Prior Analytics - Book I   

figure when the universal statement is affirmative, and the particular

negative, and again in the third figure when the universal is

affirmative and the particular negative, the demonstration will not

take the same form, but it is necessary by the 'exposition' of a

part of the subject of the particular negative proposition, to which

the predicate does not belong, to make the syllogism in reference to

this: with terms so chosen the conclusion will necessarily follow. But

if the relation is necessary in respect of the part taken, it must

hold of some of that term in which this part is included: for the part

taken is just some of that. And each of the resulting syllogisms is in

the appropriate figure.



9



It happens sometimes also that when one premiss is necessary the

conclusion is necessary, not however when either premiss is necessary,

but only when the major is, e.g. if A is taken as necessarily

belonging or not belonging to B, but B is taken as simply belonging to

C: for if the premisses are taken in this way, A will necessarily

belong or not belong to C. For since necessarily belongs, or does

not belong, to every B, and since C is one of the Bs, it is clear that

for C also the positive or the negative relation to A will hold

necessarily. But if the major premiss is not necessary, but the

minor is necessary, the conclusion will not be necessary. For if it

were, it would result both through the first figure and through the

third that A belongs necessarily to some B. But this is false; for B

may be such that it is possible that A should belong to none of it.

Further, an example also makes it clear that the conclusion not be

necessary, e.g. if A were movement, B animal, C man: man is an

animal necessarily, but an animal does not move necessarily, nor

does man. Similarly also if the major premiss is negative; for the

proof is the same.