How are syllogisms produced?

Chapter 4

How are syllogisms produced?*

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.*

A perfect syllogism is when its 3 inter-related terms, the extremes must be related by:

• the last which is contained in the middle
• the middle which is either contained in, or excluded from, the first

The middle term 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: This is ‘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.

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 premises.

• An example of a universal affirmative relation between the extremes are the words [ideas] animal, man, horse*

• A universal negative relation are the words [ideas] animal, man, stone.

A syllogism cannot 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.

If then the terms are universally related, it is clear when a syllogism will be possible and not possible.

• A syllogism is possible and is created when the terms relate.

But if one term is related universally, the other in part only, to its subject, there must be

A perfect syllogism is:

• universal when one word is affirmatively or negatively relates to the major word
• particular when it relates to the minor term affirmatively

A syllogism is impossible whenever:

• the universality is posited in relation to the minor term, or
• the terms are related in any other way.*

• The ‘major’ word [idea] contains the middle.
• The ‘minor’ word [idea] comes under the middle.

Let:

• all B be A
• some C be B

It is necessary that some C is A. This is from being ‘predicated of all’.

If no B is A but some C is B, it is necessary that some C is not A. This is from ‘predicated of none’.

So there will be a perfect syllogism.*

This holds good also if the premise BC should be indefinite, provided that it is affirmative: for we shall have the same syllogism whether the premise is indefinite or particular.

But if the universality is posited with respect to the minor term either affirmatively or negatively, a syllogism will not be possible, whether the major premise is positive or negative, indefinite or particular:

For example, if some B is or is not A, and all C is B. As an example of a positive relation between the extremes take the terms good, state, wisdom: of a negative relation, good, state, ignorance.

Again if no C is B, but some B is or is not A or not every B is A, there cannot be a syllogism. Take the terms white, horse, swan: white, horse, raven. The same terms may be taken also if the premise BA is indefinite.

Nor when the major premise is universal, whether affirmative or negative, and the minor premise is negative and particular, can there be a syllogism, whether the minor premise be indefinite or particular: e.g. if all B is A and some C is not B, or if not all C is B.

For the major term may be predicable both of all and of none of the minor, to some of which the middle term cannot be attributed.

Suppose the terms are animal, man, white: next take some of the white things of which man is not predicated-swan and snow: animal is predicated of all of the one, but of none of the other.

Consequently there cannot be a syllogism. Again let no B be A, but let some C not be B.

Take the terms inanimate, man, white: then take some white things of which man is not predicated-swan and snow: the term inanimate is predicated of all of the one, of none of the other.

Further since it is indefinite to say some C is not B, and it is true that some C is not B, whether no C is B, or not all C is B, and since if terms are assumed such that no C is B, no syllogism follows (this has already been stated) it is clear that this arrangement of terms will not afford a syllogism: otherwise one would have been possible with a universal negative minor premise. A similar proof may also be given if the universal premise is negative.

Nor can there in any way be a syllogism if both the relations of subject and predicate are particular, either positively or negatively, or the one negative and the other affirmative, or one indefinite and the other definite, or both indefinite. Terms common to all the above are animal, white, horse: animal, white, stone.

If there is a syllogism in this figure with a particular conclusion, the terms must be related as we have stated: if they are related otherwise, no syllogism is possible anyhow.

In this figure:

• all the syllogisms in this figure are perfect. They are all completed by means of the premises originally taken
• all conclusions are proved by this figure, viz. universal and particular, affirmative and negative. Such a figure I call the first.