6 a 32 : not def.
= pain -f consciousness of be
ing slighted , I5i a 15-16 (rela
tion being causal and not ex
pressible by + ) : not a kind of
pain, I25 b 29, I26 a 6-i2; but
the effect of pain, 125^3-4:
pain and conception of a
slight seem to have equal

claims to be the genus of a.,
I27 b 30 : situated in the spiri
ted faculty , 113*36: not fol
lowed by hatred, Ii3*35- b 3-
To make answerer angry by ap
pearing unscrupulous, a good
trick in contentious argument,
174*20-3. Good temper not
def. = control of a. , i25 b 2i-7.
Animal: its properties (i) to
have sensation (nioA/o-iy
fX ftv \ i29 b 26-9: (2) to be
naturally sentient (TO mo-dtive-
a-0(u rre(f)vKt is), I33 a 8-II, cf.
i37 b 23-7: (contr., 129^3-5,
where disallowed as improperly
expressed berause of ambiguity
of ai&duvfcrdai = (a) madrjirti
f Xfiv (b) alcrdTjtrei xPW^ai : but
not disqualified as a property in
former sense) : (3) sensation
(TO alvQavta-Qui) , belongs to it
because it has species which
partake of its nature (r<u /xer-
XT0ni), I34 b I, 138* 28. Not a
property of it (i) actively to
perceive (<u(Td<ive(T6<iL = alo-t)r](T(i
XM<JO<" of 129 34), 138*6-8:
(2) to be a substance of which
man is a species (because vir
tually circular, and . . uninstruc-
tive), 131*4-6: (3) sometimes
to move and sometimes to
stand still (because not perma
nent), i3i a 35-7, i33 b 3-4> M4 b
33-145* i : (4) to be sensible
(altrdijTov) or divisible (/*pi-
o-roV), 138*23-5.

A. not a kind of perceptible
or visible thing , 126*22-5 : its
body only a part of a., 126*26-
9. Anything of which a. is predi-
cable is an animal , 109*14-
17 : all animals either species of
a., or individual animals, I44 b
2-3. No common type of life in
a. and plant, 148* 29-31. A.
always take nutriment, but do
not always grow, 1 1 l b 25-6.

Its differentiae: walking
biped , flying biped , 107* 26-
7, 111*26, I33 b 7-n (cf. a i-5)>
i43 b i-2, I44 b i6-i8, 22-4:
quadruped , 111*26: land-
and aquatic , I43 b 2, I44 b 3.6-
I45 a i. ( Walking a quality,
not a kind, of a., 128*25-9.)

INDEX

A. the genus of ox , 102* 39,
144* 34 ; of bird and raven ,
io7 a 21 foil. ; of man , io2 a
34-5, 38 (cf. loi b 29-34) ; 144*
34 : more familiar than man ,
I4l b 29-34: not a property of
man, 136* 19 foil., 137* 23 foil. :
cannot be differentia of any
thing, 143*32: a substance,
I03 b 30-1. A. that walks on 2
feet the defn. of man , io3 a
26-7 (cf. ioi b 29-34) : the addi
tion six-feet high inadmis
sible, i4O b 23-6. Flying biped
a. the defn. of bird , 107* 26-7.

Idea of a. (avrb </uoi/), I43 b

31-

Answerer : his role )( questioner s
role, in dialectic, I59 a 18-24:
in contentious reasoning, 159*
30-32. Rules how to answer,
in dialectic, Bk. VIII, chh. 5-
10; in contentious reasoning,
Soph. EL, chh. 16-32 [v. Solu-
tion~\. May be required to cite
objection, I57 a 35, i6o b I [v.
Objection} ; to bring counter
argument (dvTfjrixfipfiv), see
i6o b 5, 10 ; to furnish a divi
sion, if he refuses the one of
fered, 158*22-4. May ask for
explanation of ambiguous
phrase, i6o a 18-22; or distin
guish its meanings for himself,
l6o a 26-8. To assent without
such distinctions a mistake,
I75 b 28-33, 38-9; though an
swerers shy of drawing them,
for fear of seeming obstructive,
I 75 b 33-6. Must answer Yes
or No to clear question, i6o a
33-4 (cf. I58 a i5-i7).

A. may be to blame for de
generation of argument into
contentiousness, i6i a 17 foil.; or
for petitio principii, or self-con
tradiction of questioner, i6i b
11-17. A. and questioner,
partners in a common task,
i6i a 37-9.

Answers prescribed (in con
tentious argument) to suggest
merely apparent solutions, I76 a
23 foil.

Perplexity (an-opai) of a. two
fold in reasoned arguments,
which proposition is to be de

molished, lS2 b 33-4; in con
tentious arguments, how to
grant the point asked, l82 b 34.

Antiphon, his method of squaring
the circle, I72 a 7.

Antisthenes, his paradox that con
tradiction is impossible, lo4 b 2 1.

did>na.Ta merely = admissions
claimed as premisses, I56 a 23,
I59 a 4, i6o a 7, b 29.

(Apollonides], i82 b 20.

Aporeme, defined, i62 a 17.

Arithmetic (dpid/toi), I53 a 10, l63 h
24.

Arrangement (rdif) of argument :
importance of, in dialectic, Bk.
VIII, ch. i ; in contentious ar
gument, I74 a i3. Rules of, in
dialectic, Bk. VIII, chh. 1-2;
in contentious argument, Soph.
EL, ch. 15.

Astonishment (eWX ; ?)> usually
def. = excessive wonderment ,
I26 b 1 7 : not excess of wonder
ment , I26 b 14-33.

Athenians, l76 b i-2.

Babbling (abo\f<Txtii>) def. = be
ing constrained to say the same
thing a no. of times , 165^ 16.

Results from repeating (i)
same term in a formula, I3o a
34 : (2) same question in a dis
cussion, 158*28: (3) from re
placement of words by their
definitions, I3o a 38: also in
dealing (4) with relative terms,
J 73 bl ~5 : (5) w tn an Y term
whose defn. mentions the sub
stance of which it is the state,
affection etc., I73 b 5-n. Ap
parent )( real b., I73 b 12-16.

To entrap into b., a principal
aim of contentious reasoners,
l65 b 15 : methods employed,
Soph. EL, ch. 13 : how avoided,
Soph. EL, ch. 31.

Bad (i) = KnKov, H5 b 5-7: see
Evil.

(2) = $av\os, io9 b 38. Bad
)( reasonable (fmtiK.es) disposi
tion, ii3 a 13.

To do harm to friends, or
good to enemies, the mark of a
b. disposition, H3 a 9-16.

B. knowledge )( good
8aid), ii 1*23.

INDEX

Badness (</>uvAorr/j) depends
on choice (irpoaipea-is), not on
capacity (dvvafjus), 126* 36.

Bad temper (dwricoXta) def., i6o b
11-13 : how shown in argument,
I56 b 34, i6o b 2~3, :6i a 17 foil. ;
forces questioner to do best he
can, i6l b 9-10. [Cf. Anger.}

Balance (a-vufierpia) : must be
inherent in things whose b.
it is, 125*35-37, i45 9-io.
Health not well def. = b. of
hot and cold elements for (i)
b. is ambiguous, I39 b 2i ; (2)
health is not inherent in hot and
cold elements, I45 b 7-10.

Bandy leg (poiKov), i8i b 38.

Beautiful (K.a\6v) : syn. ( becom
ing (irpfnov), IO2 a 6, I35 a 13 :
statement that the becoming is
beautiful said to be defini-
tory , io2 a 5. To be becom
ing , not its property, since
identical, I35 a 12-14. Not def.
= what is pleasing to the eyes
or to the ears , 146*22-31.

Neither genus nor species of
white , I28 a 3~4.

Beauty (xaXXos) valued only for
appearance (So), and . . not so
desirable as health, Ii8 b 20-21.
Genuine and sham b., i64 b 20.

Becoming (i) generation , com
ing-to-be (yeVeo-ts), a species of
motion, Ili b 7: not def. = a
passage into being (ayojyr/ ds
ovcrinv), for passage is am
biguous, I39 b 20. Modes of b.,
as tests of predications of Acci
dent, 1 1 4 b 16-24, H9 b 8-i5;
of comparative values of things,
n? b 3-9; of Genus, I24 a 2o-
30; of Property, I37 a 2i- b 2;
of Sameness, 1 51 b 36-1 52* 4.
(2) rrpeVoi/. v. Beautiful.

Being: ambiguous and difficult
to divide, i6g a 24, i7o b 2i-2
(but cf. i82 b 24~7) : to be ca
pable of being acted on or of
acting , a property of B., 139*
4-8 ; but B. not definable so,
146*22-3, 31-2; esp. by a
Platonist, 148*18-21. A uni
versal predicate, 121*17, b 7,
127*27,33: has no genus, I2i a
16-19 : commensurate with
Unity (TO tv) and . . neither

genus nor species of it, 121
7-8 : generally thought to be
long in highest degree to sub
stance or what is one with sub
stance, 169* 35.

Object of opinion (<5on-
0-roV ) not a species of being, 1 2 i a
21-5 ; but taken as basis of so
phistical proof that what is not,
is, 167*1-6, 180*32-4, 36-8.
Melissus 1 view that B. is one
a thesis (paradox), iO4 b 23.
Tests of predications of Pro
perty derived from interchange
of verbs to be , to become ,
to be destroyed , with both S
and P, 137* 21 foil.

Bekker, 1 49*29 n.

Bird : species of animal , genus
of raven , 107* 23 : flying bi
ped animal its definition, 107*
26-7; flying biped its property,
I33 b 7-n (if text be kept, but
see n. ad loc.).

Black: (i) a species of colour,
I23 b 26: its differentia, that it
compresses the vision (o-uy-
KpirLKov m/moy), I53 a I, C f. IO7 b
29-30 : b. and white are con
traries, io5 b 36, i I9 a 27-8 ; be
tween which all other colours
are intermediate (pfrav), I23 b
27 : grey an intermediate,
lo6 b 6.

(2) Applied to sounds = ob
scure , io6 a 25, b 6-7 : its con
trary = clear (Xeu/cds) : but
no intermediate, unless perh.
harsh (<rop(p6s), Io6 b 7~8.

Blind: def. = not having sight
when it would naturally have it
(negative defn., but permissible,
because inevitable), I43 b 34.

Blindness : def. = privation of
sight in the eye , !47 b 34-5:
cf. I09 b 22, 114*10, 124*38: a
species of insensibility ,i24 b 6:
its property not to see, inas
much as we have not got our
natural sight , 136*2-4.

Body: not ambiguous, 130*10:
not well defined = that which
has 3 dimensions (genus being
omitted), I42 b 24. To be col
oured , allowed to be its pro
perty, belonging to it deriva
tively (u>s KUT ( iAXo), because it

INDEX

possesses a surface, 134^ 10-
13 ; but elsewhere denied to be,
because (l) an attribute of sur
face as well, !34 a 22-5; (2)
what is more or less a body
is not . . more or less coloured,
I37 b 18-20; (3) whether the
property of surface or not, it
cannot in either case be that of
body , 138* 15-19. Einpedo-
cles doctrine of 4 elements of
bodies, lo5 b 17. Of bodies, fire
the readiest to move upwards
in space, 130* 13; the most
rarefied and lightest, I3o b 29~
31: light consists of most rare
fied particles, 146*16-17: earth
specifically the heaviest, I32 b
313. B. cannot mingle with
what is incorporeal, I49 b 1-2.

The body : less good and im
portant than the soul, 118*32-
3 : to be fitted to obey (vnrj-
pfTtKov) a relative property of it
(rel. to the soul ), I28 b 18-19.
B. not the genus of animal ,
being only a part, I26 a 28-9 : to
be compounded of soul and b.
a permanent property of a
living creature , 129*2, 131*
8, I37 b 13. Bodily )( spiritual
sense and want of sense, io6 b
23-8 ; bodily )( spiritual virtue
and vice, I53 b lo: those in a
sound state of b., the standard
of what is absolutely healthy,
142* II.

Bone not well defined = the com
position of fire, earth, and air ,
1 5 i a 23-3 1 (cf. Flesh}.

Breathing (n-poo-wS/a), I77 b 3- (Cf.
Accent.}

Bryson, his method of squaring
the circle, I7i b 16, 172*4.

Builder: not his property to
produce a house , 137* I. 13. :
production of house = doctor :
production of health, 136 35.

Building, a kind of activity, I24 a
21.

Bywater, /., I74 b 27 n.

Calltas, 176*1, 7, 179*5.
Callicles, 173*8.
Calliope, I73 b 3o.
Capacity (8vvnfjLis\ considered as
kind of disposition (ftuiOea-ts),

124*32. Not the genus (i) of
the state (eiy) which it accom
panies, I25 b 2o: (2) of any
blameworthy or objectionable
act, 126*30 foil.: (3) of any
thing intrinsically precious or
desirable, I26 b 4~6. Always
desirable, I26 a 37 (cf., however,
H9 b 25), but only as means to
something else (fit* dXXo), I26 b
5-6.

As test of genus, 124*31-3 ;
of property, I38 b 27~i39 a S.

Distinction of c. )( state as
source of test for predication of
Genus, i25 b 20-7.
Sensation aurdipow not al

ways a c., 1 19 1-2.

Self-

control (e-yKpdrein) a c. rather
than a virtue, I28 a 8.

Carpentry, n6 a 1 8.

Carriage ($opd) : (l) a kind of
locomotion (.ara -ronov KLV>)-
ats), viz. involuntary )( walk
ing (/SdSitm), I22 b 32~5, I23 a

3-5 : Plato s def. of locomo
tion = carriage criticized,

I22 b 26.

(2) same word (0<>p) in wider
sense = locomotion (q.v.),

I42 b 3 (<j)opa 17X1011 VTTfp yri?).

Categories : ten distinguished, iO3 b
21 : as sources of tests of am
biguity, 107*3-17; of Genus,
I2o b 36-121* 9, 122*3-19, b 1 6-
17, I24 b 15-22, 128*13-19 (cf.
125" 15-19); of Differentia, 128*
20-9 ; of Property, 132* 10 foil,
(requires S first to be placed in
its essence by mention of its
genus), I32 b 35 foil, (forbids ren
dering of any essential attribute
as property) ; of Sameness, 152*
38-9 : as source of solution of
fallacy of Form of expression,
178*4 foil.

Diff. meanings of good ,
illustrated in different c., 107*
5-11 ; argts. to be developed on
each, !O5 b 13.

Choerilus, 157* 1 6.

Clearness in argument (TO cra^eV-
Tfpov tivui TOV \6yov) one of the
aims of non-necessary pre
misses, I55 b 23: how secured,
157* 14-1 7 : of three kinds, 162*
35- b 2.

INDEX

Clean, 182*32.

Cleophon, I74 b 27.

Cloud not def. = a condensation
of the air , I46 b 29.

Coal (= live coal, <"vdpa), a spe
cies of fire , !34 b 28-29: to
burn , not its property, I38 b
18-20.

Colour, ambiguous (i) of bodies,
(2) of tunes, I07 b 28-32 : genus,
not accident, of white , 109*
36, 1 23^26; also genus of
black , I23 b 26; and of all
intermediate colours, I23 b 27.
Its differentiae (as applied to
bodies) = sight-piercing (8ia-
KpiriKov o\|/-eoK, cf. 1 19*30, I53 a
38) and sight-compressing
(crvyK.piTiK.6v ox^ftof, cf. I53 b l),
Io7 b 29-30. Not a kind of com
pressing (<rvyKpiriKoi>), I23 a 2.

Combination (avvQecris}, Fallacy
of: one of 6 fallacious refuta
tions dependent on diction, i65 b
26: illustrated, 166*23-32:
why deceptive, 169*25-7: its
solution, Soph. El., ch. 20 and
179*12-13: a form of ign.
elenchi, 168*26 foil.

Composition (a-wfao-it) : contrary
of decomposition (fiidXutm),
151*28 :)( compound (avvdc
TOV), or whole (o\ov), 151*20-

31-

Compound (crvvderov), rule for
definition of, I48 b 33 foil. [cf.
Composition}.

Concave (KOL\OV), general t. ap
plied to snub-nose and bandy-
leg, I8l b 38 foil.

Concealment of intended conclu
sion (Kpv\l/is TOV crvp.TTfpnap.n-
TOS), an aim of non-necessary
premisses, 155* 23 ; contentious
in motive, I55 b 26. Rules for
obtaining, in dialectic, 156*7-
157*5; in contentious argu
ment, Soph. El., ch. 15.

Conception (vn6\ij\l/ts) : genus of
knowledge , 114*18, H9 b 3,
125*9-11, cf. I30 b i5, 131*23,
I46 b 2 : not = kn., 149* 10. Not
genus of conviction (/rumr ),
I25 b 29, 35-126*2: though def.
of conviction = vehement
conception (imd\r;^is crcpodpd)
usually accepted, I26 b 18.

Consequences (TO. aKo\ov6d ,m b
17 foil., 112* 1 6 foil. ; ra napf-
-rro^fvn, 1 17* 5 foil.) : as tests of
predication of Accident, m b
17-23, 112*16-23; for distin
guishing values otherwise in
distinguishable, 117*5-15; as
tests of definition, I45 b 11-20,
and I5o a 22- b i8 (definition of
X as the product of A + B

TO (K TOVTUtv).

Prior )( later c. \npoTfpov )(
viTTfpov fTTf>p.ti>a\, 1 1 7* 1 1.

Consequent, Fallacy of: one of 7
fallacious refutations not depen
dent on diction, l66 b 25: ana
lysed and illustrated, 167 1-20:
its solution, Soph. EL, ch. 28 :
why deceptive, i69 b 6-7 : a form
of ign. elenchi, l68 b 27-169* 5.
A branch of fallacy of Accident,
i68 b 27-8, l69 b 6-7 : its dis
tinctive feature, always to re
quire more than one subject,
i68 b 28 foil.

Contact (ctyty) ; the genus, not a
species, of juncture (awo^fj),

I22 b 25-8.

Contentious (f piariKos) Reason
ing : defined, ioo b 23, i6s b 7-8 :
effects only apparent refutation,
165*19-24, 175*33 foil.: those
properly )( those improperly
called reasoning , 101* I.

C. )( dialectical reasoning,
108*33-7, 112*4-11,161*33-4,
162* i6-i8,i7i b 6-7, 34-172* 1 S
(so too refutations , I7o b 9~
10). C. r. to be avoided, if pos
sible, in dialectic, 108*29-37
(use of fallacy), 112*9-11 (ap
parent confutation on irrelevant
side-issue), 161*33-4; but
sometimes inevitable, I33 b 36-
134*4, i55 b 26-8, 161*21-4.
C. )( dialectical way of bringing
round an opponent, 162*33-4.
C. argument : dialectical do. =
drawer of false diagrams : geo
metrician, 1 7i b 35-7 ; but with a
difference, 171" 38-172* 7, b 1-4-

C. )( Examination - argu
ments, i69 b 23-9 : (so too refu
tations , I70 b 10-11).

C. )( Sophistical argument,
distinguished by motives of ar-
guers, 1 7 i b 25-34.

INDEX

possesses a surface, I34 b 10-
13 ; but elsewhere denied to be,
because (l) an attribute of sur
face as well, !34 a 22-5; (2)
what is more or less a body
is not . . more or less coloured,
I37 b 18-20 ; (3) whether the
property of surface or not, it
cannot in either case be that of
body , 138* 15-19. Empedo-
cles doctrine of 4 elements of
bodies, io5 b 17. Of bodies, fire
the readiest to move upwards
in space, 130*13; the most
rarefied and lightest, I3o b 29-
31: light consists of most rare
fied particles, 146*16-17: earth
specifically the heaviest, I32 b
313. B. cannot mingle with
what is incorporeal, I49 b 1-2.

The body : less good and im
portant than the soul, 118*32-
3 : to be fitted to obey (vnr)-
pfTLKuv) a relative property of it
(rel. to the soul ), I28 b 18-19.
B. not the genus of animal ,
being only a part, I26 a 28-9 : to
be compounded of soul and b.
a permanent property of a
living creature , 129*2, 131*
8, I37 b 13. Bodily )( spiritual
sense and want of sense, io6 b
23-8 ; bodily )( spiritual virtue
and vice, I53 b io: those in a
sound state of b., the standard
of what is absolutely healthy,
142* II.

