Prior Analytics - Book I   

states simple belonging: but that syllogisms will result if the

modality of the premisses is reversed, must be proved per impossibile.

At the same time it will be evident that they are imperfect: for the

proof proceeds not from the premisses assumed. First we must state

that if B's being follows necessarily from A's being, B's

possibility will follow necessarily from A's possibility. Suppose, the

terms being so related, that A is possible, and B is impossible. If

then that which is possible, when it is possible for it to be, might

happen, and if that which is impossible, when it is impossible,

could not happen, and if at the same time A is possible and B

impossible, it would be possible for A to happen without B, and if

to happen, then to be. For that which has happened, when it has

happened, is. But we must take the impossible and the possible not

only in the sphere of becoming, but also in the spheres of truth and

predicability, and the various other spheres in which we speak of

the possible: for it will be alike in all. Further we must

understand the statement that B's being depends on A's being, not as

meaning that if some single thing A is, B will be: for nothing follows

of necessity from the being of some one thing, but from two at

least, i.e. when the premisses are related in the manner stated to

be that of the syllogism. For if C is predicated of D, and D of F,

then C is necessarily predicated of F. And if each is possible, the

conclusion also is possible. If then, for example, one should indicate

the premisses by A, and the conclusion by B, it would not only

result that if A is necessary B is necessary, but also that if A is

possible, B is possible.

Since this is proved it is evident that if a false and not

impossible assumption is made, the consequence of the assumption

will also be false and not impossible: e.g. if A is false, but not

impossible, and if B is the consequence of A, B also will be false but

not impossible. For since it has been proved that if B's being is

the consequence of A's being, then B's possibility will follow from