Prior Analytics - Book I   

saw) other than the possible.

Moreover it is not possible to prove the convertibility of these

propositions by a reductio ad absurdum, i.e. by claiming assent to the

following argument: 'since it is false that B may belong to no A, it

is true that it cannot belong to no A, for the one statement is the

contradictory of the other. But if this is so, it is true that B

necessarily belongs to some of the As: consequently A necessarily

belongs to some of the Bs. But this is impossible.' The argument

cannot be admitted, for it does not follow that some A is

necessarily B, if it is not possible that no A should be B. For the

latter expression is used in two senses, one if A some is

necessarily B, another if some A is necessarily not B. For it is not

true to say that that which necessarily does not belong to some of the

As may possibly not belong to any A, just as it is not true to say

that what necessarily belongs to some A may possibly belong to all

A. If any one then should claim that because it is not possible for

C to belong to all D, it necessarily does not belong to some D, he

would make a false assumption: for it does belong to all D, but

because in some cases it belongs necessarily, therefore we say that it

is not possible for it to belong to all. Hence both the propositions

'A necessarily belongs to some B' and 'A necessarily does not belong

to some B' are opposed to the proposition 'A belongs to all B'.

Similarly also they are opposed to the proposition 'A may belong to no

B'. It is clear then that in relation to what is possible and not

possible, in the sense originally defined, we must assume, not that

A necessarily belongs to some B, but that A necessarily does not

belong to some B. But if this is assumed, no absurdity results:

consequently no syllogism. It is clear from what has been said that

the negative proposition is not convertible.

This being proved, suppose it possible that A may belong to no B and

to all C. By means of conversion no syllogism will result: for the

major premiss, as has been said, is not convertible. Nor can a proof