Prior Analytics - Book I   

and R to some S, then P belongs to some S: but we assumed that it

belongs to no S. Our point, then, must be proved from the indefinite

nature of the particular statement.

Nor is a syllogism possible anyhow, if each of the extremes

belongs to some of the middle or does not belong, or one belongs and

the other does not to some of the middle, or one belongs to some of

the middle, the other not to all, or if the premisses are

indefinite. Common terms for all are animal, man, white: animal,

inanimate, white.

It is clear then in this figure also when a syllogism will be

possible, and when not; and that if the terms are as stated, a

syllogism results of necessity, and if there is a syllogism, the terms

must be so related. It is clear also that all the syllogisms in this

figure are imperfect (for all are made perfect by certain

supplementary assumptions), and that it will not be possible to

reach a universal conclusion by means of this figure, whether negative

or affirmative.



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It is evident also that in all the figures, whenever a proper

syllogism does not result, if both the terms are affirmative or

negative nothing necessary follows at all, but if one is

affirmative, the other negative, and if the negative is stated

universally, a syllogism always results relating the minor to the

major term, e.g. if A belongs to all or some B, and B belongs to no C:

for if the premisses are converted it is necessary that C does not

belong to some A. Similarly also in the other figures: a syllogism

always results by means of conversion. It is evident also that the

substitution of an indefinite for a particular affirmative will effect

the same syllogism in all the figures.

It is clear too that all the imperfect syllogisms are made perfect