every animal is just' and 'some animals are just' are both true.
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, a certain
positive proposition is also true. Thus, if the question were asked
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 inference 'Not every man is
wise' is correct. This last is the contradictory, the former the
contrary. Negative expressions, which consist of an indefinite noun or
predicate, such as 'not-man' or 'not-just', may seem to be denials
containing neither noun nor verb in the proper sense of the words. But
they are not. For a denial must always be 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'.
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 proposition 'nothing that is
not man is just'.
The conversion of the position of subject and predicate in a
sentence involves no difference in its meaning. Thus we say 'man is
white' and 'white is man'. If these were not equivalent, there would
be more than one contradictory to the same proposition, whereas it has