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On Interpratation   

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

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