Prior Analytics - Book I   

merely a negative problematic but also a negative assertoric

conclusion; but if the affirmative premiss is necessary, no conclusion

is possible. Suppose that A necessarily belongs to no B, but may

belong to all C. If the negative premiss is converted B will belong to

no A: but A ex hypothesi is capable of belonging to all C: so once

more a conclusion is drawn by the first figure that B may belong to no

C. But at the same time it is clear that B will not belong to any C.

For assume that it does: then if A cannot belong to any B, and B

belongs to some of the Cs, A cannot belong to some of the Cs: but ex

hypothesi it may belong to all. A similar proof can be given if the

minor premiss is negative. Again let the affirmative proposition be

necessary, and the other problematic; i.e. suppose that A may belong

to no B, but necessarily belongs to all C. When the terms are arranged

in this way, no syllogism is possible. For (1) it sometimes turns

out that B necessarily does not belong to C. Let A be white, B man,

C swan. White then necessarily belongs to swan, but may belong to no

man; and man necessarily belongs to no swan; Clearly then we cannot

draw a problematic conclusion; for that which is necessary is

admittedly distinct from that which is possible. (2) Nor again can

we draw a necessary conclusion: for that presupposes that both

premisses are necessary, or at any rate the negative premiss. (3)

Further it is possible also, when the terms are so arranged, that B

should belong to C: for nothing prevents C falling under B, A being

possible for all B, and necessarily belonging to C; e.g. if C stands

for 'awake', B for 'animal', A for 'motion'. For motion necessarily

belongs to what is awake, and is possible for every animal: and

everything that is awake is animal. Clearly then the conclusion cannot

be the negative assertion, if the relation must be positive when the

terms are related as above. Nor can the opposite affirmations be

established: consequently no syllogism is possible. A similar proof is

possible if the major premiss is affirmative.

But if the premisses are similar in quality, when they are