induction. The objection, to have any weight, requires this to be established, that every general rule or universal principle at the head of a reasoning is a simple generalisation, or product of induction,-nay, it even requires the rule to be the result of the inspection of every individual, actual and possible, under it. This is ridiculous, even as an account of the inductive process. But if it be not shown that we have no universal a priori truths, the objection to synthetic syllogistic reasoning is futile. If we have such, and one principle is enough, the moment it is applied to an existence under it, be it actual or possible, that moment is the allegation of the petitio principii in the reasoning disproved. If it be true a priori that every event which takes place has a cause, then the subsumption of any particular event under the rule annihilates the whole of this criticism.1

1 For a very able and complete exposure of the fallacies in the theory of the Syllogism as a reasoning from particular to particular, see Janet, De la Valeur du Syllogisme Rev. Phil., tome 12, p. 105 (1881).

387

CHAPTER XXX.

CATEGORICAL SYLLOGISMS-ON ARISTOTELIC PRINCIPLES

MOOD AND FIGURE.

§ 489. Syllogism as a combination of propositions must be stated in the forms and relations of those propositions. The number of syllogistic forms must, therefore, be limited by the number of propositions, and their possible combinations. This, in the first place, is quite independent of Figure, or the position of the middle term with reference to the extremes. But, as will appear, the validity of the possible moods will be limited or determined by the general rules of reasoning, and the special rules applicable to Syllogistic Figure. If Mood in the end be emancipated wholly from Figure, then we shall have moods determined only by the general syllogistic rules or conditions of reasoning.

$490. The mood of a syllogism (modus, Tрorós) represents the nature of the combination of the premisses, or of the premisses and conclusion, according to quantity and quality. The early logicians regard Mood as composed of two propositions only, the major and minor premiss. In this case there would be but sixteen moods. If, however, we extend mood to the conclusion, the three propositions of the Syllogism, taken along with the four Aristotelic kinds of proposition, A, E, I, O,-would give us sixteen pairs of premisses and four different conclusions,-in all sixty-four moods. The sixteen pairs of premisses are as follows:

The combinations now spoken of are wholly numerical; their logical validity remains to be tested by the general rules of Syllogism, and by the special rules of each Figure.

§ 491. The essence of the Categorical Syllogism being that there are three terms, and one of them common, the rules of valid syllogistic inference follow from the application of the Laws of Identity and Non-Contradiction to the construction of the Syllogism itself, or to its form. These are-(1.) No inference follows from two negative premisses, for the community of the middle term with the extremes is thus excluded. There is no means of mediation, no ground of comparison, and therefore no ground of inclusion or exclusion in the conclusion. There is no constitution of the relation of whole and part. Thus

No Y is (any) X.

No Z is (any) Y.

The possibilities here are either (1) No Z is any X; or (2) Some Z is X; or (3) All Z is X. But nothing is determined. So equally with negative premisses, universal and particular, and both particular. Hence the moods EE, EO, OE, OO are logically inadmissible.

§ 492. (2.) The second rule of exclusion applicable to all the figures follows on the same principle-viz., that there is no valid conclusion from two particular premisses; ex meris particularibus nihil sequitur. The general ground of this rule is that no community of the middle term with the extremesmajor and minor-is laid down. The part of the one proposition is not necessarily identical with the part of the other. If, for example, it is said :

Some Y is X,
Some Z is Y;

Or,

Some men are negroes,

Some Africans are men.

I am not told whether the some Y (men) who are negroes in the major are the same or not with the some men who are Africans in the minor. So long as this doubt remains, inference is paralysed. The same principle applies whether the premisses be particular affirmative and particular negative, or both particular negatives.

The moods inadmissible on this rule are obviouslyII, IO, OI.

(a) In all Syllogisms, according to Aristotle, it is necessary that some term be affirmative and universal. Without a universal there will either be no syllogism, or it will not relate to the point proposed, or what is sought from the commencement will be begged. Thus,-Is

the pleasure of learning honourable? If it be said pleasure is honourable, not adding all, there will be no conclusion. If only some pleasure be understood, either another pleasure may be posited, which is nothing to the point, or the pleasure of learning itself, in which case we beg and accept that which was to be demonstrated from the first.-(An. Pr., i. 24.) (Thus

§ 493. (3.) There is given as a third general rule of exclusion that no valid conclusion follows from a particular major premiss combined with a negative minor premiss. Thus

Some A is (some) M,
No B is (any) M,

it does not follow either that some B is not any A, for all B may not be quite separated from all A; and thus some of B may be A, or even all B may be included in A as a part, although some other part of A is included in M. Thus

In other words, there is no conclusion in the form B A.1 According to this view, the mood I E is specially excluded in all the figures, and I O, O E, O 0; these, however, fall to be excluded on other grounds as well. This leaves only eight forms of combination of the premisses. I confess I do not see that there is proper ground for the exclusion of IE. It is made to depend on a certain arbitrary distinction of majority and minority in the premisses which does not necessarily exist, especially in the second and third figures. With the premisses I and E,

Some A is (some) M,

No B is (any) M,

it follows, even on Aristotelic principles, that some A (at least) -namely, that which is M, is not any B. And there follows also a conclusion in terms of B A, on the full scheme of propositional forms; for we can infer some B is not (some) A, and convert some A is not (some) B.

(B)

(A)

but not Some plant is not any organised.

§ 494. Supposing always the Syllogism to be simple, or to include three terms and three propositions, we have (1.) The middle term must be distributed—that is, taken in its full extent or quantity, once at least in the premisses.

(2.) No term may be distributed—that is, taken at its full quantity in the conclusion, which was not distributed in one of the premisses; or no term may be taken in the conclusion at more than the greatest quantity assigned to it in the premisses. The violation of this rule results in an illicit process of major or minor

term.

(3.) If one premiss be negative, the conclusion must be negative. (4.) If one premiss be particular, the conclusion must be particular.

1 Ueberweg, Logic, p. 388.