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 expressing 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.
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 propositions. 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.
6
An affirmation is a positive assertion of something about
something, a denial a negative assertion.
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. 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
contradictories. 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 not be ‘equivocal’.
Indeed there are definitive qualifications 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’ an individual.
Our propositions necessarily sometimes concern a universal
subject, sometimes an individual.
If, then, a man states a positive and a negative proposition of
universal character with regard to a universal, these two
propositions are ‘contrary’. By the expression ‘a proposition of
universal character with regard to a universal’, 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. 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’ 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 universal character.
If, however, both predicate and subject are distributed, the
proposition thus constituted is contrary to truth; no affirmation
will, under such circumstances, 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’. 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 subject; for instance ‘not
every man is white’ and some men are white’ are both true. Of
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 expressing 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.
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 propositions. 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.
6
An affirmation is a positive assertion of something about
something, a denial a negative assertion.
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. 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
contradictories. 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 not be ‘equivocal’.
Indeed there are definitive qualifications 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’ an individual.
Our propositions necessarily sometimes concern a universal
subject, sometimes an individual.
If, then, a man states a positive and a negative proposition of
universal character with regard to a universal, these two
propositions are ‘contrary’. By the expression ‘a proposition of
universal character with regard to a universal’, 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. 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’ 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 universal character.
If, however, both predicate and subject are distributed, the
proposition thus constituted is contrary to truth; no affirmation
will, under such circumstances, 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’. 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 subject; for instance ‘not
every man is white’ and some men are white’ are both true. Of
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