Prior Analytics - Book I   

some of the other, or belongs to neither universally, or is related to

them indefinitely. Common terms for all the above are white, animal,

man: white, animal, inanimate.

It is clear then from what has been said that if the terms are related

to one another in the way stated, a syllogism results of necessity;

and if there is a syllogism, the terms must be so related. But it is

evident also that all the syllogisms in this figure are imperfect: for

all are made perfect by certain supplementary statements, which either

are contained in the terms of necessity or are assumed as

hypotheses, i.e. when we prove per impossibile. And it is evident that

an affirmative conclusion is not attained by means of this figure, but

all are negative, whether universal or particular.



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But if one term belongs to all, and another to none, of a third,

or if both belong to all, or to none, of it, I call such a figure

the third; by middle term in it I mean that of which both the

predicates are predicated, by extremes I mean the predicates, by the

major extreme that which is further from the middle, by the minor that

which is nearer to it. The middle term stands outside the extremes,

and is last in position. A syllogism cannot be perfect in this

figure either, but it may be valid whether the terms are related

universally or not to the middle term.

If they are universal, whenever both P and R belong to S, it follows

that P will necessarily belong to some R. For, since the affirmative

statement is convertible, S will belong to some R: consequently

since P belongs to all S, and S to some R, P must belong to some R:

for a syllogism in the first figure is produced. It is possible to

demonstrate this also per impossibile and by exposition. For if both P

and R belong to all S, should one of the Ss, e.g. N, be taken, both

P and R will belong to this, and thus P will belong to some R.