Prior Analytics - Book I   

4



After these distinctions we now state by what means, when, and how

every syllogism is produced; subsequently we must speak of

demonstration. Syllogism should be discussed before demonstration

because syllogism is the general: the demonstration is a sort of

syllogism, but not every syllogism is a demonstration.

Whenever three terms are so related to one another that the last

is contained in the middle as in a whole, and the middle is either

contained in, or excluded from, the first as in or from a whole, the

extremes must be related by a perfect syllogism. I call that term

middle which is itself contained in another and contains another in

itself: in position also this comes in the middle. By extremes I

mean both that term which is itself contained in another and that in

which another is contained. If A is predicated of all B, and B of

all C, A must be predicated of all C: we have already explained what

we mean by 'predicated of all'. Similarly also, if A is predicated

of no B, and B of all C, it is necessary that no C will be A.

But if the first term belongs to all the middle, but the middle to

none of the last term, there will be no syllogism in respect of the

extremes; for nothing necessary follows from the terms being so

related; for it is possible that the first should belong either to all

or to none of the last, so that neither a particular nor a universal

conclusion is necessary. But if there is no necessary consequence,

there cannot be a syllogism by means of these premisses. As an example

of a universal affirmative relation between the extremes we may take

the terms animal, man, horse; of a universal negative relation, the

terms animal, man, stone. Nor again can syllogism be formed when

neither the first term belongs to any of the middle, nor the middle to

any of the last. As an example of a positive relation between the

extremes take the terms science, line, medicine: of a negative

relation science, line, unit.