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