XXI.

always, it is self-evident, in the first place, from the LECT. affirmation of anything in extension, indefinitely affirm it in comprehension, as, reciprocally, from the affirmation of anything in comprehension, we may indefinitely affirm it in extension; and, in the second place, from the negation of anything in extension, we may absolutely deny it in comprehension, as, reciprocally, from the negation of anything in comprehension, we may absolutely deny it in extension.

nature of the

the Fourth

Now, what has not been observed, such is exclu- This the sively the inference in the Fourth Figure; its two inference in last rules are in fact nothing but an enunciation of Figure. these two conditions of a cross inference from the one quantity to the other; and the first rule will be hereafter shown to be only an error, the result of not observing that certain moods are only founded on the accident of a transposed order of the premises, and, therefore, constitute no subject for a logical legislation.

illustrated.

To prove this statement of the nature of the infer- Proved and ence in the fourth figure, it is only necessary to look at its abstract formula. In extension this is :

P is M;

M is S;

S is P.

Here in the premises P is contained under M, and M is contained under S; that is, in the premises S is the greatest whole and P the smallest part. So far, this syllogism in extension is properly a syllogism in comprehension, in which the subject of the conclusion is the greatest whole, and its predicate the smallest part. From such premises we, therefore, expect, that the conclusion carrying out what was established in

XXI.

LECT. the antecedent, should affirm P as the part of S.-In this, however, our expectation is disappointed; for the reasoning suddenly turns round in the conclusion, and affirms S as a part of P. And how, it may be asked, is this evolution in the conclusion competent, seeing that it was not prepared, and no warrant given for it in the premises? To this the answer is prompt and easy. The conclusion in this figure is solely legitimated by the circumstance, that from an identity between the two terms in one quantity, we may always infer some identity between them in the other, and from a non-identity between them in one quantity, we can always infer a non-identity in the other. And that in this figure there is always a transition in the conclusion from the one quantity, is evident; for that notion which in the premises was the greatest whole, becomes in the conclusion the smallest part; and that notion which in the premises was the smallest part, becomes in the conclusion the greatest whole. Now how is this manoeuvre possible ?-how are we entitled to say that because A contains all B, therefore, B contains some A? Only it is clear, because there is here a change from the containing of the one quantity to the containing of the other; and because, each quantity necessarily implying the indefinite existence of the other, we are consequently permitted to render this necessary implication the ground of a logical infer

This hybrid inference is,

ral.

ence.

It is manifest, however, in the first place, that such 1. Unnatu- a cross and hybrid and indirect reasoning from the one quantity to the other, in the fourth figure, is wholly of a different character and account from the reasoning in the other three figures, in which all inference, whether upwards or downwards, is equable

XXI.

and homogeneous within the same quantity. The LECT. latter in short is natural and easy; the former unnatural and perverse.

In the second place, the kind of reasoning compe- 2. Useless. tent in the fourth figure, is wholly useless. The change from the one quantity to the other in the course of a syllogism is warranted by no necessity, by no expediency. The reasoning in each quantity is absolute and complete within itself, and all that can be accomplished in the one process can equally well be accomplished in the other. The jumping, therefore, from extension to comprehension, or from comprehension to extension, in the conclusion of the fourth figure, is a feat about as reasonable and useful in Logic, as the jumping from one horse to another would be reasonable and useful in the race-course. Both are achievements possible; but, because possible, neither is, therefore, a legitimate exercise of skill.

We may, therefore, on the ground that the fourth figure involves a useless transition from one quantity to another, reject it as a logical figure, and degrade it to a mere logical caprice.

invalid.

But, in the third place, there is a better ground; 3. Logically the inference, though valid in itself, is logically,—is scientifically, invalid. For the inference is only legitimated by the occult conversion of the one quantity into the other, which takes place in the mental process. There is thus a step taken in the reasoning, which is not overtly expressed. Were the whole process stated in language, as stated it logically ought to be, instead of a simple syllogism with one direct conclusion, we should have a complex reasoning with two conclusions; one conclusion direct and immediate, (the inference, to wit, of conversion), and from that immediate con

XXI.

LECT. clusion another mediate and indirect, but which, as it stands, appears as the one sole and exclusive conclusion from the premises. This ground, on which I think the fourth figure ought to be specially abolished, is stated with the requisite details in the Logical Appendix contained in the second edition of my Discussions on Philosophy."

a P. 663.-ED.

IN

LECTURE XXII.

STOICHEIOLOGY.

SECTION II.-OF THE PRODUCTS OF THOUGHT.

III.-DOCTRINE OF REASONINGS.

SYLLOGISMS.-THEIR DIVISIONS ACCORDING TO

EXTERNAL FORM.

C. REGULAR AND IRREGULAR.

FIGURE-REDUCTION.

XXII.

tion.

In my last Lecture, after terminating the view of the LECT. nineteen Moods of the Four Syllogistic Figures, according to the doctrine of logicians, I entered on the Recapitulaconsideration, how far their doctrine concerning the number and legitimacy of these various figures and moods was correct. In the conduct of this discussion, I proposed, first, to treat of the Figures, and, secondly, to treat of the Moods. Commencing, then, with the Figures, it is manifest that no exception can possibly be taken to the first, which is, in point of fact, no figure at all, but the one regular, the one natural form of ratiocination. The other three figures divide themselves into two classes. The one of these classes comprehends the fourth; the other, the second and third figures. The fourth figure stands, on the common doctrine of the logicians, in a more unfavourable situation than the second and third. It was not