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 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 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