Bone not well defined = the com
position of fire, earth, and air ,
151*23-31 (cf. Flesh}.

Breathing (Trpoo-w& a), I77 b 3- (Cf.
Accent.}

Bryson, his method of squaring
the circle, I7i b 16, 172*4.

Builder: not his property to
produce a house , I37 il I. B. :
production of house = doctor :
production of health, 136 35.

Building; a kind of activity, 124*

21.

Bywater, /., I74 b 27 n.

Callias, 176*1, 7, 179*5.
Callicles, 173*8.
Calliope, !73 b 3O.
Capacity (8vvnfjus\ considered as
kind of disposition (ftiadTis),

124*32. Not the genus (i) of
the state (eiy) which it accom
panies, I25 b 2o: (2) of any
blameworthy or objectionable
act, 126*30 foil.: (3) of any
thing intrinsically precious or
desirable, !26 b 4-6. Always
desirable, 126*37 ( c f-> however,
H9 b 25), but only as means to
something else (6V uXAo), i26 b
5-6.

As test of genus, 124*31-3 ;
of property, I38 b 27-139*8.

Distinction of c. )( state as
source of test for predication of
Genus, I25 b 20-7.
Sensation (aiad^ns) not al
ways a c., H9 b i-2. Self-
control (eyKpdreia) a c. rather
than a virtue, 128* 8.

Carpentry, 116* 1 8.

Carriage (<$>opa) : (i) a kind of
locomotion (Kara -ronov KIV>]-
(Tis-), viz. involuntary )( walk
ing Oa&o-iy), I22 b 32-5, 123*
3-5 : Plato s def. of locomo
tion = carriage criticized,

I22 b 26.

(2) same word (</> >p) in wider
sense = locomotion (q.v.),
I42 b 3 (0opa 17X1011 v

Categories : ten distinguished, ic-3 b
21 : as sources of tests of am
biguity, 107*3-17; of Genus,
I20 b 36-i2i*9, 122*3-19, b 16-
17, I24 b 15-22, 128*13-19 (cf.
125 15-19); of Differentia, 128*
20-9 ; of Property, 132* 10 foil.
(requires S first to be placed in
its essence by mention of its
genus), I32 b 35 foil, (forbids ren
dering of any essential attribute
as property) ; of Sameness, 152*
38-9 : as source of solution of
fallacy of Form of expression,
178*4 foil.

Diff. meanings of good ,
illustrated in different c., 107*
5-1 1 ; argts. to be developed on
each, io5 b 13.

Choerilus, 157* 1 6.

Clearness in argument (TO <ra$e<r-
Tfpov fivai TOI> Adyov) one of the
aims of non-necessary pre
misses, I55 b 23: how secured,
157*14-17: of three kinds, 162*
35- b 2.

INDEX

Clean, 182*32.

Cleophon, 174*27.

Cloud not def. = a condensation
of the air , 146^29.

Coal (= live coal, avdpa), a spe
cies of fire , I34 b 28-29: to
burn , not its property, I38 b
18-20.

Colour, ambiguous (i) of bodies,
(2) of tunes, lo7 b 28-32 : genus,
not accident, of white , 109*
36, 1 23^26; also genus of
black , I23 b 26; and of all
intermediate colours, I23 b 27.
Its differentiae (as applied to
bodies) = sight-piercing (8ta-
KptriKov 3\|/-eoK, cf. H9 a 3o, 153*
38) and sight-compressing
(crvyKpiriKov o\^fo>f, cf. I53 b l),
I07 b 29-30. Not a kind of com
pressing (o-uyKpn-iKoi/), I23 a 2.

Combination (a-vvdea-is), Fallacy
of: one of 6 fallacious refuta
tions dependent on diction, i65 b
26: illustrated, 166*23-32:
why deceptive, 169*25-7: its
solution, Soph. El., ch. 20 and
179*12-13: a form of ign.
elenchi, i68 a 26foll.

Composition ((rw6f<ris) : contrary
of decomposition (fiuiXuo-is),
151*28 : )( compound (avvdf-
TOV), or whole (oW), 151*20-

31-

Compound (o-vvdfrov}, rule for
definition of, I48 b 33 foil. [cf.
Composition}.

Concave (KolXov), general t. ap
plied to snub-nose and bandy-
leg, I8l b 38 foil.

Concealment of intended conclu
sion (Kpv\l/is TOV crvfjiTTfpaap.n-
TOS), an aim of non-necessary
premisses, I55 b 23 ; contentious
in motive, I55 b 26. Rules for
obtaining, in dialectic, 156*7-
157*5; in contentious argu
ment, Soph. El., ch. 15.

Conception (VTTO\>]\)/IS) : genus of
knowledge , 114*18, Ii9 b 3,
125*9-11, cf. I30 b i5, 131*23,
I46 b 2 : not = kn., 149* 10. Not
genus of conviction (TTLO-TIS),
I25 b 29, 35-126*2: though def.
of conviction = vehement

conception (viro\T)\lris cr<po8pd)

usually accepted, I26 b 18.

645-26

Consequences (to. aKo\ovdd ,m b
17 foil., I12 a l6 foil.; TO. napf-
iroufva, 1 17* 5 foil.) : as tests of
predication of Accident, m b
17-23, 112*16-23; for distin
guishing values otherwise in
distinguishable, 117*5-15; as
tests of definition, I45 b 11-20,
and I5o a 22- b i8 (definition of
X as the product of A + B -

TO (K TOVT(M>1>).

Prior )( later c. [rrpoTtpov )(

VtTTfpOV fTTOflflHl], 117*11.

Consequent, Fallacy of: one of 7
fallacious refutations not depen
dent on diction, i66 b 25: ana
lysed and illustrated, 167 1-20:
its solution, Soph. El., ch. 28 :
why deceptive, i6g b 6-7 : a form
of ign. elenchi, l68 b 27-169* 5.
A branch of fallacy of Accident,
i68 b 27-8, l69 b 6-7: its dis
tinctive feature, always to re
quire more than one subject,
i68 b 28 foil.

Contact (a\l/ts) ; the genus, not a
species, of juncture (awo^fj),

I22 b 25~8.

Contentious (epuTTiKos) Reason
ing : defined, ioo b 23, i65 b 7-8 :
effects only apparent refutation,
165*19-24, 175*33 foil.: those
properly )( those improperly
called reasoning , 101* I.

C. )( dialectical reasoning,
108*33-7, 112*4-11, 161*33-4,
162* i6-i8,i7i b 6-7, 34-i72 a 15
(so too refutations , I7o b 9-
10). C. r. to be avoided, if pos
sible, in dialectic, 108*29-37
(use of fallacy), 112*9-11 (ap
parent confutation on irrelevant
side-issue), 161*33-4; but
sometimes inevitable, I33 b 36-
134*4, !55 b 26-8, 161*21-4.
C. )( dialectical way of bringing
round an opponent, 162*33-4.
C. argument : dialectical do. =
drawer of false diagrams: geo
metrician, 1 7l b 35-7 ; t> ut with a
difference, 1 7 i b 38-172* 7, b 1-4-

C. )( Examination argu
ments, i69 b 23-9 : (so too refu
tations , I70 b 10-11).

C. )( Sophistical argument,
distinguished by motives of ar-
guers, 1 7 i b 25-34-

S

INDEX

5 aims of c. (sophistical) rea-
soners (Refutation, Fallacy,
Paradox, Solecism, Babbling),
Soph. EL, ch. 3.

2 types of c. (sophistical) rea
soning, i69 b 2o-4, 17 i b 8-10, II
foil.

C. Refutation ; its forms dis
covered by same method as
forms of apparent reasoning,
Soph. EL, ch. 8: does not refute
absolutely, but always relative
ly to answerer, I7o a 12-19.

C. reasoning sometimes de
mands apparent rather than
real solutions, I76 a 19 foil. : un
scrupulous, !59 a 3o-2, I7i b 24-
5, 174* 21-3 : like a foul (d8i-
/aa) in a race or fight, 171^22-
5, I74 a 22 : c. tricks and rheto
rical tricks, I74 b 19 foil.

How to put questions in c.
reasoning, Soph. EL, ch. 15 :
questioners less inclined than
formerly to seek Yes or No
answer, I75 b 8-io.

Most incisive (Spi/ni/raTor) of
c. argts., l83 a 7- Traditional
teaching of c. argt. compared
to Gorgias teaching of rhetoric,
i83 b 36foll.

Contradictory terms (KCIT dvrifya-
cnv aVTKtifuva : (f)dcris Kal drro<pa-
trif), as sources of tests of am
biguity, io6 b i3~2o; of Acci
dent, 1 1 3 b 1 5-26; of Genus,
I24 b 7-14 ; of Property, I36 a 5-

b 2.

Contrary terms (fvavria) : as tests
of ambiguity, io6 a 9~ b 12; of pre
dications of Accident, H2 b 27-
H3 b 14, H3 b 27-ii4 a 6, Ii4 b 6-
15, Il9 a 37- b l ; of comparative
values of things, Ii7 b 4~7; of
comparative estimates of any
quality, H9 a 27-8; of predica
tions of Genus, I23 b i-I24 a 9,
I 53 a 33~6 ; of Differentia, I53 a
36- b 24; of Property, I35 b 8-
16; of Definition, I4o a 18-20,
I47 a 32- b 25, I5i a 32- b 2, i53 a
26, 29-31.

Terms with c. )( terms with
none, io6 a 36. C. with inter
mediate terms, io6 b 4- C. in
same thing (e. g. Tightness and
wrongness in sensation), how

shown, II i a 14 foil. C. cannot
coexist in same subject, H3 a
22 ; but contr. Heraclitus (on
good and evil), I59 b 3o~3.
Whatever subject admits one of
a pair of c. must admit the other
too, ii3 a 34-5. C. subjects
have c. attributes, Ii3 b 27 foil.,
and associations, H3 b 34 foil.
C. have either same ore. genera,
I53 a 35~6 ; have same differen
tiae (if genera be c.) or c. (if
genus be same), 153*36-7, b 4~
12, 17-18.

Knowledge of c. one, lo5 b 5-
6, 23, iio b 2o, !55 b 3o-4, i56 b
II, i63 a 2-3, i64 a i-2, I7i a
36-8.

If any statement generally
accepted (and . . a fit premiss
for dialectic), so will contradic
tion of its c. be, io4 a 13.

Contrary used loosely =
opposite , I47 b 7, 10, 17, 20.

Contrary acts : Of the six
combinations (av/jTrXoKai) pos
sible between the acts formed
by combination of 2 c. verbs and
2 c. objects, four produce c.
acts, I I2 b 27-8, I I3 a 8-14, each
of these acts having 2 contraries
among the others, H3 a 14-18.
Acts are c. if they treat same
thing in c. ways ( 1 1 2 b 34, 1 1 3 a 9),
or c. things in same way (ll2 b
36, II 3 a 9), but not if they treat c.
th ings in c. ways ( 1 1 2 b 3 1 , 1 1 3 a I ).

Contumely (Trpon-^Xn/cio-^dj) not
def. = insolence accompanied
by jeering (for j. is a species,
not differentia, of insolence),
I44 a 6.

Conventional language, breach
with, a fault, io9 a 28 : c. to be
followed in regard to connota-
tations, but not denotations, of
terms, I lo a 14 foil., I48 b 20 foil.

Conversion (ovnirTptfaiv) = (l)
transition from P belongs to S
to S is P ; valid if P is defini
tion, or genus, or property, but
precarious if P is accident, of
S, lO9 a 10-26.

(2) conversion by negation
(17 Kara rr\v dvTl<f>a<TlV aKoXovdr)-
cris dvdnahiv yivo^fvf]), from A
is B to Nonot-B is A ; as

INDEX

test of Accident, ii3 b 15-26;
applied to Genus. I24 b 7-14.

(3) reductio per impossible,
163*32-6.

Conviction (TriVriy) : not a kind
of conception (vnoX^is), I25 b
2 9i 35~l26 a 2: not = ve
hemence of conception , I26 b
14-33 : but definition = a ve
hement conception passed as
generally accepted, 126 17-18.
Genus of knowledge , I28 a 35-7.

Cooling: def. = privation of
heat , I4i a 12-13 : not properly
def. = privation of natural
heat ( natural implied in pri
vation ), 141* 10-14.

Co-orltinates (o-ucrroi^a) of X, def.
= (i) terms related to X as are
just deeds (or a just man )
to justice, U4 a 27.

(2) anything tending to pro
duce or preserve X, I I4 a 29.

)( inflections , 114*32; but
often held to include them, i I4 a

34-

As tests of Accident, 114*26,
38 foil.; Ii9 a 38, b 6-8; of
Genus, I24 a 10-14; of Defini
tions, i47 a 2i-2, I53 b 25-35 ; of
Sameness, 15 i b 28-33. Reck
oned among most generally
handy tests, I54 a l2-i3. Put
ting question about co-ordinates
of S, instead of about S direct,
recommended as method of
concealment in dialectic, I56 a
27 foil.
Knowledge ofc. one, i64 a 1-2.

Co-ordinates in a division (di/ri-
diyprjp.{va) : as tests of Property,
I36 b 3-14 ; of Definition, I42 b
7 foil.; of Differentia, I43 a 34
foil., b 2, 6, 35-i44 a 4-

Coriscus, i66 b 32, I73 b 3 1 .38,
I75 b 19-23,25, I76 a 7, I78 b 39>
I79 a i, b 2-3, 9,28, 32, i8i a io,

l82 a 20-I.

Correct rendering (TO Ka\o)s O.TTO-
Movai) : of Properties, Bk. V,
chh. 2-3 : of Definitions, 139*
34, b 6, !2-i4i a 24. Sources of
incorrectness (i) obscurity
(q.v.), I39 b i2, (2) redundancy
(q.v.), I39 b i5.

Courage: not properly def. = (i)
control of fears ; rather im

plies total immunity from fear
!25 b 22-7: (2) daring + right
reasoning (no guarantee that
the two are found in same circs,
and relations), 151* 3-13. Found
in soul, I5o b 36.

Is justice same as c., how
determined, I5i b 3i~3: justice
not def. = temperance and cour
age, 150*3. Good intrinsically
(contr. means of health), 106*
4 foil. (cf. 107*5-8): more de
sirable in youth than in age,
117*30: less desirable than
justice and temperance, 117*
36, 38; than justice, n8 a i7,
36 : goodness of c. transcends
evil of false opinion, I5o b 4~5.
Courageous , syn. strong at
heart (fityi^or), 112*33.
Covetous man (^iXo^p^udTos), not
def. = one who strives for
money (for quantity of money
should be stated), I46 b 25.

Day : def. = passage of the sun
over the earth , I42 b 3.

Deafness : not its property to be a
lack of sensation , i35 b 3l-2.

Debility (/ca^e^ia) : contrary of
vigour , H3 b 35-6, I57 b 18-
20, 23: follows on disease, H3 b
36: less evil than disease, I57 b
20.

Decomposition (Sri Xwir) ; con
trary of composition (vvvQf-
<ris), 151*28. Considered as
kind of destruction ((pdopii],
124* 23-4, 28-9 : but contr.
I53 b 3i, where (pdopd is sug
gested as kind of decomposi
tion (SiaXucrts oucrt ar).

Defect (eWieia) : contrary of ex
cess ({nrepftoXr)), in same genus
(Evil), I23 b 28: moderate
amount (TO ptTpiw) intermedi
ate between them, I23 b 29.

Definition (5,)os, 6picrp.6s) : def. =
an attribute peculiar (like Pro
perty), and essential (contr.
Property), ioi b 19-21, 39: of
term (wopa) or of phrase (X6-
yor), 102* i : always consists of
a phrase, 102*4, H8 b 36-149*4-
Always same as definitum, 102*
7-14; though what is same as
definitum not always its d., 102*

S 2

INDEX

14. Examination of likeness of
things useful for d., io8 b 9, 19
foil. Rules for d., Bk. VI,
passim.

Must (l) consist of genus and
differentia, lO3 b 15, 139*28,
!43 b 8-9, 19-20, 153*15-21,
b 14-15, I54 a 26-7 : (2) be true
universally, 1 39* 26-7, 1 4o b 21-3,
I54 a 36- b i: (3) be peculiar,
ioi b 19-21, I09 b 10, 139*31, b 3,
!49 b 22-3, 154 b 1-3, 10-12, I55 a
20: (4) express essence, ioi b 2i,
39,139*33: (tests for this, 141*
24 foil.): 155* 21 : and whole es
sence, I53 a 16-17, 21-2, 154 a 29:
(5) render appropriate genus,
I39 a 29, b 3,i43 a i2, I55 a 2o:
viz. proximate (eyyvTa.Ta>) genus,
I43 a 19 : (6) add appropriate
differentiae, I39 a 2g : (tests for
this, I43 a 29 foil.): must state
them fully, I46 b 2ofoll. : (7)
make clear also d. of contrary
term, i4O a 18-20: (8) not be
circular, I42 a 34: cf. I47 b 12
foil., 20 foil.

D. more scientific (eVumj/iow-
Kwrf poi>) , if rendered of posterior
through prior terms, I4i b i6;
but d. through terms more in
telligible to A or B sometimes
necessary ad hominem, I4i b 17
foil. 2 different d. of same es
sence impossible, I42 b 35, I53 a
21-2 : treated as absurd, 141*
31-2, I48 b i4, 151*33-4, b 16-
17. One d. of 2 different
essences also impossible, 154*
10-11 : treated as absurd, I53 b
24. Equimembral d. def.,

Definition and other predicables :
D. amenable to all tests for
other predicables, io2 b 27 (cf.
I55 a 7-io), though distinctions
should be kept for clearness,
io2 b 35: cf. Accident, 139*36-
b 3 ; cf. Genus, io2 b 27, I2o b 13,
I39 b 3-5. J 43 a 12-14 ; cf. Pro
perty, I2o b i3, I39 b 3~5, I54 b
18-23 : es P- (0 no term must
be repeated, 130*29-31, I4o b
27 foil. : (2) no universal predi
cate must be used, I3o b 11-14,
I4o a 24 : (3) nothing super
fluous must be added, I3o b 25-8,

I39 b 15, 14o a 24foll.: (4) neither
S nor any of its species must be
mentioned, !3O b 38 foil., and
cf. 1 42* 34 foil.

Tests for d. not all applicable
toother predicables, 155* 10. Of
other predicables, Property
most like d., 155*23 : but d. not
to be rendered as property, 13 i b
37 foil. Of elements in d., Ge
nus is principal mark of essence,
139*29-31.

Science of d. (Apurruaf) a
branch of speculative science
dfuprjTi CT]), 141*8: exact ac
count of d. not the business of
dialectic, 153* 11-12,24-5. D-
generally assumed by the sci
ences, not proved, 153*7 ; but
dialectical proof possible, 153*
13-22. D. the only way to
grasp the fundamentals in sci
ence, 158* 33, b 1-4 (one of the
principal uses of dialectic study,
101*36). Dialectician should
collect d., esp. of primary and
recurrent concepts, i63 b 2o. For
lack of d., problems often prove
intractable, in dialectics, 1 58" 1 7,
24 foil.; in maths., I58 b 29 foil.

Disproof of d. the easiest of
all tasks of dialectic, 155* 3-10 :
proof of d., the hardest, 155*18-
22. Both d. and Property easier
to disprove than to prove, and
for like reasons :

(1) disproof requires one con
clusion only, proof requires
many, 154*32-6, b 15-18.

(2) proof of either must be
universal, whereas one neg. in
stance disproves, 154* 36- b 10,
19-22.

(3) proof of either requires
that formula be shown to be not
only universally true, but pecu
liar, 154 b io-i2, 22-3.

