Prior Analytics - Book I   

might be used in two senses. First then we must state the nature and

characteristics of the syllogism which arises if B is possible of

the subject of C, and A is possible of the subject of B. For thus both

premisses are assumed in the mode of possibility; but whenever A is

possible of that of which B is true, one premiss is a simple

assertion, the other a problematic. Consequently we must start from

premisses which are similar in form, as in the other cases.



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Whenever A may possibly belong to all B, and B to all C, there

will be a perfect syllogism to prove that A may possibly belong to all

C. This is clear from the definition: for it was in this way that we

explained 'to be possible for one term to belong to all of another'.

Similarly if it is possible for A to belong no B, and for B to

belong to all C, then it is possible for A to belong to no C. For

the statement that it is possible for A not to belong to that of which

B may be true means (as we saw) that none of those things which can

possibly fall under the term B is left out of account. But whenever

A may belong to all B, and B may belong to no C, then indeed no

syllogism results from the premisses assumed, but if the premiss BC is

converted after the manner of problematic propositions, the same

syllogism results as before. For since it is possible that B should

belong to no C, it is possible also that it should belong to all C.

This has been stated above. Consequently if B is possible for all C,

and A is possible for all B, the same syllogism again results.

Similarly if in both the premisses the negative is joined with 'it

is possible': e.g. if A may belong to none of the Bs, and B to none of

the Cs. No syllogism results from the assumed premisses, but if they

are converted we shall have the same syllogism as before. It is

clear then that if the minor premiss is negative, or if both premisses

are negative, either no syllogism results, or if one it is not