On Interpratation   

consequent upon the proposition 'it may be' and the corresponding

positive in the first case upon the negative in the second. For 'it is

impossible' is a positive proposition and 'it is not impossible' is

negative.

We must investigate the relation subsisting between these

propositions and those which predicate necessity. That there is a

distinction is clear. In this case, contrary propositions follow

respectively from contradictory propositions, and the contradictory

propositions belong to separate sequences. For the proposition 'it

is not necessary that it should be' is not the negative of 'it is

necessary that it should not be', for both these propositions may be

true of the same subject; for when it is necessary that a thing should

not be, it is not necessary that it should be. The reason why the

propositions predicating necessity do not follow in the same kind of

sequence as the rest, lies in the fact that the proposition 'it is

impossible' is equivalent, when used with a contrary subject, to the

proposition 'it is necessary'. For when it is impossible that a

thing should be, it is necessary, not that it should be, but that it

should not be, and when it is impossible that a thing should not be,

it is necessary that it should be. Thus, if the propositions

predicating impossibility or non-impossibility follow without change

of subject from those predicating possibility or non-possibility,

those predicating necessity must follow with the contrary subject; for

the propositions 'it is impossible' and 'it is necessary' are not

equivalent, but, as has been said, inversely connected.

Yet perhaps it is impossible that the contradictory propositions

predicating necessity should be thus arranged. For when it is

necessary that a thing should be, it is possible that it should be.

(For if not, the opposite follows, since one or the other must follow;

so, if it is not possible, it is impossible, and it is thus impossible

that a thing should be, which must necessarily be; which is absurd.)

Yet from the proposition 'it may be' it follows that it is not