D. of terms used, as test of
ambiguity, 106*3, io7 a 36- b l2;
of Accident, !O9 b 3o-iio a 9, m b
12-16; of comparative estimates
of any quality, 119*29-31 ; of
Genus, !2o b 3o-5, I2i a 10-19,
I22 a 7~9, b 7~ii; of Property,
130*38 ; of Definition, I4o b 29
foil., !42 b 2-6, 146*33-5, I47 b

INDEX

Definitory (opiicov) ; applied (i) to
elucidation of term by synonym,
102*5: (2) to every problem
respecting sameness and differ
ence, I02 a 6: (3) to any pro
blem bearing on inquiry into
definitions, 102* 9. In a sense all
inquiries on any predicable do
this last, iO2 b 27 foil. (cf. s.v.
Definition}^ and are therefore
derinitory, io2 b 33 : but better
to distinguish d. problems )(
generic do. (yei iKa), iO2 b 35~
103*4.

Demonstration: def., ioo a 27:
requires systematic deduction
from principles appropriate to
subject, 158*36-7. Every d.
also a refutation, !7o a 24-6.
)( Dialectic [q.v.], does not pro
ceed by question and answer,
172*15-21. )( Examination-
argument held ace. to principles
of dialectic, I72 a 21 foil., 39~ b I.
Demonstrations, like sciences,
perh. infinite in no., 170*22-3.

Desirable (alptrov) : = (i) expedi
ent, (2) honourable, (3) plea
sant, I05 a 27, I l8 b 27 : contrary
of objectionable (06v/crot- ), 1 1 3 a
I2> b 33> I35 b i5 : s y n - proper
object of pursuit (SicoKrov), 133*
28. A property of good , 135
15-16 : but more desirable )(
better , Ii8 a 8-i5: the same
thing may be equally desirable
and objectionable, Ii8 b 37: re
lative to individual, Ii6 a 22,
Il8 a ll, cf. b i5.

Not a property of the d. to
appear good to some people ,
I33 a 26-8. Intrinsically (Si 1
avrci) d. )( d. for sake of some
thing else (fit XXo, fit erepoi/),
Ii6 a 29, I49 b 31 foil. (Tests for
definition of former, I49 b 3i~9.)
Essentially (KH$ avro) d. )( d.
accidentally (Kara a-vuJSffirjicos),
116*31.

Rules for distinguishing de
sirable )( undesirable, and less
)( more desirable, Bk. Ill chh.
1-4. Doing good to friends,
and evil to enemies, both d.,
H3 a 2. Capacity of any kind
d., even of bad man, I26 a 36.
Most desirable , used of 2

terms, does not imply their
identity (unless each is an in
dividual), but only that the one
contains the other, 152* 28-30.

Desire (tnidv^ia) : def. = cona
tion (i) for pleasure , I46 b
11-12: (2) for what appears
pleasant , l47 a i-5. Said not
to be def. = conation for the
pleasant , I4o b 27 foil., though
objection here not really well
founded, I4o b 31-141* 4 : but cf.
I46 b n-i2, 147*1-5. Sexual
love not desire for intercourse*
(see Love). Desire of X am
biguous, iio b 37 foil.

Desire, jaculty of ((mdn^rjriKoi/) :
the seat of friendship ($iXi a),
Il3 b 2: of pleasure and pain,
I26 a 9~io. Incapable of know
ledge, and /. of ignorance, H3 b
3-6. Its property, to be the
primary seat of Temperance
(TO 7Tp>Tt>v crvCfipov), I38 b I 5 :
not its property, to desire
(fTTidv^lv), I38 a 34~5. A pro
perty of the soul to be the pri
mary whole of which faculty of
desire is part, I38 b 13-14.

Destruction (0#opa, (frOdpfa-dai) :
a species of motion (icivtia-dui),
m b 5-7.

Modes of d., as tests of pre
dications of Accident, H4 b 16-
24, 1 1 9 b 8-1 5; of comparative
values of things, U7 b 3~5; of
Genus, I24 a 20-30; of Property,
I37 a 2i- b 2; of Definition, 150*
33-6; of Sameness, 152*1-4.
D. and decomposition (v.
Decomposition} .

Dialectic: critical approach to
common principles of all inqui
ries, ioi b 3 : no definite kind of
being for its province, I72 a 12 :
so of refutations, d. studies only
those based on common prin
ciples, !70 a 38-9, i.e. such as
are (i) really dialectical, (2) so
phistical and only apparently
dialectical, (3) suited to exami
nation, 170 8-1 1. Uses of
studying d., 101*25, 36; cf.
i65 a 19-31, 175 a 5-16. D.comp.
with rhetoric and medicine, loi b
5. Divisions of D., v. Table of
Contents. Problems how to

INDEX

arrange and put questions pecu
liar to d. (contr. philosophy),

I55 b 9-

Dialecti cal proposi ti on and prob
lem (s. v. Propositions and Prob
lems).

Dialectical Reasoning : def., ico a
29, i65 b 3-4, = epichireme,
i62 a 16. Inductive )( deduc
tive, I05 a 10-19.

)( Philosophy, ic>5 b 30-1, 1 55 b
7-16, i62 a i5-i6, "31-3, I75 a
31-3 : but useful for philosophy,
ioi a 34- b 4, i55 b 7-8, i63 b 9-i2,
I75 a 5-i2.

)( Demonstration, 162* 15-16,
I57 b 34 foil., I72 a 12-21.

)( Teaching (Didactic], I59 a
11-14, 26 foil.; i6i a 24-5; i6s b
1-4, I7i a 3i- b 2, i;2 a 15-21.

)( Contentious reasoning
(Eristic, Sophistic], see Con
tentious Reasoning.

D. r. and Examination-argu
ments, I59 a 25, 33, i6i a 25:
distinguished, l65 b 3~6. Ex
amination a branch of d., aimed
at exposing ignorant pretender,
i69 b 25~7, !7i b 4-6: cf. i83 a

37- b I-

D. r. a mode of examination,
I72 a 23- b I : everyone in a sense
an examiner, i72 a 3O-5 : expert
examiner (dialectician) differs in
possessing technique of the
syllogism, !72 a 35-6.

D. r. and Rhetoric, see Rhe
toric.

Dialogue-form, arguments in : 4
kinds (i) Didactic, (2) Dialectic,
(3) Examination-arguments, (4)
Contentious arguments, l65 a

Didactic argument: def. = those
that reason from principles ap
propriate to each subject, and
not from opinions held by an
swerer , i65 b l-2: = demon
stration, cf. together i65 a 39 and
b Q-H. D. )( dialectical reason
ing, see Dialectical reasoning.

Differences of things to be ob
served, io5 a 24 and Bk. 1, ch.
16 : importance of them, io8 a
3 8- b 6.

Differentia : D. and species : D.
belongs to essence of S., io8 b 4~

6, i33 a i-3, I53 a i8, 154^7-8 ;
(but contr. I22 b 15-17 and cf.
I28 a 2o):must . . be appropriate
(l&ia) to S., I43 a 30-1 ; a perma
nent attribute, I23 a 15-19, I45 a
1 1 ; not a property, 1 33" 1 9, 21 ;
not an accident, I44 a 23-7 ; not
merely S. s place or habitat,
I44 b 3i. Absolutely more in
telligible than, and prior to, S.,
I4l b 27-34, I44 b 9-u. Com
mensurate with, or wider than,
S.,i22 b 39-i23 a I,l44 b 6. Iden
tical terms have same d., !O7 b
27-31, I52 b 3. Specific (i8o-
noios] d., I43 b 7-8.

D. and genus : closely asso
ciated, ioi b 1 8 : d. cannot be S. s
genus, nor vice versa, I22 b i2-
15, i23 a 3-5, i26 b i3-33, i28 a
20-9, I44 a 9foll. : nor genus of
S. s genus, I23 a i, 6-10. A
quality, not essential attribute,
of genus, !28 a 26-8 (?cf. I22 b
16-17), I44 a 18, 20-2.

Of narrower denotation than
genus, I2i b 11-14, I23 a 6-io,
I28 a 22. Less expressive than
genus of essence of S., I28 a 23-
6. Cannot be a species of S. s
genus, io7 b 33-4, I44 a 5~8: cf.
!22 b 2o-4. Posterior to genus,
I44 b 10 : genus not a quality of
d., I28 a 27~9. Must be one of
a number of co-ordinates dis
tinguished within S. s genus,
I43 a 34~ b 5. Different and non-
subaltern genera must have
different d., unless the genera
be themselves in same higher
genus, I07 b 19, I44 b 13-25.

Must not be rendered nega
tively, i43 b ii foil. Must be
rendered fully, !42 b 3O, !46 b 2O
(with full determinations of
quantity, quality, manner, cause,
&c.).

Of relative terms, d. must ren
der correlate that isbetter rather
than worse (i43 a 9), natural
(l45 a 19-27) and primary (l45 a
28-32). Of contraries, d. are
contrary if in same genus, or
same if in contrary genera, I53 a
37- b 24.

Dionysius, I48 a 27-

Disease a."km>dioi evil, I23 b i7~l8:

INDEX

brings debility (Ka^f i<0> 1*3
36: a greater evil than debility
I57 b 2o: worse than ugliness
(because greater hindrance to
both pleasure and goodness)
Ii8 b 35= contrary of health ,
with no intermediary, I23 b i7~
18 : but particular diseases
(fever, ophthalmia, &c.) have no
contrary, I23 b 34-7.

Disposition (fiiu$e<7iy),the genus of
knowledge , m a 23, I2i b 38,
I25 a i, I45 a 36 (cf. State}: of
virtue , I2i b 38 : considered as
genus of capacity , I24 a 32.
Must be inherent in the thing
whose d. it is, I25 a 33~7, 145**
33- b 1 1. Knowledge a state and
d. of the soul, I24 b 34, 145"*
36.

Division of terms (into species or
individuals) recommended, !O5 b
31-7 : as test for Accident, lO9 b
13-29, iii a 33- b ii, I2o a 34-
b 6; of Genus, I2i a 27-37; of
Property, I32 a 27- b 3: one of
most general and effective tests,
I54 a i7.

Fallacy of Division : one of
6 fallacious refutations depen
dent on diction, l65 b 26 : illus
trated, l66 a 33-8: why decep
tive, i69 a 25~7: rules for its
solution, Soph. El., ch. 20 and
I79 a 13-14: a form of ign.
elenchi, i68 a 27 foil.

Doctor: his business to take all
possible means to heal, ioi b 5-
10: his views, the accepted
standard in medicine, iO4 a 33~
7, no a 2o-2: his property, to
have ability to produce health ,
I 37 a 3~75 not to produce
health , 136*" 37. D. : produc
tion of health = builder : pro
duction of house, I36 b 35~7
D. : ability to produce health
= trainer (yvfiwzorijf) : ability
to produce vigour (fvcia), I37 a
3-5. [Cf. Medicine.}

Donkey ambiguous, lo/ a 19, 29 :
bears inferior likeness to horse,
il7 b 25-7.

Double (8in\iicriov) : def. of d.
through half (its opposite) per
missible, because inevitable,

Double of X def. = that
which exceeds X by an amount
equal to X , I47 a 3o.

A kind of multiple , I2i a 4~5;
but only in ref. to same unit, 1 24 b
24-7 : )( < multiple , 152" 15-16.
Like multiple , a relative term,
i2i a 3 -5, I24 b 15-18: rel. to
half, 124^ 24, 29, i35 b 19 : pos
sible exception to rule that
genus and species are related to
anequal no. of things, 1 25 a 1 8-24.

Its property, to be in pro
portion of ~ , I35 b 25; not its
property to exceed (TO i

Dull (afriXvs), used (i) of edges,
io6 a 13,32: (2) of flavours, io6 a
32.

Earth: its properties (i) to be
specifically heaviest body ,
!32 b 3i-4: (2) naturally to
fall downwards , !35 b 3-5 ( c ^
I3o b 1-2 for incorrect rendering
of this). Not def. = a nurse ,
I39 b 33= n ot genus of mud ,
I27 a 14. Sun s movement over
e. , I3i b 25-30, I42 b 1-6. Sha-
dow on the e. not adequate def.
of night ; movement of the
e. , not adequate def. of earth
quake , I46 b 28~30.

Enipedocles, his doctrine that there
are 4 physical elements, io5 b 16.

Empty, not = full of air , 152
19-24.

Epichireme, def., i62 a 16.

Equity (enifiKfui), not def. = re
mission of what is expedient
and just (redundant), I4i a 16-
19. Reasonable (equitable)
disposition )( bad one (<f)av-
AOP), Il3 a i3.

Ethiopian, the ; l67 a 11.

(Euarckus), i82 b 2o.

EuthydemuS) 177^12: E., the,
i66 a 14 n., I79 a 35 n.

Even : )( odd, the differentiae of
number , I2o b 3~6, 123 a 11-13,
I42 b 9-io.

E. number not def. = a no.
divisible into halves (circular),
I42 b l2. 2 (17 dvas) = the
only prime no. among even
nos. , I57 a 39-

Events occur (i) of necessity, (2)

INDEX

usually (o>r eVt TO rroXu), (3) by
chance (oitortpa m ^e), H2 b I-2.

Evil (KUKOV) : opposite (oirtKet/ie-
vov) of good , H9 a 36- b i:
contrary (tvavriov) of good,
I05 b 36, I35 b 14-15: e. and
good thing cannot be same,
I52 b i: Heraclitus paradox
that good and e. are same, 1 59 b
30-3 (cf. i63 a 16-17). Sophisti
cal proof that same two things
can be both good, and both e.,
and neither good nor e., i8i b 9-
i6(cf. l8o b 9~2i). Like good , a
genus not referable to any higher
genus, I23 b 8-12. Its property,
to be objectionable (</>eu/cro i ),
1 3 5 b 14-16. Must not appear in
rendering a property of good
(circular), I3i a 17-20; nor in
definition of good , 142*23
(because opposite, and . . not
prior, to g.), and I47 b 18-25
(because circular). The genus
of disease , I23 b 17-18; of
defect and excess , I23 b 28.
That whose destruction is e.
is itself good ; that whose pro
duction is e. is itself e., I I4 b 19-
24. What destroys good, or
produces e., is e. (and vice
versa), ii 9 b 8 foil. What causes
e. essentially (Kaff OUTO) more
objectionable than what causes
it accidentally (KUTCI o-u/xjSf/fy-
KOJ), Ii6 b 4~6: cause of less
e., preferable to cause of more,
117*8-9: what is less con
nected with e., preferable, Ii7 b
31-2. Injustice an e., 115*1 (cf.
ii9 b 4) ; but not its property to
be the worst , I35 b 10-12. If
all (or some) pleasure be good,
all (or some) pain is e., 119* 39-
b i. Any contrary of a good
thing is e., 119*36 foil.; but
principle that greater e. is con
trary to greater good amended
by addition unless one good
involves the other , i57 b 17-24.
Whole formed by addition of
good to e. not necessarily good,
Ii5 b I. Quality of products of
things good, evil, and neutral,
I5o a 36- b 1 8.

Examination-argument : 1 59* 25
foil. : rules how to answer in

such arguments, Bk. VIII, chh.
5-io.

)( Teaching^ 159*33, 161*25.
)( Scientific reasoning: e. de
mands Yes or No an
swers, I7i b 3, cf. 172*15-17.
Requires no scientific know
ledge, but only general know
ledge indispensable to student
of science, 172*21-7; 39- b l :
concerned only with common
principles, 172*27-30: prac
tised by all, 172* 30-4.

( cf. Dialectical Reasoning).
)( Contentious or Sophistical
argument, 159*25, i69 b 2O~9:
but possible toexamine sophisti-
cally as well as dialectically,
i83 b 1-3-

Eye : primary seat of sight and
of blindness , I47 b 34~5 (cf.
29) : not to be described in
definition as brow-shaded
(unfamiliar), 140*4. Sight :
eye = reason : soul, io8 a n.

Fallacy, Fallacious Argument,
False Reasoning (cf. Misreason-
/#.$, and see Soph. E\., passim).
Study of ambiguous terms valu
able both for avoidance and for
perpetration of f., 108* 26-33 ;
though deliberate perpetration
of f. to be avoided where pos
sible in dialectic, 108* 33-7. 4
kinds of f. a., 162^-15: 2
kinds of f. r., I76 b 31-3. F. a.
a fault of arguer rather than of
argument, i62 b 16. Difficulty
of classifying f., in some cases,
Soph. El., ch. 33 init. One of
principal aims of contentious
reasoners, to entrap into f.
(v^ftSo?), i65 b i4: methods em
ployed, 172 10-28: test ques
tions for detecting, i62 b 24-30,
177*2-6.

False Cause, Fallacy of (non
caiisa pro causa], one of 7 falla
cious refutations not depen
dent on diction, i66 b 26: ana
lysed and illustrated, i67 b 2i-
36: its solution, Soph. El., ch.
29 ; why deceptive, 169 13-17 :
a form of i%n. elenchi, i68 b 22-
5 : described as an argument

INDEX

dependent on some addition

l8l a 3i.
Falsehood: sophistical proof that

a man can speak f. and truth at

same time, i8o b 2-7.
False diagrams (^fuSo-ypa^fli/,

\l/(voypd(j)r)/jia), IOI S 6-I7, 132*

33, 157*2, i6o b 36, I7i b i2-i6:
drawer of f. d. : geometrician
= contentious : dialectical ar-
guer, I7i b 35-7; but with differ
ence that f. d. employ genuinely
geometrical principles, I7i b 38-
172*8, I72 b 1-4.

Faults of argument: )( faults of
questioner, Bk. VIII, ch. 11-12
(i6i a i6 foll.- b i8, i62 b 3-24
N.B. 1 6). F. of a. in itself )(
in relation to proposed conclu
sion, i6i b 34-i62 a 3.

5 f. of a. in itself, i6i b 19-33 :
another, 162*24-34. 5 test-
questions for f. of a. in itself,
i62 b 24-33. Argt. always bad
if premisses generally rejected,
esp. if also false; though not bad
because premisses false, if gen
erally accepted, i62 b 27-30.

Fever, I23 b 36.

Fire : its species, live coals
(5v6pa), flame (0Ao), light
($>y), !34 b 28-9: embodied
more in flame than in light ,
I46 a 15-16. Its properties (l)
to be body quickest to move
upward in space , 130" 10-14:

(2) to move naturally upward ,
103*29, I37 b 37 = cf. I37 b 37-
138*2: (3) to consist of most
rarefied particles (belongs spe
cifically), 134*31; but contr.
I34 b 3i foil., 135* 4-5 (property
of light ), and 139*9 fN- ( su ~
perlatives forbidden) : cf. (for
incorrect rendering) 130*36-8:
also cf. i3O b 29-32 (forbids ren
dering of (i) and (3) in one):
I32 b 2i~4 (forbids rendering of

(3) in reverse order). Not def.
= body consisting of most
rarefied particles , 146*13-18.
Not its property (i) to be very
like the soul , I29 b 10 : (2) to be
primary element in which the
soul naturally exists , I29 b i8:
(3) to be the lightest body
(forbidden, as superlative), 139*

14-16. Cannot mix with
colour to form white , 149*
39~ b 3. Flesh and bone not
compositions of fire with earth
and air , 151* 23.

Flame, a species of fire , I34 b
28-9 : more of nature of fire
than light is, 146* 15 ; but con
sists of less rarefied particles
than light, 146* 16. Not its
property to burn, I38 b 1 8-20.

Flesh, not def. = the composition,
of fire, earth, and air , 151*23-
31 (cf. Bone).

F~or get fulness = loss of know
ledge , I53 b 27: but not vice
versa, unless the object be pre
sumed to remain unchanged,
I57 b ii-i6.

Form of Expression (Figura dic-
tionis), Fallacy of; one of 6
fallacious refutations depending
on diction, i65 b 27 : illustrated,
i66 b 10-19. Why deceptive,
169* 29-36 ; more so in argu
ment than in solitary reflection,
169*37-40; though here too,
if reasoning becomes verbal,
l69*4o- b 2. Rules for solution,
Soph. El., ch. 22, and 179*20-
4 : depends on ambiguity, 168*
23-6 ; results esp. from ten
dency to treat all predicates as
if indivl. substances, 168*25-6,
169*33-6, 170*15, and Soph.
EL, ch. 22, esp. 178* 5-8, b 36-
179* 10. Compared to solecism,

!74 a 5-9-
Fraction (TroXXoo-r^optoi ). J, a

fraction, 114*15: relative to
multiple , 114*17, 125*7-9:
genus of half, 125*26-7.

