Prior Analytics - Book I   

comes about and how it differs from the proof of a simple statement.

We proceed to discuss that which is possible, when and how and by what

means it can be proved. I use the terms 'to be possible' and 'the

possible' of that which is not necessary but, being assumed, results

in nothing impossible. We say indeed ambiguously of the necessary that

it is possible. But that my definition of the possible is correct is

clear from the phrases by which we deny or on the contrary affirm

possibility. For the expressions 'it is not possible to belong', 'it

is impossible to belong', and 'it is necessary not to belong' are

either identical or follow from one another; consequently their

opposites also, 'it is possible to belong', 'it is not impossible to

belong', and 'it is not necessary not to belong', will either be

identical or follow from one another. For of everything the

affirmation or the denial holds good. That which is possible then will

be not necessary and that which is not necessary will be possible.

It results that all premisses in the mode of possibility are

convertible into one another. I mean not that the affirmative are

convertible into the negative, but that those which are affirmative in

form admit of conversion by opposition, e.g. 'it is possible to

belong' may be converted into 'it is possible not to belong', and

'it is possible for A to belong to all B' into 'it is possible for A

to belong to no B' or 'not to all B', and 'it is possible for A to

belong to some B' into 'it is possible for A not to belong to some B'.

And similarly the other propositions in this mode can be converted.

For since that which is possible is not necessary, and that which is

not necessary may possibly not belong, it is clear that if it is

possible that A should belong to B, it is possible also that it should

not belong to B: and if it is possible that it should belong to all,

it is also possible that it should not belong to all. The same holds

good in the case of particular affirmations: for the proof is

identical. And such premisses are affirmative and not negative; for

'to be possible' is in the same rank as 'to be', as was said above.