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Full text of "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 

New Tork Toronto Melbourne Capetown 

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 w