Friendship: if found in faculty of
desire, not a kind of wishing,
126*12-13: cf. H3 b 2. More
desirable than wealth (i) be
cause prized for itself, n6 b 38-
117* 4, (2) because excess of it
better than e. of money, Ii8 b 6.
Friends )( man in the street,
118*2-5. Friends as test of
comparative values of things,
1 1 8* i -2, cf. b 7~9-

Fusion, species, not genus, of
mixture , I22 b 25-6 ; for it ex
cludes m. of dry things, I22 b
30-1.

INDEX

Generic questions, 102* 36 : )( de-
finitory, 103* 3. Differentia
generic , ioi b 18.

Genus, ioi b 17, 25, 38 : ranked
with differentia, ioi b 18-19:
how distinct from, !28 a 2O-9
[and see Differentia], Def.,
102*31-2. Tests for g., apply
to definition too, io2 b 27, 120
13, I39 b 3~5> J43 a i2-i4. Sel
dom made subject of separate in
quiry, i2O b 14. Rules for, Bk. IV,
passim. 2 different g. of same
term must be in subaltern rela
tion, I07 a i8 foil., I2l b 29-30.
All attributes of species belong
to g., 1 1 i a 20-3, 27-9; not
vice versa, m a 25-7: but
contr. !43 b 26-8 (attributes of
g. true of all species) : proper
ties belong in different manner
to a genus (r<a/ire xeo-$ni)and to
a species (T&> ^fre ^ftv), I34 b 1-4,
18-22. Described as species or
kind OiSoy), I33 a 35, b I, 6, 10.
G. and species synonymous ,
123*28-9, I27 b 6, (cf. I54 a i8).
Subaltern )( non-subaltern
genera, 107*19, 22, 33, b 19-
26: I44 b i3> 19. 21. 23,28.

God: cannot be injured, and /.
cannot be wronged. !O9 b 33:
better than man, i i6 b 12-15 : a
living being, who partakes
of knowledge , I32 b ii: an
immortal living being , I22 b
13-14, cf. 37-8 and i36 b 6-7
(Bekker): a permanent pro
perty of G., I28 b 19-20. Nei
ther species nor genus of im
mortal , I22 b 12, 37. Has, but
does not use, capacity to do bad
things, i26 a 34-6. Not His
property to be an intelligible
living-being , i36 b 6-7.

The gods to be honoured,
ios a 5, ii5 b 32.

Gold, genuine and sham, l64 b
22-4.

Good : a quality, I2i a i : contrary
of evil, I05 b 36, I35 b l4-i5.
Different meanings in diff. cate
gories, iO7 a 5-1 1 : arguments on
each to be drawn up, !O5 b i3;
question, how many, not dia
lectical, I58 a 16. Not referable
to any higher genus, I23 b 8-i2.

Not def. through evil (be
cause opposite, and . . not prior,
to g.), I42 a 23-4 ; and . . not as
contrary of evil (circular),
I47 b 18-25. I ts property, to
be desirable , I35 b 15-16 :
more conspicuous g. the more
desirable, H7 b 28: better
generally more desirable , but
distinguished, I l8 a 8-I5(cf. ]) 37).
Not its property to be most
direct opposite of evil (circular),
I3i a 18-20. G. intrinsically )( g.
as means, io6 a 4, J49 b 3i-2,
though intrinsic g. may also be
g. as means, I49 b 35 : intrinsic
g. better, Ii6 a 2g, h 22~3: cf.
Ii6 b 37-H7 a 4. Good )( useful,
I24 a i6; cf. 147*34, I53 b 38
G. absolutely )( g. for X (TU/I),
Il6 b 8. What is g. in a particu
lar respect or at pr. time or for
pr. person, not necessarily g.
absolutely, H5 b 15 foil. Stan
dard of what is better absolutely
is verdict of better science,
though to X (e. g. doctor) it may
be that of his own science, Il6 a
21-2. [For better science , v.
I 57 a 9-] Natural g. )( acquired
g., n6 b 10-12, cf. H9 a 9-ii.

G. the genus of justice ,
Ii6 a 23~4; of health , I23 b
17-18; of the moderate (or
right) amount, I23 b 29-30; of
virtue , I24 h 2o-i, I44 a lo.
Not genus of pleasure (for
some p. not g.), I2o b 17-20.
[For good and pleasure cf.
also ii4 h 7-8, 39, H9 a 38- b i,
19-21, 120*7 foil., 124* 17, b 8-
14 : and see also The Good .]

A g. thing tested by its con
traries, 113*1-14, b 27-34; by
its co-ordinates, 114* 39-" 5 ; by
the modes of its generation,
production, and destruction,
1 1 4 b 1 6-24 ; by its variations in
degree, 114^8-115*2 : by add
ing it to other things, 1 15* 27-
9 (a positive test only, Ii5 a 33~
b 2). Tests of better )( worse,
Bk. Ill, chh. 1-3 : do. applied
to simple distinction good )(
evil, Bk. Ill, ch. 4. Of things
g. as means, that is better (i)
which does g. per se than that

INDEX

which does g. peraccidens, n6 b
1-4 : (2) which is nearer to the
end, Ii6 l} 23 : (3) whose end is
better, Ii6 b 23, 26, Ii7 a 7, Ii8 b
32-

The good : not def. = the
state of virtue (circular), I42 b
12. Its property, to be the
best , i36 b 3i-2. Of goods,
that is more desirable which is
nearer, or more like, the g.,
H7 b 10-11. Doctrine that plea
sure = the g., shows depravity
and is invidious, 160^19-22.

G. man, not jealous, 109 36 :
has capacity, but not charac
ter, of doing evil, 1 26*34-6.

G. life, failure of Xenocrates
proof that it = happy life, 152*
7-10, 26-30.

G. and evil, see s.v. Ei il.
G. = merely expert ( good
thief), 149^9.

Wishing = conation for g.,
I46 b 6; i.e. for apparent g.,

i47 a i-5-

Sophistical proof that some
thing can be both g. and not g.,
i8o b 9-2i (cf. i8i b 9-i6).

Doing good )( evil, to friends
)( enemies, iO4 a 22-33, Ii2 b
32-1 1 3 a 1 6.
Goodeno ugh - King (Euarchus),

I82 b 20.

Good temper (Trpadrrjy), not def. =
control of anger (rather im
plies complete immunity), I25 b
21-7.

Gorgias, i83 b 37. G., the, I73 a
8.

Grammar, def. = science of
reading and writing , I42 b 33~
4: not def. = (i) science of
writing from dictation , I42 b
31-5; (2) science of letters ,
I46 b 6. A single science, 104*
17-18: a kind of knowledge ,
ni a 37, I24 b 19, I26 a 5, 19:
not (like knowledge ) a rela
tive term, I24 b 19. To be cap
able of learning grammar , a
property of man , io2 a 19-22.

Greater and less degrees (TO ^XXov
/cm TITTOV) : attributes not admit
ting of, 1 1 5 a 32-3, b 8-9- As
tests of ambiguity, io7 b 13-18;
of Accident, Ii4 b 37-U5 a 14,

H5 b 3-lo, Ii9 b i7-30; of Genus,
I27 b i8-I28 a i2 ; of Property,
I37 b i4-I38 a 29 ; of Definition,
I46 a 3-18, 154" 4-1 1 ; of Same
ness, I52 b 6~9: reckoned among
most generally handy tests,
154*12.

Greeks, I52 a 13.

Grey, intermediate colour between
white and black , io6 b 6.

Growth (avgetrdai), a species of
motion , in b 5: does not al
ways accompany being nour
ished (rpffandai), Ill b 25.

Half; species of fraction , 125*
26-7 : its property, to be in
proportion \ , I35 b 26: not its
property, to be exceeded (TO
{.nfpfxofjLfvov), i35 b 2i-2 : rel. to
double , I35 b 20

Harmony ((rv^xavia), not the
genus of temperance , 123*
33-7 > !39 b 33 : always found in
notes ((fiBayym), i23 a 36-7.

Harsh (ao/^oj), intermediate
sound between clear (Awcf>s)
and obscure (^Any), io6 b 7.
[Cf. Grey.]

Hatred: contrary of friendship,
Io6 b 2, Ii3 b I : found in faculty
of desire (if friendship be so),
H3 b 2: does not follow anger,

"3 a 35 f - b 3-

Health (vyifia) : a kind of good,
I23 b 17-18 : desired as an end,
ill* I, 1 1 6*29- 30: contrary of
disease , with no intermediary
(/jLtragv), I23 b 17-18 (cf. H2 a
24-5), I23 b 34~5. Not def. =
balance of hot and cold ele
ments , for ( I ) balance is am
biguous, I39 b 2i: (2) h. is not
inherent in hot and cold
elements, I45 b 7-io. Follows
vigour (fi *|i<i), H3 b 35i.lS7 b
23-4 : less good than vigour
I57 b 19. Superior to means of
h. , but still more markedly
inferior to happiness , and
therefore inferior to means of
happiness , I i6 b 29-36. Better
than strength or beauty, Ii6 b
18; than beauty, ii8 b 2o.
Medicine the science of pro
ducing h., no b i8, I4l a 19,
143*3-4. Ability to produce

INDEX

h., a property of the doctor,
I 37 a 3~7 : actual production of
it, not so, I36 b 37. Recovery
of h. (TO vyidf<rdai) good abso
lutely, Ii6 b 8-io: desirable as
means to h., 117*20.

Healthy (vyiewov) : ambiguous,
io6 b 34-6, (i) productive of h.,
cf. I07 b 8, Iio a i9, Ii4 a 30-i;
(2) preservative of h., cf. H4 a
30-1 ; (3) indicative of h., cf.
I07 b 8. Good as means, io6 a
5-8 (contr. courage, good in
trinsically), cf. io7 a 5-8. The
doctor the judge of what is h.,
no a 2o-2. H. absolutely =
h. to those in sound state of
body, I42 a ii. Means of health
contrary of means of disease,
i63 a 18-19, cf- I S b ll -

Hearing (aKot i,aKov(Tis): to possess
h. cf. to hear , I I4 b 27 : not a
property of hearing (aKovais) to
be a sensation , I35 b 31-3 : h.
not a property of man, I38 b
8-10. Clearness (in sound)
distinguished by h., io6 a 30-2 :
cf. io7 b 1-2. Beauty not def.=
the pleasure that comes through
sight or through h. , I46 a 22 foil.

Heraclitus : his paradoxes (i)
that all things are in motion,
I04 b 22 (cf. i6o b i9): (2) that
good and evil are the same (in
volving denial of view that con
trary predicates cannot coexist
in same thing), i59 b 3o-3.

Hippias Major, the ; 146" 22 n.

Hippocrates, his method of squar
ing the circle, I7i b I 5.

Homer, I57 a i5, i66 b 3, I7i a io
(Epic cycle). Cf. Iliad.

Hypothetical reasoning (ol e VTTO-
6f<r(cov oruXXoyioTioj) : examina
tion of likeness between things
useful for, io8 b 8, 12, As test
of Accident, i I9 b 35-120*5 (cf.
Preliminary admission} ; of
Sameness, 152 17-24.

Ideas (Platonic) : motionless,
H3 a 27, I48 a 2o: intelligible,
H3 a 28: cannot be said with
out self-contradiction to exist in
us, U3 a 25 foil. As sources of
tests of Property, I37 b 3~i3 ; of
Definition, I43 b 23 foil., I47 a 3

foll.,i48 a i3 foil. : classed among
most effective, tests, I54 a 19.

Ignorance (ayvoia) : def. = pri
vation of knowledge in the
rational faculty , 1 47 b 29-34
I. of contraries one, I56 b 12.

Ignoratio elenchi [cf. Refutation]
one of 7 fallacious refutations
not dependent on diction, l66 b
24 ; but cf. i67 a 35 : analysed
and illustrated, i67 a 21-35 : i ts
solution, Soph. El., ch. 26 ; why
deceptive, 1 69 b 9-12. All falla
cies analysable into it, Soph.
El., ch. 6.

Iliad, the, i66 b 5 n., 9 n., 180* 21.

Imelman, conj. I28 a 3l.

Immortal: not def. = a living
being immune at present from
destruction , I45 b 21-3 : differ
entia, rather than genus, of God,
I22 b 12 : not species of God,
I22 b 38. Immortal living be
ing a permanent property of
God, I28 b 19-20.

Immortality : not def. = ever
lasting life , I26 b 35; nor anv
kind of life ; rather an accident
(cr\)\mTu>\ia) or affection (nuQos)
of life, I26 b 36-i27 a 2.

Impossible. Argument per impos-
sibile, suitable for demonstra
tion, not for dialectic, I57 b 34
foll.-i58 a 2: called conver
sion , i63 a 32-6. A. ad im-
possibile, i62 b 7, 19-22, i67 b 23,
I7o a 2 : ex., i67 b 27-34.

Incisive (S/jt/xvy) argument: def.
*= one which produces great
est perplexity , iS2 b 32: most
incisive of syllogistic arguments,
l82 b 37; of contentious argu
ments, l83 a 7.

Incontinent man, not def. = one
who is mastered by pleasures
(unless quality of p. be stated),

.

India, ii6 a 38 : Indian, i67 a 8.

Indignant (yf/^ecr^TiKos), def. =
grieved at prosperity of
wicked , 110*3: )( jealous,
iio a i.

Induction def., io5 a 13, cf. I56 a
4-6 : more convincing and
clearer than deduction, !O5 a 16 :
appeals more to senses and to
mass of men, io5 a 17-18, I56 a

INDEX

4-7> T 57 a 19-20; should be prac
tised with the young, 164* 12
(to secure stock of parallel cases,
napatfo\ai) . Study of like
ness useful for, io8 b 7, 9. Re
commended, ic>5 b 27, H3 b 17,
29; 115*5: cf. 120*32: 122*
17-19: I23 b 7 : I55 b 34-156*
I. I. and argument from like
ness (analogy), their resem
blance and difference, I56 b 14-
1 7 : the 2 usual ways of estab
lishing a universal, 160*37-9.
Inductive premisses, not ne
cessary premisses, i55 b 2o-2.
Superfluous i., a method of se
curing ornament for argu
ment, 157* 7. Results of i., to
be accepted, unless neg. in
stance forthcoming, 157*34.
I. through the view laid down ,
through the thesis , as means
of diversion to more favourable
subject, ui b 38-112* i, 112*5-
6. Difficulty in i. arising from
absence of suitable common
names (see Likeness).

Inequality def. = privation of
equality , 1 47 b 5, 14-15.

Inflections (TrroxTfiy) of X def. as
forms related to X as adverb
to adjective, 1 14* 33 (cf. io6 b 29
foil., 124*12-14, 148*11-13,
I5i b 32) : also gender-endings,
I73 b 27~9; case-endings, I36 b
20-2, I73 b 32 foil. )( co-ordi
nates, 1 14* 32 ; often held to be
included in them, 1 1 4* 34: treated
together, 124* 10-14, 15 l b 30-3,
I53 b 25 foil.

As tests of ambiguity, lo6 b 29
foil. ; of Accident, 114* 26 foil.;
of Genus, 124*10-14; of Pro
perty, I36 b 15-32; of Defini
tion, 148*10-13, I53 b 25-35;
of Sameness, I5i b 28-33: reck
oned among most generally
handy tests, 119*36-8, 154* 12-
13. Confusion of i., a great
source of solecism, I73 b 26-174*
11.

Inherence in... (TO ey TW, eV vnoKei-
fjifi-ai, \eytvdai) : )( predication
of . . . (Xfyeadai, KaT iyupilcrQai,
Kara . . .), I27 b 1-4 : but syn.,
I32 b 19-34. As test of compara
tive values of things, Ii6 b 17

foil.; of Genus, 125*33 fH->
I27 b 1-4 ; of Property, I32 b 19
foil. ; of Definition, 145* 33-

b ll, 150*26-33, I5I*32- b 2.

Disposition , state , ba
lance , affection must be in
herent in the thing whose dis
position, &c., it is, 125*35-7,

*45 a 33- b II-

Injure: God cannot be injured,
I09 b 34-5.

Injurious (/3\a(3tp6v) = (i) pro
ductive of evil ; (2) destruc
tive of good, 147* 34-5 : con
trary of useful , ib.

Injustice, a species of Vice , I23 b
15, 21, 32 : a vice of the soul ) (
of the body, I53 b 8-io.

Not its property to be lowest
evil (TO x f ipio"rov), because its
contrary (justice) not highest
good , I35 b 10-12. Of a foul
(in raceorfight), I7i b 22, 174*22.
Do injustice (ddiKelv) def. =
injure deliberately , io9 b 33-4.

Intelligible : absolutely i. )(i. to
us , I41 b 4: same to persons of
sound understanding, 142*9.
Prior terms more i. absolutely
than posterior, I4i b 5 ; but pos
terior sometimes more i. to us,
I4i b 9 (cf. 156*6-7). Objects
of sense more i. at first ; then
objects of thought, 142*2-4 : o.
of sense more i. either absolutely
or to most people, I4i b 9~l2,
156*6-7. Exx., 111*9-10, I29 b
10-12, 26-8, i4i b 6-9, 149*5-7,
16-17. More i. terms required
forcorrect rendering of Property,
I29 b 2 foil, (in 2 senses, 5 foil.,
13 foil.), cf. 131*3, 12 : in Defi
nition, I4I*26- b 2, I42 b 2O-I (cf.
!5o b 22-3): sources of failure
here, (i) 14^3-142*18, (2) 142*
19-21 : cf. 26.

Intractability in a problem (Surrt-
Trix^ P 7 ? 1 " ") : it 5 sources, I58 b 16-
159*4-

Jealousy def. = pain at the ap
parent success of some well-
behaved person , !O9 h 36: not
an attribute of the good man,
ib. )( Indignation, I09 b 38.

Jttdging(Kpivti.v), the genusof per
ceiving , (tiiaBavtadni), 111*19.

INDEX

Juncture (o-woxfi), species, not
genus, of contact (av//is), i22 b
25-6.

Just, ambiguous, lo6 b 30 : one of
the meanings of good, as applied
to the soul, in categoryof Quality,
io/ a 5-8. What is j., sometimes
evil, 1 1 9^4. Not a property of
what is j. to be beautiful ,
I36 b 17-18. Sophistical proof
that what is unjust may be
preferable to what is j., l8o h 21-

39-

Justice, a good 1 1 6 a 24 : good in
trinsically, io6 a 4-8 : contrary of
injustice, I35 b lo; )( courage,
io8 a 1-2 (cf. !5i b 3i-3): may
belong in one respect only,
109*21-2. Not = knowledge,
H4 b 8, I20 a 30 (cf. I24 a 12-14) I
not a species of knowledge,
1 2 i b 26-30. A species of virtue,
I09 a 35- b i, I2i b 26, I23 b 15, 21,
32, I2y b 2o: of the expedient,
I4l a l7. Found in soul, I5o b
35, cf. I53 b 8-io. Not def. (i)
control of gains , I25 b 22~7;
(2) state that produces equality 1
or that distributes what is
equal (too wide), I43 a 15-19;
(3) ability to distribute what is
equal ( choice rather than
ability ), I45 b 35~i46 a 2 ; (4)
what preserves the laws , I49 b
32 ; (5) temperance and cour
age , 150*3-21.

Not its property to be highest
good, I35 b u. Praiseworthy,
H4 b 2; better than a just man,
Il6 a 23, b 10, H7 b ii; than
strength, I i6 b 38 ; than courage,
"7 a 36i 38, u8 a i7, 36. In
friends desirable essentially, in
enemies per accidens, I i6 a 31-5.
Happiness better than j. and
courage combined, 1 1 7 a 2 1-3.
Genuine j. more desirable than
apparent n8 a 3-4. Legal )( na
tural valuation of j., I73 a II (cf.
Law}.

