Prior Analytics - Book I   

by means of the particular syllogisms in the first figure: and these

(we have seen) may be reduced to the universal syllogisms in the first

figure: consequently also the particular syllogisms in the third

figure may be so reduced. It is clear then that all syllogisms may

be reduced to the universal syllogisms in the first figure.

We have stated then how syllogisms which prove that something

belongs or does not belong to something else are constituted, both how

syllogisms of the same figure are constituted in themselves, and how

syllogisms of different figures are related to one another.



8



Since there is a difference according as something belongs,

necessarily belongs, or may belong to something else (for many

things belong indeed, but not necessarily, others neither

necessarily nor indeed at all, but it is possible for them to belong),

it is clear that there will be different syllogisms to prove each of

these relations, and syllogisms with differently related terms, one

syllogism concluding from what is necessary, another from what is, a

third from what is possible.

There is hardly any difference between syllogisms from necessary

premisses and syllogisms from premisses which merely assert. When

the terms are put in the same way, then, whether something belongs

or necessarily belongs (or does not belong) to something else, a

syllogism will or will not result alike in both cases, the only

difference being the addition of the expression 'necessarily' to the

terms. For the negative statement is convertible alike in both

cases, and we should give the same account of the expressions 'to be

contained in something as in a whole' and 'to be predicated of all

of something'. With the exceptions to be made below, the conclusion

will be proved to be necessary by means of conversion, in the same

manner as in the case of simple predication. But in the middle