Page - 51 - in The Complete Aristotle

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 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 51