Justly: ambiguous, io6 b 29-33:

not = knowingly and skilfully

H4 b 9. J .and knowingly , 1 24 a

, 13: j. and bravely , !5i b 32-3.

Not a property of what is

done j. to be done beautifully

(Ka\S>s), I36 b i7-i8, or well

(dya&o?), I36 b 27-8: to act j.
more desirable than bravely,
n8 a 36: an act done j. may be
evil, H9 b 5. v. also i8o b 21-3.

Knowledge (see also Science) : a
kind of disposition (Siddeais),
iu a 23, I45 a 36; of state and
disposition , I2i b 38, 124^3-4,
I25 a i; of conceiving (tm-o.Vi;-
iM> Ii4 a i8,ii9 b 3, I25 a 9-ii ;
cf. I30 b i5, I3i a 23; of con
viction (nia-Tts), 128 a 25~7. Not
a kind of good (for k. a rel.
term, good a quality), I2l a I-
3; of sensation, I25 a 28-32. Not
= a knower, I26 b 33. Def. =
conception of a knowable ,
I46 b 5: not def. =(i) unsup-
plantable (metaph.) 139* 32; (2)
incontrovertible conception
(c. of />&/?), I46 b 2. To know ,
not a property of man, i38 a 6-8:
)( be thinking of (8iavofl(rdm},
H4 b 32-7. K. sometimes bad
1 1 1*23, 1 1 9 b 9 foil. A relative
term (contr. its species, e.g.
grammar ), I24 b ig; rel. to
object of k. , I24 b 33, I49 b n ;
should be defined in rein, to
its best object, I43 a 1 1 : fourfold
ambiguity of phrase, the know
ledge of A , I30 a 19-22. Its
property, to be (i) the most
convincing conception , I3i a
23-61(2) incontrovertible by ar
gument belongs to k. because
k. is the state of some one (ro>
exeo-dai), as also to scientist TUJ
e\fiv, I34 a 36 b - b 1,17 [the solu
tion of the objection raised in
133*28-31]. K. and justice ,

II4 b 9, I2I"26-30 (cf. I24 a l2-

14). K. and prudence , I2o a
28-31, 137 a 14. K. and memory ,
I25 b 6-io. K. and ignorance :
def. of k. implies def. of ignor
ance, I47 a I7(cf. I5t b 1-2) : ig
norance = privationof K., I47 b
30 ; though not so error , 1 48 a 8.
K. and forgetfulness , 1 53 b 27,
I57 b ll-l6. K. and sensation ,
I05 a 28-30, 108*4, I56 b 11-14:
k. of objects of sense assumed
possible, 114*21; but often
denied, Ii4 a 23: obj. of k. not
a kind of obj. of s., I25 a 29.

INDEX

Obj. of k. not the genus of
obj. of opinion (bo^avrov),
12 i a 21-5. That k. of many
things is one , ambiguous, iio"
17 : k. of opposites one , io5 b

33, 109*17, I55 b 3 2, i63 a 3
(noted as opinion of some
people , 142* 24-5) ; do. of con
traries , I04 a i6, io5 b 5-6, 34,
I 55 b 3 I > *56 b II, l63 a 2 (cf. Ig
norance) ; do. of relatives , io5 b

34. To be capable of receiving
k. a property of man , 103* 28,
I28 b 35,i3o b 8, I32 a 19-21, b 1-3,
!33 a 2o-3, 134*14-17; though
no part of his definition, 140*
35-6 :cf. io2 a 1 9-22 ( capable of
learning grammar ) : not a
differentia of soul , 15 i b I. To
partake of k. not a property of
man (true also of God), I32 b
10-13. Faculty of desire not
capable of receivingk. and . . not
of ignorance, H3 b 3-6. Self-k.
possible, not necessary, to soul,
I25 a 39-4o(cf. b 3-4). Specula
tive k. not = speculative con
ception , 149*9-13; )( practical
knowledge, I52 b 4.

Lang, P., I74 b 27n.

Law : not def. (i) a measure of
what is by nature just : (2) an
image of do. , I4o a 7-8 : (3) an
image of what is by nature
noble and just , 141*20-1. L.
(convention) opp. Nature ; fre
quently leads to paradox, 173*
7-18, 27-30: 1. represents
opinion of majority , as opp. to
the true nature of things, 173*
29-30.

Learning, as species of recollec
tion, I24 a 22. Rules for teachers
and learners )( those who argue
contentiously or in spirit of
inquiry , I59 a 11-14, 26-8: cf.
161*24-5. Cf. Didactic argu
ment.

Length (/^KO?), genus of line ,
I43 b 1 6 : its differentiae without
breadth )( with breadth ,
I43 b 14, 19. Idea of 1- (i>r6
^Kos),^i43 b 24, 31.

Life = co7j : ambiguous ; no single
type of 1. in animals and plants,
rendering single def. impossible,

I48 a 27 foil. : hence Dionysius
def. of it = a movement of a
creature sustained by nourish
ment, congenitally present with
it fails. A property (0 of
living being absolutely, 134*
32, cf. 138* 27-9 : (2) of a parti
cular kind of living being, be
cause it partakes of 1. b. (T<U
H(r<x<i), I34 b 4, 20-2. L. ) (
good L, Ii8 a 7. Not genus of
immortality, I26 b 35: the soul
has a share of 1., 123*25.

(<$) = jSios. L. of virtue )( of
enjoyment, iO2 b 1 7 : Xenocrates
proof that happy 1. = good L,
1 5 2 a 7- 10, 26-30. The end of
1. , Ii6 b 24.

Light (a) = </)o>s-, a species of fire,
I34 b 28-9 : less of nature of fire
than flame is, 146* 15-16. Its
property, to consist of most
rarefied particles of all species of
fire, i34 b 32-4, !35 a 4-5. M6 a
16-17.

(b)=$apv, contrary of heavy ,
106*18-19.

Like degrees (TO> o^oivs), argument
from, as test of ambiguity, io7 b
13-18 ; of Accident, 115* 15-24,
H9 b i7, 21-6; of Genus, I27 b
26-36, 128*5-6, lo-ii ; of
Property, !38 a 3O- b 22 (contr.
argt. from like relations ,
I38 b 23-6) ; of Definition, 146*
18-20,154*4. Reckoned among
handiest tests, 154*12.

Likeness of things to be studied,
105*25 and Bk. I, ch. 17: im
portance of observing, io8 b 7 foil.
2 draughts of water from same
spring differ from others only by
more marked 1., 103* 19-22.

L. or like objects (TU o/zom), as
tests of Accident, I I4 b 25-36 ; of
comparative values of things,
H7 b 10-14, 20-1 : objections,
that likeness of A to 13 may be
irrelevant to good points of B
(14-1 7), or inexact, i.e. unflatter-
ingor flattering to B (17-19, 25-
7), or but slight (21-5) : as
tests of sameness, I56 b 10-17.
Argument from 1. (analogy) and
Induction [v. Induction}. Diffi
culty of argument from 1. when
no common name to express

INDEX

point of 1., 157* 21-33 : c f- I 74 a
37-40 : answerer shd. then
plead ambiguity, 176*33-5.

L. of relations of things (rd
6/iotcof ( xovm Ttpbs oXXrjXa), when
A : B = a: 3 ; as tests of Genus,
I24 a i5-2o; of Property, I3& b
33~i37 a 7 (cf. !38 b 23-6); of
Sameness, 152*1-2. For con
trast with argument from Mike
degrees , v. I38 b 23~6.

Line: not def. (l) = length with
out breadth , I43 b 12-23 : (2)
length with breadth , 144* 1-2:
(3) limit of a plane (except when
necessary ad homineni) I4i b 5~
25. Prior to, and . . more intelli
gible absolutely than, plane ;
posterior to, and . . less intelli
gible absolutely than, point ,
I4i b 5~7. No product of 1.
and number , 150*24-5. Fal
lacy produced by misdrawing 1.,
loi a 1 6 (and see False dia
grams). Straight Is. all one
species, I2i b 22~3: finite str.
1. not def. = the limit of a
finite plane such that its centre
is in line with its extremes ,
I48 b 26-32 [for end of def.,
which should define straight-
ness , inapplicable to infinite str.
1., which has no middle or ex
tremes]. Indivisible Is. , I2l b
19: indivisible not their
genus, 19-23.

Liquid (vypov) : a species of body ,
I 3 b 35 : i ts property, to be a
body adaptable to every shape ,

i3o b 34-7-

Literal ) ( usual meanings of words,
1 1 2 a 34-8.

Living being (fwov) : its differen
tiae, mortal )( immortal ,
122" 13-14 : its property, to
live , belongs absolutely ,
134* 32, 136* 25-8 : cf. 138* 10-
12: hence also of not-living
being (p.f] a>oi>), not to live
(w &") 136*25-8. A parti
cular species of 1. b. has
property of living by reason
of partaking in nature of 1. b.
(r$ prrix*iv) t I34 b 4-

To be (i) a l.b. that partakes
of knowledge not a property of
man, for belongs also to God,

I32 b 10-13 : (2) an intelligible
1. b. not a property of God, 136**
6-7 : (3) a sensible l.b. , not a
property of 1. beings other than
God, 5b.

Living creature (<oi>) : not def. =
a composition of soul and
body , 151*21-31. Itsproper-
ties (i) to be compounded of
soul and body (permanent
property), 129*2, 131*8, I37 b
11-13: (2) to have a soul ,
correctly stated so far as no
universal predicate is introduced
!3o b 2O-2, and attribute is
convertible with subject, 132**
16-18 ; but defective in so far as
genus of 1. c. (viz. substance )
is not stated, 132*15-16: (3)
to be an animate substance ,
135* 16-19, f- J 36 a 12. Hence
being inanimate not its pro
perty, 136*12-13; and being
animate not property of what
is not a I.e. (p.f] t<aoj>), 136*33-4.
Idea of I.e. (avrofwo^), I37 b
II.

Locomotion (a) = rj Kara TOTTOV
Kivrjcris or /uera/3oA?7 : genus of
carriage (<opd), I22 b 27,
32 foil., 128* 3-5 : Plato s identi
fication of 1. and carriage
rejected, I22 b 26 foil. [cf.
Carriage}. (b) = (fropd. A
species of motion (KII^O-IS),
121*31, 122*23-6: Pleasure
not = 1., 121*31. L., genus of
walking , OdSttri?), 122*21-30.
[N.B.c^opd here = 17 Kara T.K.ii>rj(ns,
or p-erafioXr), of I22 b 27, 32 ; for
walking (8d8i<ris) and carriage
(4>opd) are co-ordinate species of
same genus, locomotion ] : cf.
I42 b 3 (<popa 17X1011 vn(p yijs-)

Love: (i) sexual (epwy) : not def. =
desire for intercourse (do not
vary in degree together), 146*
9-12, i52 b 7-9.

(2) =dytt7rd : problem whether
parents shd. be loved not
dialectical, 105*3-7.

(3) = (pi\elv : ambiguous ; spiri
tual )( physical meaning, io6 b
2-3. In former sense, contrary
to hate ; in latter, no con
trary, ib.

Lycophron, his response to a call

INDEX

for an encomium on the lyre,
i 74 b 32.
Ly sunder, I76 b 5.

Man: a substance, iO3 b 29-31;
does not admit variations in
degree, i I5 b 9,butsee I37 b 32~3:
a species of animal , 102*34-
5 (cf. Ii2 a i8, Ii3 b i7, I25 b 37-
9), 128*24-5, i3i a 4-5- D ef- =
animal that walks on 2 feet ,
!4o b 33-4; cf. 112*18-19: his
defn. an ex. of a dialectical
problem or proposition, ioi b 3o:
not well def. (i) with addition,
capable of receiving knowledge
(v. Plat. Def. 415 a), 140*35-7
(cf. I5i b i): (2) = a walking
biped animal, six ft. high , i4o b
2 3-6 : (3) = that which knows
how to count , I42 b 24. M. the
same inter se (specifically) ; as
horse or dog (generically), 103*
10-14, io8 a 14-16: better than a
horse, H7 b 35. A property of
m. to be (i) by nature a civi
lized animal an essential
property, I28 ; 17, 130* 27-8,
132*6-9, 138*11, I39 a 18-20:
(2) a biped a relative
property [ )( a horse], I28 b 25, of
a kind universally and always
present, 129*8-10: Contr., how
ever, 134*8-1 1, where disal
lowed as being normal (cf. 134*
29) but not invariable: (3) a
walking biped , I33 b 8, I36 b 2o-
2 : but contr. 133* 3-5, 132* 1-4 :

(4) a mortal living being, cap
able of receiving knowledge -
an essential property, I2& b 35 :

(5) an animal capable of re
ceiving knowledge , iO3 a 28 (cf.
112*18-19), I3o b 8, 132* 19-21,
b i-3. i33 a 2o-3, i34 a M-I7 (cf.
102* 19-22, capable of learning
grammar ) : but contr. I32 b 10-
13 (see (3) below) : (6) a mor
tal (3pordr) ; hence of becom
ing a man , to become a mor
tal ; of the destruction ofa man ,
the destruction of a mortal ,
137* 34-7 : (7) possessed of a
tripartite soul , 133*30-2. Not
a property of man (i) to be an
animal , 1 36" 1 9 : hence not of
what is not man not to be

an animal ; nor of becoming a
man to become an animal ;
nor of the destruction of a man
to be the destruction of an
animal , 137*24-7 : (2) to be a
walking biped (belongs as
part of essence, KHTO iU6tui),
I 33 a 3-5; or a walking biped
animal (his def.), 132*1-4: (3)
to be a living being who par
takes of knowledge (true also
of God), I32 b 10-13: (4) to
move by his own initiative ,
I33 b i-S : (5 to walk through
the market-place (never, or not
always, a property), I33 a 15-18 :
(6) to be motionless (fjpentlv):
belongs to idea of man only
qua idea , not qua man ,
!37 b 6-8: (7) to be virtuous
(rorrTTovSalov) : hence not of what
is more human (^aXXov avOpv-
nos) to be more virtuous, I37 b
31-3 : (8) to know , 138* 6-8 :
(9) to see or hear , I38 b 8-
10: (10) to sleep , 102*22-4.
To be sitting , an accident
of m., but a temporary property
of any one who alone is sitting,
or a relative property )( those
not sitting, !O2 b 2l-4. M. )(
white m. : sophistical puzzle
regarding their attributes, I33 b
1 6 foil. : different mode of being,

I33 b 33-5-

A particular man (6 T\S
<iv6p(OTTos) ; his property (i) to be
walking in the gymnasium ,
a temporary property, I28 b
20- 1 : 129*3-5: (2) to be walk
ing now ,- a property of the
present time, I3l b 1 6- 1 8 : (3) to
possess 4 fingers an actual
property (TO vnapx "^ I34 a 3-
Not his property, to be
sitting with X rather a tem
porary property, I3i b 11-14
(cf. io2 b 2O-6). Third man
(rpLTos "ivdpunos), neither Man
nor a man , I78 b 36-9.

MandrobuluS) the, I74 b 27.

Many questions (double question),
Fallacy of: one of 7 fallacious
refutations not dependent on
diction, i66 b 27: illustrated,
l67 b 38-168* 16 : rules for solu
tion, Soph. El., ch. 30: why

INDEX

deceptive, i6g b 14-17 : a form of
ign. elenchi, 169* 6-18. At root
of fallacies of ambiguity and
amphiboly, 175^9-41.
Marrow, not to be described in
definition as bone-formed ,

Maxim (-yi^r?) = (i) true opinion,
(2) general assertion, I76 b 18.

Medea, i83*2n.

Medicine (a) = (/xip^oKa : to take
it expedient at times, but not
absolutely, U5 b 26.

(b) = iarpiKT], the science both
of producing health and of
dieting, no b 18 : not def. (i) =
knowledge of what makes for
health in animals and man
(redundant), 141*19-20: (2) =
knowledge how to produce
disease and health [= kn. how
to produce health essentially,
disease only accidentally], 143*
3-8 : (3) = science of reality
(Hippocrates defn. : much too
wide), I49 b 6-10. Enables not
always to cure, but to do all
that is possible to cure, ioi b 8-
10. In m. the good = what
produces health, 107*6; in m.
that is more desirable which
most or all doctors would choose,
116* 17-18.

Melissus: (i) paradox that Being
is one, !O4 b 22: (2) argument
that universe is eternal, i&7 b 1 3-
18, i68 b 35-4o, 181*27-30: (3)
i68 b 37, 40-169* 3.

Memory, an activity, not a state,
I25 b i8. Notdef. (i) = abiding
of knowledge , I25 b 6 foil. : (2)
a state retentive of a concep
tion , I25 b 17. Knowledge not
remembering , for may be of
present or future, m b 27-31.
Mnemonic loci, i63 b 29-30.

Metaphor always obscure, 1 39 b 34 :
based on resemblance, hence
renders subject partly intellig
ible, 140*9-11. M. condemned
in rendering genus, I23 a 33~7:
so too metaphorical definition,
I39 b 32 (cf. I58 b 8-i5), though
not so bad as def. inapplicable
even metaphorically, 140*6-17.
Makes a problem intractable

ipr)T01>), I58 b 17.

Misreasonings (irapaKoyurpoi) from
premisses proper to special
sciences, 101* 5-17, 170*31-4:
exx. from maths., 101*15-17,
I7i b 38-i72 a 5 : due to ignor
ance of force of words (ambigui
ties, c.), 165* 15.

Mixture (/utis) ; the genus, not a
species, of fusion (Kpao-tj), I22 b
25-6, since includes m. of dry
things and /. of wider denotation,
1 22 b 30-6: not a differentia of fu
sion (for same reason), i23 a 3-4.

Moderate (or right) amount (TO
fjLfrpiov) : intermediate between
defect and excess , I23 b 29:
a species of good , 12 3 b 30 (in
category of quantity, 107*10-11).

Motion, Movement (/aV^cm), a
kind of activity , I25 b l7:
genus of growth, destruction,
coming-to-be, &c. , Iii b 5; of
locomotion (<opa), alteration,
&c. , 121*31-2 : of locomotion,
growth, decrease, &c , 122*28-
9; of walking , 128*32-3.
Possibly not found in soul, 123*
15-16. Not genus of soul
(even if found in it, is liable to
fail), 120 b 24, 123*15-17, I27 b
15-17. Heraclitus doctrine that
all things are in m., !O4 b 2l (cf.
i6o b 19) : Zeno s doctrine that
there is no m., i6o b 8, 19.
Wind = a m. of air , rather
than air in m. , 127*4.

Mud, not = earth mixed with
moisture , I27 a i4; nor any
kind of earth at all, ib.

Multiple (Ko\\cnr\a(nov), genus of
double , 121*4-5, but only in
rein, to same unit, I24 b 24~7.
a kind of excess , I24 b 29-31 :
rel. to fraction , 114*17,125*
6-9, 26-7: cf. 121*4-5. fa
multiple, 114* 15.

Multiplication-table, to 10 (of

Music, a kind of science m a
37, b 2, 128*31-3. M. and
grammar, !O4 b 26.

Natural ability (tixpvia) for philo
sophy, def. = the power rightly
to choose the true and shun the
false , l63 b 13-15 : appearance

INDEX

of, cultivated bydisclaiminglove
of hard work, 118*22.

Nature : )( convention : see Law.
A particular n. = a particular
kind (yei/of) of being, 172*37.

Necessary: N. events )( usual
events (ra ir tVi TO TTO\V), 1 1 2 b I :
)( the contrary of usual (i.e.
comparatively rare ) events
(ra eV eXarrov), II2 b 9 foil.: )(

H2 b 2, 13: be n. )( be possible
(fi/8f xt(rdai), I21 a lo, I5232. N.
premisses (see Premisses).
Changes of subject, n. )( appar
ently n., )( neither really nor ap
parently n., Bk. II, ch. 5 init.
Attributesthatarenotn., require
renewed confirmation by sense,
!3i b 2l-5. Necessaries) (super
fluities (TCI tK ncpiova-ias), Il8 a 6
foil. : superfluities the better,
though not more desirable unless
necessaries are already present,
ib. N. predicates (of S and P) as
tests of Accident, H2 a 16-23.

Nestor, ny b 24.

