On Interpratation   

impossible, and from that it follows that it is not necessary; it

comes about therefore that the thing which must necessarily be need

not be; which is absurd. But again, the proposition 'it is necessary

that it should be' does not follow from the proposition 'it may be',

nor does the proposition 'it is necessary that it should not be'.

For the proposition 'it may be' implies a twofold possibility,

while, if either of the two former propositions is true, the twofold

possibility vanishes. For if a thing may be, it may also not be, but

if it is necessary that it should be or that it should not be, one

of the two alternatives will be excluded. It remains, therefore,

that the proposition 'it is not necessary that it should not be'

follows from the proposition 'it may be'. For this is true also of

that which must necessarily be.

Moreover the proposition 'it is not necessary that it should not be'

is the contradictory of that which follows from the proposition 'it

cannot be'; for 'it cannot be' is followed by 'it is impossible that

it should be' and by 'it is necessary that it should not be', and

the contradictory of this is the proposition 'it is not necessary that

it should not be'. Thus in this case also contradictory propositions

follow contradictory in the way indicated, and no logical

impossibilities occur when they are thus arranged.

It may be questioned whether the proposition 'it may be' follows

from the proposition 'it is necessary that it should be'. If not,

the contradictory must follow, namely that it cannot be, or, if a

man should maintain that this is not the contradictory, then the

proposition 'it may not be'.

Now both of these are false of that which necessarily is. At the

same time, it is thought that if a thing may be cut it may also not be

cut, if a thing may be it may also not be, and thus it would follow

that a thing which must necessarily be may possibly not be; which is

false. It is evident, then, that it is not always the case that that

which may be or may walk possesses also a potentiality in the other