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Written 350 B.C.E
Translated by E. M. Edghill
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. do not apply this word 'one' to those things which, 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 affirmation. In both cases the unity is linguistic,
but not real.
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 proposition. For as I have explained in the Topics, 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 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 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 white man so on indefinitely. Or, again, we may combine the predicates
'musical', 'white', and 'walking', and these may be combined many times.
Similarly we 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. Thus it is manifest that if man states
unconditionally that predicates can always be combined, many absurd consequences
We will now explain what ought to be laid down.
Those predicates, and terms forming the subject of predication, which
are accidental either to the same subject or to one another, do not combine
to form a unity. Take 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
Thus, again, whereas, if a man is both good and a shoemaker, 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 predicates are
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 any one instance, and to say
that some one particular man is a man or that some one white man is a white
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 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 them
no contradiction when the nouns are expanded into definitions, and wherein
the predicates belong to the subject 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
As these distinctions have been made, we must consider the mutual
relation of those affirmations and denials which assert or deny possibility
or contingency, impossibility or necessity: for the subject is not without
We admit that of composite expressions those are contradictory
each to each which have the verb 'to be' its positive and negative form
respectively. Thus the contradictory of the proposition 'man is' is 'man
is not', 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
Now if this is the case, in those propositions which do 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' merely equivalent to saying
'man is walking'.
If then this rule is universal, the contradictory of 'it may be'
is may not be', not 'it cannot be'.
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 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
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
not by the addition of the verbs 'be' and 'not be', respectively, 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, 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' 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' indicated that certain things
were or were not the case.
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 cannot be'. Thus the propositions 'it may be' and 'it
may not be' appear each to imply the other: for, since these two propositions
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, for they are contradictory. Nor can the propositions
'it may not be' and 'it cannot not be' be at once true of the same
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 'it is not necessary
that it should be', 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 'it is impossible that it
should not be' is 'it is not impossible that it should not
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 into affirmations and denials
we must combine them with 'that it should be' and 'that it should not be'
We must consider the following pairs as contradictory
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.
Logical sequences follow in due course when we have arranged the
propositions thus. From the proposition 'it may be' 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 it is impossible that it should be. From
the 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
It may be. It cannot be.
It is contingent. It is not contingent.
It is not impossible It is impossible that
that it should be. should be.
It is not necessary It is necessary that
that it should be. should not be.
It may not be. It cannot not be.
It is contingent that it It is not contingent
should not be. it should not
It is not impossible It is impossible thatit
that it should not be. should not be.
It is not necessary that It is necessary that
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 of the proposition 'it is impossible' is consequent upon the 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 impossible' is negative.
We must investigate the relation subsisting between these propositions
and those which predicate necessity. That there is a distinction is clear.
In this case, contrary propositions 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 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'. 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
without 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.
Yet perhaps it is impossible that the contradictory propositions
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 not
impossible, and from that it follows that it is not necessary; it comes
about therefore that the thing which must 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 proposition
'it is necessary that it should not be'. For the proposition '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 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
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' 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
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 cannot be, or, if a man should maintain that
this is not the contradictory, then the proposition 'it may not
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 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 potentiality 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 rational principle are potentialities of
more than one result, 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 even of those potentialities which are irrational admit of opposite
results. 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 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), 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
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.
We may perhaps state that necessity and its absence are the initial
principles of existence and non-existence, and that all else must be regarded
as posterior to these.
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. Some things are actualities without potentiality, namely,
the primary substances; 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; a third class comprises those things
which are never actualized, but are pure potentialities.
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 proposition 'no man is just', or in
the proposition 'every man is unjust'. Take the propositions 'Callias is
just', 'Callias 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 contrary 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 good with regard to spoken
But if, in thought, it is not the judgement which pronounces 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.
Let me illustrate. There is a true judgement concerning that which
is good, that it is good; another, a false judgement, that it is not good;
and a third, which is distinct, that it is bad. Which of these two is contrary
to the true? And if they are one and the same, which mode of expression
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, 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, as also those that
opine that some other attribute does not subsist which does subsist, for
both these classes of judgement are of unlimited content.
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; therefore error is a like
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 is good is not good is a false judgement concerning its intrinsic
nature, the judgement that it is bad is one concerning that which is accidental.
Thus the judgement which denies the true 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. 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.
The judgement that that which is good is bad is composite. 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 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 that is not good is good. Let us consider, therefore,
what would form the contrary of the true judgement 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 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 subject.
It remains, therefore, that of the judgement concerning that which is not
good, that it is not good, the 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 universalize
the positive judgement, for the universal negative judgement will form
the contrary. For instance, the contrary of the judgement that everything
that is good is good is that nothing that is good is good. For the judgement
that that which is good is good, if the subject be understood in a universal
sense, is equivalent to the judgement that whatever 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
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 contrary 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 good is good', 'no man is good'.
The contradictory propositions, 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
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