Night, not def. = a shadow on
the earth , u6 b 28.

Not-being (fj.f) w) : contradictory
of Being, 1 09*" 23 (cf. 1 9) : always
predicable of what is coining
to be , I28 b 6 ; but not convert
ible with c.-to-be, I28 b 7; nor
its genus, I28 b 8 : nor the genus
of anything at all, I28 b 9.

Number: always either odd or
even, I2o b 4, I42 b 9-io, cf. 123*
13-14: odd as differentia,
I22 b 19, 23-4. Not the genus
of odd , I22 b i8; nor its
species, 123*1-2. Unable to
combine with line to have a
product (fK TOUTWJ/), 1 5o a 24-5.
Posterior to, and . . less intellig
ible absolutely than, unit ,
!4i b 5-9: though unit generally
defined through it, = starting-
point of number , ioS b 26, 29.
The soul not a n., I2o b 3-6, 123*
11-14, 23-6.

Numerical sameness [v.Same-
ness],

Oath : Sophistical proof that o. can
be broken and kept at same time,
180*34-5, 3 8- b I.

Objection (Hi-amuris) : Exx. of, 1 14*
20; iis b i5; 117*18, b i4;
I23 b i7, 27, 34; I24 b 32; I28 b
6; 134*25 (cf. 135*6); 156*35;
I57 b 2, 8, 17; 160^2, 8 foil. O.
to be invited, !O9 b 28, 120*37,
I57 a 34, b ii i6o b i ; to be
brought, 110*10, 156 1 8.
Should not be directed to actual
point asked, if other ground can
be found, 1 57*37^2. 4 kinds
of o. : (i) Solution of fallacy :
(2) O. ad hominem : (3) O. to
questions asked : (4) O. to time
allowed (cf. Time), 161*1-15.
Readiness ino. a principal aim of
dialectic training, i64 b 1-4 : ob
jecting )( putting propositions,
l64 b 4-7. How to meet o., 134*
3-4, 1 57 b 6, 9, 20, 24 : easy if pro
position be partly true, partly
false, 157 b 2 5-3 1 : exx., 114*22,
156*38, I57 b 11-16, 17-24.

Captions o. (of answerer) or
false suggestion (of questioner)
(o-vKo(j)(ivTfw), I39 b 26, 157*32.

Objectionable (favurov) contrary of
desirable (q. v.), H3 b 33-4, I35 b
15 (cf. Ii7 b 5, n8 b 34) : property
of evil , i35 b 14-16.

Obscurity (TO a<ra$is) : sources of,
I39 b i9 foil, (i) ambiguous
terms (l39 b 19-31, cf. 130*2-3),
(2) metaphorical terms (l39 b
32-140*2), (3) unfamiliar terms
(140*3-5), (4) inappropriate
terms, whether lit. or metaph.
(140*6-17), (5) expressions
which conceal their contrary
(140* 18-20) or their own mean
ing (20-2). Renders defin.
intractable (8vo-f7nx f ^pT l ov), I58 b
12-13. Hints for examining
Accident, when indeterminate
(ddtopio-Tov), 1 20* 6 foil.; for
examining obscure defin., 15 1 b
7-17; for answering obscure
questions, Bk. VIII, ch. 7 (160*

17-33).
Odd, the differentia of number,

I22 b I9, 23-4, 123*11-13, I42 b

10 ; not its species, I22 b 18-24 ;
not its genus, 123*1-2. Odd
no. not def. (i) = that which is
greater by one than an even no. ,
I42 b 8 : (2) = a no. with a
middle , 149*30-7^. I73 b 8~9).

T 2

INDEX

Odysseus, U7 b l3, 24.

Opinion : true or false not differ
entia of o., for it may be neither,
I23 a 15-18.

Conformity with general o.
the aim in dialectic, as truth in
philosophy, io5 b 3o-i (and v.
Dialectic). Dialectic must study
o. of crowd, ioi a 3l, 105*35;
of majority, io5 a 36; of philo
sophers, ib. ; of experts, io5 b i ;
also unusual o., io5 a 37. One o.
may have more than one object,
I I4 b 25-6. O.-in-itSelf (a{irdoa),
162*30-1.

Object of "0.,not akind of being ,
because wider (including things
non-existent), I2i a 2i~5, b 3~4:
not a kind of object of knowledge,
because wider (including things
notknowable), !2i a 2i-5. Basis
of sophistical proof that what is
not, is, i67 a 1-2 (cf. i8o a 32-4).
Obj.-of-o.-in-itself (8oa<rr6i/
aiVo), l62 a 28.

Opposites (avriKfi/jifva) : 4 kinds
(l) relatives, (2) contraries, (3)
privation and state, (4) contra
dictories, I09 b 18-19, H3 b i5.
Simultaneous bynature, 14^24.
Def. of term through its o.
a fault, I42 a 22 foil., but some
times inevitable, I42 a 26 foil,
def. of o. should be o., 147*29
foil. As tests of Genus, I25 a
25-32; of Property, 13 i a 14-26,
I35 b 7-i3~ a I3> I36 b 23-31; of
Definition, I53 a 26~9 ; of Same
ness, i5i b 33-6: reckoned
among the handiest and most
general of tests, H9 a 36.
Knowledge of opposites one (see
Knowledge].

Ornament (Ko o-^oy) in argument,
how secured, 157*6-13 (cf.
Weightiness).

Pac^^ts > edition, I32 a 36 n., b 3~8n.
137* 12-17 n., i83 a 2n.

Pain (a) \imrj : not genus of
anger , I25 b 29, I26 a 6-I2;in
spite of apparent claim, I27 b 3o:
rather a cause of anger, I25 b
33-4 (cf. Anger}. Jealousy
a kind of p., io9 b 36, uo a i;
Indignation , a kind of p.,
Ho a 2-3. P. of thirst contrary

of pleasure of drinking, lo6 a 37.
Things better without p. than
with, H7 a 24. That p. is evil,
as general a belief as that
pleasure is good, H9 a 38- b i.
To cause p. and repentance may
be sufficient punishment, I56 a

39-

(b} = a\yr]8a>v : not def. =
violent disruption of parts
naturally conjoined , 145" 2-7
(pain not inherent in sundered
parts), I45 b 12-14 (gives cause
rather than def. of p.).

Paradox. To lead into p., one of
chief aims of questioner in dia
lectical reasoning, I59 a l8-2o;
in contentious argument, i65 b 14
(cf. i83 a 2g): methods em
ployed in contentious argument,
I72 b 10-24, and 29-i73 a 3o;
I74 b 15-17 : often results from
leaving ambiguity undisclosed,
I 75 b 33~7- Should not be asked
point-blank in contentious argu
ment, i72 b 2i-4. Solutions sug
gested of arguments designed
to lead to p., I72 b 19-21, 33-4 :
cf. I76 a 25~7. P. maintained
by well-known philosopher =
a Thesis (q.v.), io4 b 19 foil.
Sophistical method of over
throwing paradoxical thesis,
I74 b 12-18. Paradoxical thesis
to be avoided in dialectic, l6o b
17 : 2 forms of it, l6o b 18-22.

Paralogism (see Misreasoning}.

Parmenides: argument that Being
is one, l82 b 26.

Passivity, a category, !O3 b 23.
See Activity (noielv).

Peculiar, Peculiarity ("Siav), ioi b
17: applied either to Definition
or to Property, ioi b 19 : cf.
I39 a 3i, !40 a 33-4, b 19-22,
I49 b i9.

Peloponnesians, 152*13, 15, 17,
20, 23.

Perception (ala-Savta-dai), a kind of
judgement, m a i6, 19. Not a
property of animal , 138* 7. P.
of contraries one, lO4 a 16, lo5 b
5, I56 b i2-i4. Problems soluble
by p., I05 a 7. [Cf. Sensation.}

Perplexity (an-opia) not def. =
equality of contrary reason
ings , I45 b i-2, 4-7, 16-20:

INDEX

two kinds of, i82 b 33 foil.
Greatest p. caused by incisive
argument (q.v.), i82 b 32.

Petitio principii may be due to
answerer s fault, i6i b 11-17. 5
modes of, i62 b 34-163* 13;
i66 b 25; 167*36-9: rules for
its solution, Soph. El., ch. 27 ;
why deceptive, 169 13-17: a
form of 7^72. elenchi, i68 b 22-6:
)( begging contrary views, 163*
24-8.

Phaedrus, the, I4o b 4 n.

Philosopheme def., 162*15.

Philosophy )( dialectic [see
Dialectical Reasoning}. Stan
dards of philosophy )( of law or
convention, 173*29-30. Natural
ability necessary for ph., i63 b
12-16 (and see s.v.).

Phlegm, not well def. = the un
digested moisture that comes
first off food , I40 b 7.

Physics, the, ]6o b 8 n.

Piraeus, 177 13.

Place (nov), one of categories, lO3 b
23, H5 b i2, I46 b 2o, 30 n.
Difference of p. not a specific
difference, I44 b 32. Definition
should mention essential deter
minations of p., I46 b 30.

Plane (iiriirtbov) : def. = limit of
a solid not strictly scientific,
but may be inevitable for un
scientific man, I4i b 15-25. Pos
terior to, and . . less intelligible
absolutely than, line , I4i b 5-7;
but prior to, and . . more intellig
ible absolutely than, solid , ib.
More readily perceived than a
line , I4i b 10-11. Finiteline
def. = limit of finite plane ,
1 48" 28-9.

Plato: (a) philosopher : 122*26
(def. of locomotion = car
riage , Theaet. iSid); 140*3,
b 4 (Phaedr. 2456); I42 b in.
(Def. 411 a); 146* 22n. (Hippias
Mai. 2976, 299 c); 148*15;
i66 a i4n. (Euthyd. 3Oob-c) ;
173*8 (Gorgias 4820); 179*
35 n. (Euthyd. 2986).
(b) comedian : 140* 3 n.

Pleasure : ambiguous, io6 a 37~ b I
(p. of knowing has no contrary
pain : contr. p. of drinking,
contrary of pain of thirst, 106*

37). Is p. desirable ? a good
dialectical problem, iO4 b 7. P.
and good or the good (see
Good}. Not a kind of motion
(icu tyiric), 121*30-7: treated as
activity (tWpyfin), 146 16-19.
Makes a good thing yet better,
117*23: sometimes objection
able, H9 b 6, 10 ; sometimes
beneficial, Ii9 b 7. Prodicus
division of p. (i) joy (^np),
(2) delight (i-f p^is), (3) good
cheer (fv(f>poavi>rj), H2 b 22.
Virtue better than p., I i8 b 32-3.
Incontinence concerned with
certain p. only, !46 b 26-7.

The pleasant = productive
of pleasure , I24 a 16-17 > hence
(if p. be good) a species of the
useful (w<pe\iftov), 124*17-20.
One of the ends which makes
things desirable, n8 b 27-8
(though strictly pleasure ,
rather than the pleasant , is the
end, I46 b io-i2): whether it
self a kind of good, depends on
whether what is not good can be
pleasant, I24 b 8-14.

Point (o-Ttynrj, arifjielov}, def. = limit
of line (not strictly scientific,
but sometimes inevitable in
dealing with unscientific men),
I4l b i5 foil. Prior to, and .*.
more intelligible absolutely
than, line , !4l b 5-7: but less
readily perceived, and . . some
times less intelligible to us ,
than Mine , I4i b 9-i2.

Paste, E. ; edition of Soph. El.,
I7i b i6n.

Preliminary admission (irpoSiofjin-
Aoym) sometimes to be secured,
io8 b i4, 110*32, H9 b 35, !48 b 7-8.

Premisses (see also Propositions] :
how to put and arrange, Bk.
VIII (esp. chh. 1-2). Necessary
p. , def., I55 b 2o: how to employ,
1 5 5 b 25-156" 3 ; may be secured
byeither deduction orinduction,
I 55 b 3S- P. other than neces
sary ; , their fourfold purpose,
I55 b 2i~5: how recognized,
160*35-9. Should p. more
difficult to argue than proposed
concln. be asked or granted ?
v. 159*4 foil. False p. admis
sible in dialectic, 161*27-33,

INDEX

i62 a 8-1 1, b 18-22 : their concln.
either true or false, i62 b 12-15.
False concln. requires false p.,
i62 b 13-14 : but use of wholly or
mostly false p., if irretrievably
barren of any concln., stands first
among faults of argument in
itself , l6i b 19-24. Argument
with false p. (whatever its con
cln.) 4th among types of fallaci
ous argument, i62 b 11-15. False
and childish p. make even argu
ment with true concln. worse
than many with false conclns.,
l62 b 22-4. Reasoning employs
few p., 158* 28-9. Superfluous
p., a fault in reasoning held
for inquiry, 162*24-34; but
recommended as dodge for
concealment, 157*1 ; though a
controversial trick only, I55 b 26.
Degree of conviction attaching
to p., compared with that
attaching to concln., l62 a 19-24.

Present (fiwpea) def. = a grant
that need not be returned ,
125*18.

Prior terms, more intelligible
absolutely than posterior,
I4l b 5 ; though sometimes less
so to us , I4i b 9- Genus
should be p. to differentia,
differentia to species, I44 b lo-i i
Definition, to be scientific,
should be of posterior through
p. terms, I4i a 26~3i, b 15-16 ;
though sometimes inevitably
vice versa in dealing with un
scientific people, 141^17 foil.
Sources of failure to define
through p. terms are defn. of X
(l) through X s opposite, I42 a
22 foil., (2) through X itself,
I42 a 34 foil., (3) through
X s co-ordinate-in-a-division
(di/TtSiflprj^iei oi/), I42 b J foil, (4)
through a species or instance of
X, 1 42 1 1 foil. A is better
than B if inherent in p. subject,
I l6 b 17. What is at rest (jutW,
tv rjpt/jiia) and definite (apur^ifvov)
is p. to what is indefinite
(a(ipto-Toi ) and changing (eV
Kivrjcrei), I42 a 2O I.

Problems = propositions (q.v.),
101 14-16, but differ in turn of
phrase, loi b 28 foil. Universal

p. )( particular p., ic8 b 37.
2 kinds of error in, (i) falsity,
(2) unconventional vocabulary,
I09 a 27-33.

Dialectical p. def., io4 b I ;
illustrated, !O4 b 7-i7. Some
subjects disqualified, ic-5 a 3-9,
cf. i6o b 17-22. Some harder to
handle than others, and less
amenable to generally accepted
premisses, i6i b 34 foil- D. p.
a nd thesis, ic-4 b 29-105"* 2 (cf.
Thesis).

Prodictis, his triple division of
pleasures (v. Pleasure], H2 b

22.

Property : def. = an attribute
peculiar to, and convertible
with, S, but not essential, ioi b
19-23, I02 a 18-19 (cf. 28-30),
I03 b ii-i2, I09 b io. Sand its p.
the same , though less strictly
so than S and its definition,
!O3 a 27-9; must be different
terms, though convertible, 135*
9-19. Tests for p. applied to
Definition, io2 b 27-9, I2o b i3,
cf. I54 b 13-14, 18-23 (see
Definition} ; to Accident, 133 a
32-4 : seldom studied separ
ately, I2o b 14. Different kinds
of p. (i) Essential p., I28 b
1 6-1 8 : def., I28 b 34-6; (2) rela
tive p., io2 a 26-8, b 24-6, I28 b
18-19; def., i28 b 36-9: gives
rise to either 2 or 4 problems,
I28 b 22-33, I29 a 18-20: 2 kinds
of r. p., according as difference
is present (a) universally and
always, or (6) usually and in
most cases, I29 a 6-i6 : amenable
to tests for Accident, I29 a 32-
4> (3) permanent p., I28 b i9~
20: def. I28 b 39-I29 a 2 ; (4)
temporary p., iO2 a 24-6, b 24-6,
128 20-1 : def., I29 a 3-5. P. of
present time (v\>\>\ I3i b 5 foil.
P. of particular individual (TIV I)
I28 b 20, I3i b 12, 17. Accident
may become temporary or rela
tive p., but never a p. absolutely,
v. Accident. Different ways in
which p. may belong: (i)
naturally (normally), as opp.
permanently, I34 a 5, 29, b 5-7 :
(2) actually (Tovnupxov), I34 a 30,
b 7~io: (3) specifically (i8<t),

INDEX

I34 a 3i, b 22-135*5: (4) abso
lutely, 134*32, 135*2, I37 b 28-
138*3: (5) derivatively (/car*
AXo), 134*32, b 10-13: (6)
primarily (u>s TT/JWTOI/ avro) 134*
33, b 10-13 : (7) conditionally on
being in a certain state (TW (\(u>),
I34 a 34, b 13-18: (8) condition
ally on being the state in which
something else is (T<U Hxta-dm),
134*36, b 13-16: (9) because S is
genus of a certain species (ro>
fifT(xf(T6ai), I34 b l, b 18-22 :
(10) because S is species of a
certain genus (TJ /ir ^tv), i34 b
4, b 1 8-22: (ii) potentially
(SvviifjLfi), I38 b 27-i39*8. Most
arguable (Xoyj*) p. are the
essential (129* 17, 21-6), perma
nent (129* 1 8, 26-8), and relative
(129* 1 8-2 1). Tests for essen
tial and permanent p., Bk. V.
(a) Are they rendered correctly ?
(chh. 2-3) ; (b) Are they proper
ties at all? (chh. 4 foil.). P.
must render S more intelligible,
I29 b 2 foil., esp. 7-9, 131*12
foil. : must be unambiguous,
I29 b 3o-i3o* 14 ; likewise its S,
130* 15-28 : must . . not contain
redundancies, I3o*29- b io, or
universal attributes, i3O b 1 1-22 :
must be rendered singly, i3O b
23-37 i and not circularly, I3o b
38-131*11 : must be a perma
nent attribute, I3i a 27- b 4, unless
stated to be temporary, 13 i b 5-
18 ; not evidenced by perception
alone, I3i b 19-36; not essential,
I3i b 37-132* 9 (not definition),
I32 b 35-I33*n (not differentia),
133*18-23 (not definition or
differentia) ; though should be
prefaced by indication of
essence (genus) 132*10-21:
must be convertible, 132* 7, b 8-
18, 135*18; cf. I54 b 18-23:
must be true universally of S,
I32 a 27- b 3, 154 19-22; and of
whatever is same as S, as such,
133*24-34: must not be
rendered in superlative, 139*9-
20 (cf. I34 b 22 foil.) : is usually
rendered in complex phrase (eV

(TU^TrXoK^), I54 b 15-16, (fK TTOX-

Xcoj/) 155*24. Sophistical diffi
culties arising from (n) problem

whether S qualified by some ac
cident is same as S, I33 b 15-
36 ; (b) different ways in which
p. may belong, 134*5, 18, 26-
!35 a 5 : to meet them, manner
in which p. belongs must be
stated fully, 135*6-8. 1 . of
wholes of similar parts (6p.t>n.-
t*fpfi) must apply to both parts
and whole(<riii r>Xo ),i35 a 2c- b 6;
of contraries, must be contrary,
I35 b 8-i6; of relatives, must be
relative, 13517-26; of terms
opp. as state and privation, must
be so opposed, I35 b 27-136* 4 ;
of contradictories, must be con
tradictory, 136*14-27; of co-
ordinates-in-divisionmust be co
ordinates in divn., I36 b 3-14 ; of
S, must be true of idea of S
not qua idea but qua S, I37 b
3-13 ; of S that is variable in de
gree, must vary directly with it,
I37 b 14-27.

P. more easily disproved than
proved, I54 b 13-23: of predic-
ables other than definition, p.
the easiest to disprove, hardest
to prove, 155*23-7.
Propositions (see also Premisses) :
the material of reasoning, ioi b
15 : = problems, ioi b 14-16, but
different in turn of phrase, ioi b
28 foil. 4 kinds of p. dist. by
predicable involved, ioi b 17,
23 : proof of this, inductive
(iO3 b 2-6) or deductive (iO3 b 6-
19): no single system of tests
applies to all, iO2 b 35. P. always
predicate an attribute in one of
10 categories, 1 03 b 23. 3 kinds
of p., dist. by subject-matter,
viz. those dealing with ethics
(i]0iKai), nat. philosophy (</>i><rt-
Ktii), and logic (Xoyixai), I0? b 19

foil. : classifies rough (105 19)
and its branches not easily
defined ( b 25). Makes a single
statement about a single thing,
169*8.

