Prior Analytics - Book I   

perfect. For the necessity results from the conversion.

But if one of the premisses is universal, the other particular, when

the major premiss is universal there will be a perfect syllogism.

For if A is possible for all B, and B for some C, then A is possible

for some C. This is clear from the definition of being possible. Again

if A may belong to no B, and B may belong to some of the Cs, it is

necessary that A may possibly not belong to some of the Cs. The

proof is the same as above. But if the particular premiss is negative,

and the universal is affirmative, the major still being universal

and the minor particular, e.g. A is possible for all B, B may possibly

not belong to some C, then a clear syllogism does not result from

the assumed premisses, but if the particular premiss is converted

and it is laid down that B possibly may belong to some C, we shall

have the same conclusion as before, as in the cases given at the

beginning.

But if the major premiss is the minor universal, whether both are

affirmative, or negative, or different in quality, or if both are

indefinite or particular, in no way will a syllogism be possible.

For nothing prevents B from reaching beyond A, so that as predicates

cover unequal areas. Let C be that by which B extends beyond A. To C

it is not possible that A should belong-either to all or to none or to

some or not to some, since premisses in the mode of possibility are

convertible and it is possible for B to belong to more things than A

can. Further, this is obvious if we take terms; for if the premisses

are as assumed, the major term is both possible for none of the

minor and must belong to all of it. Take as terms common to all the

cases under consideration 'animal'-'white'-'man', where the major

belongs necessarily to the minor; 'animal'-'white'-'garment', where it

is not possible that the major should belong to the minor. It is clear

then that if the terms are related in this manner, no syllogism

results. For every syllogism proves that something belongs either

simply or necessarily or possibly. It is clear that there is no