Prior Analytics - Book I   

not merely a negative problematic, but also a negative assertoric

proposition; but if the affirmative premiss is necessary no conclusion

can be drawn. It is clear too that a syllogism is possible or not

under the same conditions whether the mode of the premisses is

assertoric or necessary. And it is clear that all the syllogisms are

imperfect, and are completed by means of the figures mentioned.



20

In the last figure a syllogism is possible whether both or only

one of the premisses is problematic. When the premisses are

problematic the conclusion will be problematic; and also when one

premiss is problematic, the other assertoric. But when the other

premiss is necessary, if it is affirmative the conclusion will be

neither necessary or assertoric; but if it is negative the syllogism

will result in a negative assertoric proposition, as above. In these

also we must understand the expression 'possible' in the conclusion in

the same way as before.

First let the premisses be problematic and suppose that both A and B

may possibly belong to every C. Since then the affirmative proposition

is convertible into a particular, and B may possibly belong to every

C, it follows that C may possibly belong to some B. So, if A is

possible for every C, and C is possible for some of the Bs, then A

is possible for some of the Bs. For we have got the first figure.

And A if may possibly belong to no C, but B may possibly belong to all

C, it follows that A may possibly not belong to some B: for we shall

have the first figure again by conversion. But if both premisses

should be negative no necessary consequence will follow from them as

they are stated, but if the premisses are converted into their

corresponding affirmatives there will be a syllogism as before. For if

A and B may possibly not belong to C, if 'may possibly belong' is

substituted we shall again have the first figure by means of

conversion. But if one of the premisses is universal, the other