Dialectical p. def., 104*8,
and varieties illustrated, Bk. I.
10 passim, and 14 init. (see
Opinion) : = one to which an
swer is "Yes" or "No" , 158*
15-17, 160*33-4, (cf. I75 b 8-io,
1 76* 1 1 , 1 5 ) : = one supported

INDEX

by a no. of instances with no
apparent neg. instance , I57 b
32-3 : cf. !58 a 3-6. Philosophy
regards truth of p., dialectic
their general acceptance, io5 b
30 : cf. I55 b 7-i6. P. to be
secured in most general form
and then subdivided as far as
possible, I05 b 3i: cf. io9 b 13
foil., i64 a 3, b i8. Discovery
of suitable p., a main means of
dialectic, ic>5 a 2l-3, 164^2-4.
Stock of p. should be learnt by
heart, i63 b 28; to be obtained
by practice in deduction with
expert reasoners, 164* 13-14.

Putting of p. )( objecting,
164^-7. Arrangement of p.
(see Arrangement).

Prosyllogism, in proof of pre
misses, a means of concealment,
I56 a ;.

Protagoras, I73 b 19.

Prudence (typovrja-is) : more desir
able in old age, 117*28; than
power, n8 a 18 : the form of
knowledge most generally
agreed to be good, Ii9 b 33~4 :
thought by some to be both
a moral virtue and = knowledge,
I2l b 3i ; thought by others not
to be knowledge, 12^32-3.
Fourfold disproof that, of virtues,
p. alone is knowledge, 120*27-
31. P. as knowledge of the
noble and of the base, I37 a 12
foil. What tends to bring
happiness, preferable to what
tends to brings p., Ii6 b 24-6.

Choice of prudent man, the
norm of what is desirable, Ii6 a
14; of the natural use of
anything, I45 a 25~7.

Pseudo- Alexander, i83 a l2n.

Punishment: some doubts de
serve p., ic>5 a 4-7. To cause
pain and repentance may be
p. enough, 156*39.

Quality, a category, io3 b 22, 26,
38, 179*9: essence of a term
may be a q., lc>3 b 27-8, 31-3.
Tests for comparative values
generalized as comparative tests
of any q., Bk. Ill, ch. 5. Genus
of a q. must be a q., 121*7-8.
Differentia indicates a q., 128*

26-8 (cf. I22 b 16-17), I44 a 1 8-
22. Definition should mention
essential determinations of q.,
l46 b 2o-2, 30.

White a q., not essence, of
snow , 1 2o b 27-9 ; so good ,
of virtue (l44 a 1 7-1 8), of soul
or man (107*7-8). Verbal
terminationspropertoq. )( those
proper to quantity or to activity,
a source of fallacy of form of
expression , l66 b 13, 16-8.
Quantity, a category, io3 b 22, 26,
38, 178*8, I79 a 9: essence of a
term may be a q., iQ3 b 33-5.
Definition should mention
essential determinations of q.,
!46 b 2o-2, 30. Good (of q.) =
the proper amount (perpiov),
io7 a 10-11.

For variations of q., see
Greater and less Degrees,
Superlative.

Reason (vovs) in soul, analogous
to sight in eye, 108* 1 1 : man
capable of acquiring r. , 112*
18-9.

Reason, faculty of (TO Xoyia-riKov) :
the seat of shame (atoTfuwj)
126*8: of wishing , 126* 13: of
ignorance , I47 b 29-33. Its
property (l) to command
( relative property, of kind
occurring usually and in most
cases ), 129*10-16: (2) to show
wisdom (TO (fjpovipov) ; be
longs to it, primarily (&>? TO
TT P 5>Toi>), 134*33-4 : cf. !38 b 2-4,
I45 a 30-2, and cf. I36 b 1 1. Not
its property actually to reason ,
138*33-6. Belongs primarily
to soul , I38 b 12-15.

Reasoning (syllogism), def., ioo a
25: divided, 100*27 foil.: the
division rough, 101* 19. Always
employs few premisses, 158*
28-9 : requires universal pre
misses, 164* lo-Ii ; turns on def.
of familiar and primary ideas,
i63 b 20-2. Genuine )( apparent,
l64 b 25 foil. R. per accidens
cannot be refutation, i68 b 4-5,
thougli amateurs often entrap
scientists by it, i68 b 6-io. R.
)( rhetoric, i67 b i3 (contr. 8) :
backwardness of earlier theory

INDEX

ofr. (contr. Rhetoric), 184*8-
b 2. Dialectician dist. from
amateur examiner in knowing
theory of r., I72 a 34-6.

[See Demonstration, Didactic
argument, Contentious r., Dia
lectical r., Hypothetical r.,
Fallacy, Misreasoning^\

R. = deductive r. (as opp.
inductive), io3 b 7, 105*11, i53 a
8, 23, I55 b 35, 164*13: more
forcible and effective, io5 a 18 :
more suited agst. experts, io5 a
18, 157*18, i64 a 13-14 (advised,
with view to laying up store of
premisses).

Recollection, considered as genus
of learning , 124*22. Know
ledge not = r., 1 1 i b 26-31. (Cf.
Memory).

Reductio ad absurdum, l62 b 20 n. :
and see Impossible.

Redtindancy, I39 b 15 and Bk.
VI, ch. 3. Sources of, 140*24
foil, (i) universal predicates,
140*24-32: (2) words not
required to express essence,
I4o*33- b i5: (3) words that
render defn. too narrow, 140
16-26 : (4) vain repetition of
word already used or implied,
I4o b 27-141* 14, 141* 15-22.
[See Babbling^

Refutation: genuine )( apparent
or sophistical r., i64 b 25 foil.

2 kinds of sophistical r., ( I ) only
apparently valid, (2) valid but
only apparently appropriate,
i69 b 2o-3. One of principal
aims of contentious reasoning,
i&5 b 14. Sophistical r. never
absolute, but always relative
to some one, 1 70* 12-13, v z - an ~
swerer, 170*17. R. def. (i) =
reasoning involving contradic
tory of given conclusion , 165*

3 ; or (more simply) = proof of
contradictory of given thesis ,
i7o b i, 171*5: cf. i74 b 35-6,
177*16-17; (2) 167*23-7: cf.
181*1-5, b 20-2. Defn. of r.
follows closely on that of
reasoning , except that con
clusion is described as the
contradiction of some view,
168*35-6. All demonstration
is also r., 170* 24-6 : every one

engaged in r., 172*34. R. de
pendent on diction of 6 kinds,
l65 b 24-7 ; proof of this, 27-30;
such r. sometimes due to lack of
clearness in question, 169 35-
6 ; but same lack of clearness
often obscures r., I75 a 4i- b i4,
b 28-30. Not all r. dependent
on ambiguity, I77 b 7-9 (cf .I79 b
38-180* 7) ; only ambiguity ,
amphiboly , and form of ex
pression , 168*23-5. R- n <>t
dependent on diction of 7 kinds,
i66 b 2i-7. Reasoning per acci-
dens cannot be r., , i68 b 4-5. R.
(true or false) infinite in no. ; com
plete study of r. demands omni
science, !7o a 2O-34. Study ofr.
employing principles of particu
lar science belongs to experts in
that science, 170*36-8. Dia
lectic studies only r. resting on
common principles, not peculiar
to any particular science, 170*
38-9 : this includes r. which are
(i) really dialectical, (2) only
apparently dialectical, (3) suited
to examination, I7o b 8-n.
Dialectic studies sophistical r.,
I72 b 5~8: cf. 108*26-31 (but
contr. 108*33-7).

Relation, a category, lO3 b 22.
Essential*, (npos rt Kaffavro) opp.
generic r. (np<>s TI Kara TO yevos),
I24 b 23, 146* 36 : opp. accidental
r.(-rrpusTi Kara (rvufiffi.), 143*3-4,
Refutation must prove contra
dictory true in same r. intended
in original thesis, 167*26, 170*7,
180*28-30, b 7 foil., 181* 1-4.

Relative terms : essence of term
may be a relation, 142*28-30,
!46 b 3-4 (cf. io3 b 27-9): such
essentially r. t. (Trpor TI Kad avrd)
must be def. through its corre
late, 142*30-1 ; being meaning
less in abstraction, i8i b 26-8.
Genus of r. t. must be r., 121* 3-
4, I24 b 16-17 : but this question
able (e.g. virtue a r. t., but
good not so), I24 b 19-22; and
not true vice versa (e.g. know
ledge a r. t., not so grammar ),
I24 b 18-19: r. t. and its genus
should be r. to equal no. of
things, 125* 14-23 ; though
perh. not always, 125*23-4.

INDEX

Differentia of r. t. must specify
correlate, 145*13-18. R.t. should
be def. in all its relations, 142^
30-5, esp. in that which is best
(I43 a 9-ii: cf. 146*11, I49 b 37),
natural (l4S a 19-27), and pri
mary (145*28-32): but not in
accidental relations, 142^ 35-
143*8, 1 49 b 4-6, 12-23. [Fordef.
of r. t. see also Bk. VI, ch. 8

(I46 a 36-147* 11), I47 a 23-3i-]
Test for statements about r.
t., ni a 6-7 (v. iio b 33-m*6).
Knowledge of r. t. the same,
I0 5 b 34j ic9 b 18, 164*1-2. R.
)( absolute standard of good
or desirable , 116*21-2, b 8-
10: r. ) (absolute use of expres
sion, i66 b 23, 37-i67 a 2o, and
Soph. El., ch. 25. Sophistic
refutation always r.to answerer,
170*12-13,17-8. R.t. give occa
sion for babbling , I73 b i~5:
for fallacy of form of expres
sion , if mistaken for sub
stances, 178*4-8, 36- b I, 179*
8-9.

R.t. as tests of Accident,
114*13-25, 119*37, b 3~4: of
Genus, I24 b I5~i25 b 14, 147*
23-8; of Differentia, I45 a 13-32,
146*21-32; of Property, I35 b
17-26; of Definition (see reff.
above).

Rhetoric: like dialectic, (i) aims
at doing best in circs., ioi b 5-
10 ; (2) examines inconsis
tencies of statement, I74 b i9foll.
)( reasoning (syllogism), i67 b 8
(contr. 13). History of r. com
pared with that of dialectic,
l83 b 26 foil. Rule of r., to cast
enthymemes into universal form,
164*5: in r., argument from
signs (analogy) = argument
from consequences, i67 b 8.

Rhetorician, def. of, criticized,
I49 b 26-9.

Rob-son ( ATroXXtow Sqf), i82 b 2O.

JRoss, W. D., conj., I37 b ion.

Sameness (ravrov) : ambiguous,
103* 7, 25-9 : and not easy to
divide, 169*24-5. 3 kinds of
s., 103*7, (i) numerical, def.
103* 9, (2) specific, def. 103* 10,

(3) generic, def. 103* 13. Of
these, numerical s. its most
generally agreed sense 103* 23 :
but even this ambiguous ; 3
shades of meaning distinguish
ed, 103*25-39. Testsof numeri
cal sameness, Bk. VII, ch. I.
Water from same well, same
specifically, 103* 14. Questions
of definition mostly concerned
with s.,io2 a 7: disproof of s. dis
proves defn., but proof of s.
does not prove one, io2 a 11-17,
Bk. VII, ch.2. Study of differ
ences useful for arguments
about s., 1 08* 38-^4, Sophistical
difficulties in fixing properties,
owing to ambiguity of s. and
difference (e.g. is A the
same as A qualified by an
accident , or as its accident ?),
I 33 bl 5 fU : cf- I78 b 39-179* I.
Arguments about A from what
is same as A, in fixing proper
ties, 133*24; accidents, 133*
32. Failure to distinguish s. )(
difference, a source of fallacy of
Accident, i69 b 3~6.

Sameness of relations between
2 things (A and B) and an attri
bute (a), as test of Property,
I37 a 8-2o.

Science (see also Knowledge).
Principles of s. should be self-
evident, ioo b 19-21 ; and/r/j
of all else, 101*39. Use of
dialectic in ref. to principles of
s., ioi*36- b 4. Fallacies based
on principles of special s., ioi a
5-17, 170* 31-4 (see Mis-
reasoning, Refutation). Special
s. of anything the judge of its
natural use, 145*25-7. No
special s. definable as the s.of
reality , !49 b 6-23- S. possibly
infinite in no., 170*22. One s.
better than another if (i)
concerned with better object, or
(2) more accurate, 157*9. That
the s. of many things is one ,
ambiguous, no b i6. Specula
tive )( practical s., I52 b 4 (and
cf. 149*9-13, 14, 17): specula
tive )( practical )( productive s.,
145*15,157*10. Philosophical
s., 101*34. S. of definition
(opiffTiKrj) a speculative s., 141*8.

INDEX

Exx. of sciences : (i) Arith
metic (dpiOpoi), also called a
study (/la^o-tf), 153* 10 ; (2)
Geometry, 101*7, I32 a 3i foil.,
1 70* 28-30, also called a study
(fjuWrja-is), 153*10; an art
(rfV 1 ? ) > i 4 a 34-6 (cf . 1 5 ) , i ;o a 3 1 ,

I7i b 12-13, i72 a I : cf. art and
faculty , I7o a 36 : (3) Medicine,
loi b 6-io, Iio b i8, 141*19,
I49 b 6, 19, i63 a 10, 170*29-30:
also called a faculty (Svvapis ),
loi b 6; an art , 104*34-6, 170*
31: (4) Grammar, 111*37, i24 b
19, 126* 5, 19: (5) Music, ill*
37,i28 a 31-2 : (6) Rhetoric, ioi b
6-10: also called a faculty
(ib.); an art , io4 a 34-6 (cf. 15).
[N.B. no apparent distinction
observed between science ,
art , faculty and study .]
Scientist : his property to be in
controvertible by argument -
belongs by reason of state he is
in (d>? TW ?x* u )> whereas to
science it belongs because it
is the state of the s. (T&J txf(r6ai},
I34 a 34~ b i, 15-18. [This the
solution of the objection (l33 b
28-31) that it belongs to both,
and . . is property of neither.]
Not his property not to be
deceived by argument, 132*

31-4-

Sea : not its property to be the
largest vol. of salt water (true
of whole sea, but not of particular
seas), 135*28-32. Calm : sea
= windlessness : air, 108* I l-i 2,
b 25-6.

Sensation, Sentience (ma-drjans) : a
kind of state (ftr), I25 b 17 :
its privation absence of s.

(avaio-drjaiit), 114*11. Not a

capacity , I I9 b 2 : not genus of
knowledge , 125*28-32 : not =
knowledge, because irrecover
able if lost, 105" 28-30; problem,
how different, demands study,
108*4. Problem Is s. know
ledge ? a definitory problem,
lO2 a 5-7. S : object of s. =
knowledge : object of know
ledge, io8 a 9- Not def. =
movement through the body ,
I25 b 16. Be sentient , or
have sense (aLadavtaBai) and

want sense (dvaiaQijTov tlvai)
doubly ambiguous, (i) have
sense )( active use of sense, I29 b
33-4 : (2) spiritual sense )(
bodily sense, io6 b 23-8. See
ing (Spa<rit) a species of s.,
114*19, 124*38, b 6. To be a
s., not a property of hearing,
J35 b 3i-3- Sleep not a failure
of s. , I45 b 1-4, 14-16. S. as a
property of animal (see
Animal). Object of s., assumed
to be know-able, 114" 21; but
often denied to be so, 114*23;
better known (i) to mass of
men, and sometimes to us, than
more abstract objects, I4i b 9~
12, 1 56" 6-7; (2) at first, but
objects of thought later, 142*
2-4. Objects of same kind
apprehended by same s., 106*
29-30: white (clear) in colour
and in sound, or sharp )( dull
in flavours and in edges, appre
hended by different s., 106* 30-
3. Facts evidenced by s. not
to be trusted as permanent,
I3i b i9 foil. Ideas must be
objects of s., if they exist in us,
1 1 3*27-32.

Shame (aio-xvvrj) resides in faculty
of reason, 126* 8 ; not a kind of
fear, 126*6.

Shamelessness (dvaidtia) not def. =
product of courage and false
opinion , i5o b 3-6.

Sharp (ofu), opp. (i) to flat
(@npv), of sounds : (2) to dull
(a/*/3Au), of edges, 106*13, 32,
107*13, b 23. Applied to fla
vours, 106*32, io7 b 14 : to an
angle (acute), 107* 16.

Sicily, I77 b 13-

Sight (ctyiy), a species of sensa
tion, 114*19 (Sprung), 124*38,
b 6: the state (ffrs) of which
blindness is privation, log 1 *
22, 1 47 b 34 (see Blindness]. S . :
eye = reason (vovs) : soul, 108*
II. )( hearing, 106*32. A
property of it, to see, inasmuch
as we haves. , 136*1-2. To see
(opdv), not a property of man ,
I38 b 9 : Seeing (tiKtirtiv) am-
biguous,( i ) to possess s.,(2) to use
s. actively, io6 b 15-20. (So too
failure to see TO fifj p\tn(u>.)

INDEX

Colours in bodies dist. by their
reaction on s., io7 b 29-30.
Beauty not d ef. = pleasure that
comes through s. or hearing ,
I46 a 22 foil.

Silver )( litharge and tin, i64 b
22-4.

Sleep not def. = failure of sensa
tion , I45 b 1-4, 14-16: not a
property of man, iO2 a 22-4, 28-
30.

Snow, not = frozen water , I27 a
14 ; nor is water its genus at
all, 127*15. White its acci
dent, not its genus, I2o b 22-35,

I27 b 2-4.

Snub-nose I73 b 10, i8i b 38 foil.
Socrates, 103*30, i6o b 27-8, i66 b

34, I83 b 7,

Solecism def., i65 b 20-1 : a princi
pal aim of contentious reasoners
to produce, i65 b 14 : methods
employed, Soph. EL, ch. 14:
how avoided, Soph. EL, ch. 32 :
sometimes turns on failure of
question to be explicit, i69 b 35~
7. S. real )( apparent, I73 b i7
foil. S. compared to fallacy of
form of expression , 174* 5-9.

Solid (l) = crreptov : posterior to,
and . . absolutely less intelligible
than, plane , 14^5-7: more
readily perceived than either
plane or line , and . . some
times more intelligible to us,
I4i b 9-ii. Plane def. =
limit of a s. , I4i b 22.

(2) = 6 y/coj : sharp has diff.
meaning of a s. and of a sound,
io6 a 13-14, I07 b 23: of as. and
of a flavour, io6 a 32.

Solution (Xuo-ts) def. (i) i6o b 23-
39; (2) I76 b 29-3o, !79 b 23-4- S.
of refutations appears in analysis
of their forms, being merely the
appropriate objection, I7o b 4~5,
!75 a 17-20: expounded in detail,
Soph. El., chh. 16-32. Sugges
tions for s. of arguments leading
(i) into fallacy, i62 b 24-30,
I76 b 36-177* 6; (2) into para
dox, i72 b 19-21, 33-4: cf. 176*
25-7. S. of properly reasoned
arguments )( s. of merely
apparent arguments, I76 b 35~6.
S. of fallacies dependent on
diction follows opposite of point

on which fallacy turns, 179*
II foil. Merely apparent s.
should be advanced in default
of proper (opdrj) s., 176*19 foil,
(cf. b 29). Study of s. useful (i)
for philosophy, I75 a 5~i2, (2) for
reputation as arguer, 175*13-16.

Sophism, 162*14: def. 162*16.

Sophist def. = one who makes
money from apparent but unreal
wisdom , 165* 22-3, 17i b 28-9 ;
not def. = one who can
(deceive), 1 26 a 31-2. Doctrine
of s. that all that is either has
come to be or is eternal, io4 b
25-6.

Sophistical )( contentious argu
ment [q.v.] distinguished by
motives of arguers, 171^25-34.
S. difficulties in fixing proper
ties, arising from ambiguity of
same and different , I33 b
15 foil. Arguments seem s. if
not proved step by step, 158*
34-6. Apparent hut irrelevant
proof always s., 162*12-15.
Bryson s method of squaring
circle sophistical, because not
based on appropriate premisses,
I7i b 16-18. Most s. of all
tricks of questioner, to state
conclusion as proved when
unproved, I74 b 8-1 1. S. turn
of argument on to more favour
able ground, Bk. II, ch. 5, m b
32 foil., I72 b 19, 25-8: not so
easy as formerly, because
answerers are sharper, I72 b 2o :
where neither really nor appar
ently necessary, to be avoided,
asaliento spirit of dialectic, 112*
9-11 (cf. Verbal Argument).

Sophistry def. = (i) the art of
making money from an apparent
wisdom , !7i b 27-9; (2) the
semblance of wisdom without
the reality , l65 a 2l, I7i b 34-
Akin to dialectic and the art of
examination, i83 b 2.

Soul : def. = self-mover (Plato),
I4o b 3 : but not a self-moving
number , I4o b 2 : nor a num
ber at all, I2o b 3~6. ; 123*13-
14, 23-6. Self-moved not its
genus but rather its accident,
I2o b 22-8, 32-5 : nor moved ,
for possibly not in motion, 123*

INDEX

15-17, cf. I27 b 15-17 : motion
inapplicable to s., for none of
its species will apply, m b 5.
Notdef. = substance capable of
receiving knowledge (for cap
able of ignorance too), 151^ i.
May, but need not, possess
self-knowledge, I25 a 39-4o, b 3~
4. Its property (i) to be fitted
to command the body rela
tive property, I28 b l8-i9: (2) to
show wisdom belongs deriva
tively (/car (iXXo), because
s. possesses faculty of reason,
I34 a 32 : (3) to be the primary
whole of which faculties of
desire and of reason form part ,
I38 b 12-15. Better and more
important than body, i i8 a 32-3:
virtue and vice of s. )( of body,
I53 b 8-10. Its immortality,
1 1 9 b 36-7. To have a s. not
correctly rendered as property
of living creature ((u>oi>) unless
genus ( substance ) be also
stated, 132*15-16; though
correct in avoidance of universal
predicates, I3o b 20-2. To have
tripartite soul , an essential
property of man , 133* 30-2.
Spartans, 152*14, 15, 17, 20, 22,

Species. See Genus.

Speusippus, I74 b 27n.

Spider (<pd\uyyioi>), not to be de
scribed in defn. as poison-
fanged (unfamiliar term),
I4o a 4.

Spirited faculty : (i) = dvpoddes
seat of anger, but not of friend
ship and . . not of hatred, 113*
35 foil., I26 a 10 ; seat of fear,
I26 a 8. (2) BvtiiK&v, 129* 12.

Squaring the circle, method of
Hippocrates, I7l b 15 ; by
lunules, I7i b i5, I72 a 3; of
Bryson, I7i b 16, 172*4; of
Antiphon, I72 a 7.

State : (i) = %eiv, one of the cate
gories, io3 b 23: (2) = fiy. S. )(
activity , I25 b i5: )( the
capacity that attends it, I25 b
20 : )( what is in, or is described
in terms of, the s. : a property
may belong in either way, 134"
34- b l, 13-18 : a s. and what is
in the s. have same properties,

!33 b 25-8. Genus of virtue
and of knowledge , I2i b 38(cf.
Disposition} : knowledge a s. of
the soul, 1 24 34. A s. neces
sarily found in that whose s. it is,
I 2 5 a 33-7- Tests for definition
of as., 147* 12-22. The good
not a s. of virtue , I42 b i2.
Justice not a s. that produces
equality or distributes what is
equal , I43 a 15-16. Virtue
not = a good s. , 144* 9-10.

S. and privation : as tests of
ambiguity, io6 b 2i-8; of Acci
dent, 114* 7-12, 119* 37, b 1-3 ;
of Genus, I24 a 35~ b 6; of Pro
perty, I35 b 27-I36 a 4; of Defini
tion, I47 b 4-i7, 26-148*9.

Strache, edition, 132* 36n., i66 b
25 n.

Strength less good than health,
i i6 b 1 8 ; than justice, I i6 b 38.

Strigil, not def. = an instrument
for dipping water (not its
natural use), 145*23-5.

Students (rjKpon^evoi) as opp. other
hearers of Aristotle, 184 6.

Substance, a category, io3 b 22 foil.
Tendency to treat every predi
cate as a s., a special source of
fallacy of form of expression ,
168*25-6,169*33-6, 170*15, and
Soph. El., ch. 22,esp. 178*5-8,
b 36-179*10. Predicates in
categ. of s. (e.g. man ), like
other general predicates, )(
individual s., I78 b 37 foil. In
dividuality and being usually
ascribed in fullest sense to
s., i69 a 35-6.

Sun : not def. = star that
appears by day (virtually cir
cular), I42 b I. Not its property
to be the brightest star that
moves over the earth (known
by perception only, and . . not
knowable as permanent), I3l b
25-30.

Superlative, attribute rendered m

(icad vTre p@<>\T)i; 1 34 b 24: wrp/3oXp,
139*9 M ^ 10 " onoiiv, 152* 5) :
cannot be a property. 139*9-20
(cf. I34 b 22 foil.) : of A and B,
if each an individual, implies
their numerical sameness, 152*
5-12 ; if not, implies that one
contains the other 152* 12-30.

INDEX

Surface (enifyaveia). Its property,
to be the primary thing that is
coloured , !3i b 33-6, 134 b 10-13:
belongs primarily (OK TOITPWTOV),
I34 b 10-13 : solution of objec
tion (I34 a 22~5) that it belongs
to body also, and . . cannot be
property of either. Contr. 138*
15-19, being coloured not a
property of s., and whether so or
not, cannot be property of
body . (Same solution would,
however, apply.)

Syllogism. See Reasoning. Syllo
gistic (reasoned) argument )(
contentious argument, i82 b
34-6. Most incisive form of s.
argument, l82 b 37foll. ; of con
tentious do., i83 a 7.

Synonym, Synonymous terms.
Must have same definition,
lo; b 4-5, 148 a 24-5, b 3. Genus
and species must be s., I23 a 28-
9, I27 b 6, cf. I54 a 1 8. Syllable
cannot be s. with one of the
letters in it, i5o b 2O-i. S. not
a definition, 149* 1-4 ; though
definitely , iO2 a 5. Refutation
must prove contradictory of
actual attribute asserted, not of
its s., i67 a 24. Exx., doublet
= cloak , io3 a 10, 27, i68 a 30 :
beautiful = becoming , io2 a
6, I35 a 13.

Temperance : not def. = a har
mony (<rvfi<f><i>via), because (l)
metaphorical, I23 a 34~7, I39 b
33 : (2) a harmony always found
between notes ; not so virtue j
. . harmony and virtue not in
subaltern relation, !39 b 37-i4O a
2. More desirable in youth
than in old age, 117*32; than
courage, 1 1 7 a 36. A property of
t. to be essentially the natural
virtue of the faculty of desire,
I36 b 10-14; likewise of faculty
of desire to be primary seat of
t., I38 b 4. Justice not def. =
t. and courage , I5o a 3 foil.

Terence, l66 a 37 n.

Theaetetus, the, 1 22 b 26 n.

Themistocles, 176* I.

Theodorus, i83 b 32.

Thesis (i) ace. to strict defn., I04 b
J 9> 34 I72 b 22, 30: e.g. para

doxes of Antisthenes, Heraclitus
and Melissus, iO4 b 20-2. Every
t., in this sense, a problem ;
not vice versa, I O4 b 29-34. Such
t. to be collected among other
premisses , !72 b 3l-2.

(2) in wider sense = dialec
tical problem generally, iO4 b
34-6, or (more strictly) the
answerer s position on the
problem, I u b 36 (= ro K.eififvov,
U2 a i), Ii2 a 4, 7, 13, H3 a i9,
I20 a 27, Bk. Vlll passim, I58 b
24 (clearly = Trpo/SXr^a, I58 b i6),
X 59 a 3) 39 an d foil. ( = ro Kfifjie-
vov, I59 b 24), i6o b 14, i83 a 24,
b 6. Some t. not suited for
dialectic discussion, lo5 a 3 : the
clearer in expression, the easier
to argue upon, iii a lo-n. Every
t. bound to be generally
accepted (ev8o<>s) or rejected
(fifio|os ) or neutral (/tqdc repos),
I59 a 38: rules for defending
each, !59 b 4-35- 2 kinds of
generally rejected t., i6o b 16-
22. Rules for selecting and
maintaining a t., Bk. VIII, ch.
9. Aim of questioner always
to prove opposite of answerer s
t., I59 b 5~6. Parallel arguments
to be drawn up pro and con
same t., i63 b 4~5.

Thief def. = one who wishes to
pilfer in secret ; not one who
pilfers in secret (true only of
expert t.), I4g b 27-30. The
argument of the t. , i8o b 18.

Thrasymachus, i83 b 32.

7*ime (i) = TTOTC, a category:
!O3 b 23. Good in this cate
gory = what is in season (ev
Kip<u), io7 a 8.

(2) = xpovos : neither in
motion nor a form of motion,
I2o a 39~ b 3. Discrepancies of
t. (past, present, and future) as
tests of Accident, m b 24-3l,
cf. H5 b i2, 17-21: of Genus
and Differentia, I23 a 16-19; of
Property, I3i a 27- b 4, b 5 foil.,
I33 a i2 foil.; of Definition,
I45 b 21 foil. Refutation must
prove contradictory true at time
to which thesis refers, i67 a 26-
7, i8o b 7-8, 11-12, 14, 181* 1-4
(cf. I6s b 38-i66 a 6, "23, l8o b

INDEX

13-14). Objection directed by
answerer agst. t. allowed for
discussion, i6i a 9-12, 183*22 :
questions likewise directed by
questioner, where t. is too short
tooverthrowanswerer ssolution,
183*24. T. or season (*a<por),
as determinant of values of
things, 117*26-37. Temporary
property (see Property] : re
quires ref. to present t. only,
129* 28 : property of present t.
(I f K tSioj/), I3l b 5 foil.

Tistas, i83 b 3i-2.

Trainer (yv^vua-T^} : his property,
to have ability to produce
vigour , 137*5-6. T.: ability to
produce vigour = doctor : abil
ity to produce health, 137*

3-5-

Training (yv^rna-ia) = (i) physi
cal: desired as means, 116*
30-1.

(2) tn dialectics. Study of
Dialectics useful for, 101*26:
some proofs too elaborate to be
suitable for t., 105* 9. Argu
ments held for t. and examina
tion )( contentious arguments,
and teaching, 159*25, cf. i6i a
25. [Apparently t. = in
quiry (cr/ct ^ir) : cf. 159*25 and
34.] H ints upon t. in dialectics,
Bk. VIII, ch. 14, passim. To
argue ^ro and con everything is
good t. for both questioning and
answering, i63*36- b 3.

Triangle : to have angles = 2
right angles, essential to t, but
accidental to equilateral t. ,
1 1 o b 22-5, cf. no b 6-7: acci
dental also to figure , 168*40-

b 4-
Triballi, H5 b 23, 26.

Unit (novas) : prior to number ,
I4i b 8: starting-point of num
ber , io8 b 26, 29, I4i b 8; and
more intelligible absolutely than
number , I4l b 5~8.

Unity (TO (v) ambiguous, and
difficult to divide, 169*24, I7o b
21-2; though opinions differ
about this, l82 b 24~7. Not a
kind of anything, because a
universal predicate, 121* 16-19,
b 7: cf. 127*27, 33, I3o b is-i7.

Commensurate with Being ,
and . . neither its genus nor
a species of it, I2i b 7-8. Failure
to distinguish one )( many, a
source of fallacy of Accident,
i69 b 3-4.

Universal predicates (o irao-iv
vndpxfi . K.OIVQV ), e. g. Being ,
Unity . Not to be used
where distinctive terms are
required, e.g. in rendering a
property, I3o b ii foil.; or defi
nition, 140*24-32.

Unjustly (set also Injustice). Not
a property of what is done u. to
be done badly (KKO>?), I36 b
27-8 : what occurs u. may be
preferable to what occurs justly,
l8o b 2l-3.

Useful (w<pt\ip.oi>) : def. = pro
ductive of good , 124*16-17,
I47 a 34> I53 b 38: possibly the
genus of pleasant (if pleasure
be a good), 124* 17-20. Cause
of good essentially (xad\ auni)
better than cause of good
accidentally , u6 b I. What is
u. for greater no. of desirable
ends, is more desirable, n8 b
26-30: also what is u. for
better end, Ii8 b 32~3. Most
u. of commonplace rules,
Bk. VII, ch. 4.

Uses (xpf]<rfts) of a thing, as tests
of comparative values, 118*34;
of genus, 124*31-3.

Using (xpqrrty) considered as a,
kind of activity (tvtpytiv)
124*33.

Verbal argument (TO npos rovvopa
f>ia\(y(trdai) : to be avoided in
Dialectic, 108*33, cf. !O4 b 36-
7; and 112*9, i64 b 8 (see So-
phistic turn of argument) : but
legitimate to stick at nothing
with opponent who sticks at
nothing, 134*1-4, cf. 148*21.
In Soph. El., distinction of
arguments directed at verbal
expression Xoyot irpos Tovitnp.a
)( directed against thought
(npos Tqv ftuivoiav) riddled with
criticism (ch. 10) : but argu
ment conducted verbally (8ta
T>V ovopaTatv) the commonest
source of fallacy, 165*4 foil.

INDEX

Refutation by fallacy of many
questions only verbal, i8i b

20-1.

Vice: contrary of virtue , H3 b
31-2 : the cause of evil essen
tially, n6 b 6. Genus of in
justice , I23 b i5, 21, 32; an
attribute of cowardice , ii3 b
31-2. V. of soul (= injustice)
opp. to v. of body, I53 b 8-lo.

Vigorous (cvfKTiKov) : (i) what
produces vigour, 114*30-1,
I 53 b 37 : ( 2 ) what preserves
vigour, H4 a 3o-i, cf. io6 b 35:
(3) what betokens vigour, cf.
I05 a 3oand io6 b 35- (Analogy
seems to hold completely
vigorous : vigour = healthy :
health .) The v., good as
means, 106*5-8.

Vigour (fvein) : contrary of de
bility (Krt^et a), H3 b 35, I57 b
18-20: brings health , H3 b
35, I57 b 23~4: better than
health, I57 b 18-19. Genuine
and sham v., 164*26-7. Capa
city to produce v., the property
of a trainer (yv^vaa-T^), 137*
5-6.

Virtue (i)=apri7: a relative
term (unlike its genera, good
and noble ), 124" 20-2: con
trary of vice , li3 b 3l-2.
What displays its proper v.
more desirable than anything
of same kind which does not so,
118*27-8. V. of soul (justice)
opp. to v. of body, I53 b 8-10.

(2) = moral virtue (^$1/07
(ipfrrj) : a kind of state and
disposition , I2i b 38 ; a kind of
good , I42 b 14, 17, and . . not
def. = a good or noble state ,
144*9-11 (but cf. 11-19). A
state of v. not = the good ,
I42 b 12. Cause of good essen
tially, and /. better than luck,
Il6 b 1-3 : better than pleasure,
Ii8 b 33. Its properties (i) to
be naturally situated in a
no. of faculties (contr. know
ledge) a relative property,
I28 b 38-9 : (2) to be anything
that makes its possessor good ,
I3i b 1-4. Genus of justice ,

I2I b 26, I23 b 15,21,32, I27 b 20,

not an accident of it, 109*35-

b i : genus of temperance ,
I39 b 39-140* 2 : attribute of
courage , I I3 b 31. A different
genus from knowledge , I52 b
1-2 : that of virtues prudence
alone is knowledge can be
disproved in 4 ways, 120*28-31.
Problem, whether life of v. or of
self-indulgence is pleasanter, a
problem about Accident, io2 b
17-20. To be virtuous (TO
<77rou8cuoj>) not a property of
man , I37 b 32.

Waits (edition), 132* 36 n., I55 b
3on., 157*21 n., 158* ii n.

Wai lies, M., Ii6 b 2~3n.

Walking: (i) =/3aS<o-i?, a species
of locomotion (<popa), which is
species of motion , 122*21-
30 : a kind of motion, log 15 2-4,
128* 32-3. )( carriage (<"p<i),
I22 b 32. (2) == Trt6v : differ
entia of animal (v. Animal}.

Water : not genus of snow ,
127* 14; of wine , 127* 18. W.
from same well, the same
specifically, 103* 14-23.

Wealth,\zss desirable than friend
ship, i l6 b 38, because (i) always
prized for sake of something
else, not for itself, 117*1; (2)
excess of friendship more de
sirable than of w., n8 b 6.
Happiness unquestionably
better than w., 116*6-7. To
make money less good than to
study philosophy, but more
desirable to a man lacking
life s necessities, Il8 a lo. Is
w. good, if not good to a fool ?
i8o b 9-i4.

Weightiness (oyKos) in argument,
one of the aims of non-neces
sary premisses, 15 5 b 22. (Seems
= ornament : cf. I55 b 22 and
157* 6 foil.)

White : an accidental predicate,
I02 b 8~9; a quality, ic>3 b 3i-3;
applicable in certain respect
only, 109*21-5, 167*7 >U i
i68 b 12-14. Colour its genus,
not an accident, 109*36, I23 b
26, 126*4-5. I^ e f- = a colour
which pierces the vision , 119*
30, 153*38 (cf. I07 b 29-30, 123*
2) : not def. = colour mingled

INDEX

with fire (an impossible mix
ture), I49 a 38- b 2. Contrary of
black , io5 b 36, H9 a 27-8; all
other colours intermediate, I23 b
27. Applied to sound ( =
clear ), 106*25, b s: cf. 107*
12, 37, b M, 36. (Cf. Black.)
Cannot be a genus, since white
things do not differ in kind,
127*22-5 : not genus of snow ,
since (i) an accident of it, I2o b
21-4, (2) inherent in snow, not
predicable of it, !27 b 2-4. Not
in subaltern relation to beauti
ful , 128*3-4. Addition of w.
to black does not necessarily
make the whole w., U5 b l-2.

Wind: its definition = move
ment of air better than = air
in motion , 127*4 ; but should
specify quantity of air, I46 b 29-

Windlessness : air = calm : sea,
108*11-12, b 24-6.

Wine not = fermented water ,
127*18 ; noranykindofwater,ib.
Sweet-toothed man (<f)i\6y\vKvs)
desires wine only per accidens,
because sweet ; not if dry
(avarripos), 111*3-5.

Wisdom (a) = a-o(pia : not def. =
what produces happiness ,
I49 b 33 foil. (See also So-
phistry),

(b) = <pdj>7<m, I36 b 1 1, i63 b 9,
cf. 134* 33, I38 b 1-5 : not def.=
(l) that which defines and
contemplates reality (redun

dant), 141* 7-9 : (2) the virtue
of a man or of the soul (not
primary correlate), 145*28-32.
To be essentially the natural
virtue of the faculty of reason ,
a property of w., I3& b 10-12 :
even its definition, 145*28-32.
To display w., a property of the
faculty of reason (q.v.). W.=
knowledge of evils , but not
therefore an evil, l8o a S foil.
Wishing (/3oi Xrjo-is) : def. = cona
tion for an apparent good ,
!46 b 5-6, 27-147*5 : not def.=
painless conation , I46 b 2:
always found in faculty of
reason, 126* 13: not the genus
of friendship , if latter is in
faculty of desire, 126* 12-13.

Xenocrates : 112*37: his defini
tion of soul as self-moving
number , I4o b 2 n. (cf. I2o b
3-4 n.) ; of wisdom as that
which defines and contemplates
reality , 141*6-9: his attempt
to prove that the good life = the
happy life, because both are the
most desirable life, 152*7-10,
26-30.

Zeno : argument that motion is
impossible, i6o b 8, 172*9, I79 b
20 foil. ; that Being is one, i82 b
26.

Zeus, i66 b 7.

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