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CHAPTER XXIV.

OBJECTIONS TO QUANTIFIED PROPOSITIONAL FORMS--GENERAL CONSEQUENCES OF QUANTIFICATION OF PREDICATE.

§ 389. It has been urged, that if we expressly quantify the predicate, we shall have a form or formula of judgment which is a simple repetition or tautology. This criticism must be held to be taken to the form of the proposition in Extension. Indeed, those who urge it seem utterly ignorant of any other form of proposition. In Comprehension, as we have seen, the predicate as attribute is, in affirmatives, necessarily taken in its totality, as an indivisible unity. No attribute is properly divisible, and is thus necessarily taken in its integrity. When we say A is B, or the river runs, the attribute is taken wholly or completely, but it could not be represented in the formula A is A B, the river is the river running. This is a different statement from the river runs, or has this particular mark. Gold is soluble in aquafortis-does not mean that gold is gold soluble in aquafortis; for we are speaking of gold itself, and we have added a mark, and until the mark has been added it is not, to begin with, gold soluble in aquafortis. The Black Watch were the first in the breach, does not mean that the Black Watch were the Black Watch first in the breach; for this is precisely what we have to add to what the Black Watch already is or is known to be.

§ 390. In any affirmative judgment, we necessarily, in thought, quantify the predicate to the full extent of the subject. A is B, means A is some B at least; or B is in A, all or some A; man is organised—that is, some part of the class at least, or organised is in A, all or some. If, therefore, the criticism have any force at all, it must imply that in every such

judgment, whether the predicate be expressly quantified or not, the meaning is A is A B; and it is thus not an objection, even if it be an objection at all, to the express quantification of the predicate but to the judgment as thought—that is, to the judgment as a judgment.

§ 391. But suppose the predicate expressly quantified, as A is (some) B-water is a (some) useful thing,—does this mean only or at all that A is A B, or water is water useful? In no way whatever. It means simply, that taking the two concepts or classes of things represented by A and B, water and useful, the subject is a part at least, some at least, of the predicate class, but whether all, or how far short of all, we cannot tell. Water and water useful are quite distinct concepts; we are speaking of the former, not of the latter. Useful water is not the subject of which I speak, but water; and these are two very different things. The extent of useful, of which I speak, is limited to the extent of the subject-water; but I am still speaking of water, not merely of useful water, and I am not repeating what I said in the subject, but adding to it specifying and relating it to a class which may or may not be coextensive with it. The oak is a deciduous tree— that is, some part of the deciduous. The oak is the oak deciduous, are wholly different propositions-not the least of the same import. All equilateral is (all) equiangular, the totality in the one case is convertible with that in the other; but all equilateral is equilateral-equiangular, does not assure me of the convertibility of the subject and predicate.

§ 392. It is further contended, that in the case of the express quantification of the predicate, the subject should be qualified (!) by the predicate. Why we are not told, nor what qualified judgment means in such a case. But it seems that if we say all man is some mortal, we ought to say all man is man mortal, and then man mortal is man mortal; or A is B, then A B is A B. I submit there is no equivalence in those statements or propositions, no necessary connection between them. When say all man is some mortal, I am speaking of the class man and the whole class man. But when I say man mortal, or mortal man are so and so, I speak of a part of the class man -viz., the mortal part, and I imply that there is or may be another part of which I am not speaking at all—viz., the nonmortal or immortal part. The one is a universal proposition

I

in which I speak of the whole subject; the other is a particular proposition, in which I speak only of some of the class, a supposed part of the subject. To say that the violet is blue, is not the same as to say that the blue violet is the blue violet. In the former case I am supposed to speak of all the class violet, and to say it is blue; in the latter case I am supposed to take a part of the class by restriction-viz., the blue violet, and to say simply that it is identical with itself. This arises from the elementary principle that any adjective applied to a subject is limitative. Mortal man is necessarily less than all man, and blue violet is necessarily less than all violet or all of the class. Hence to say that all of one class is equivalent to some of another or possibly wider class, is one thing; but when I say man mortal is man mortal, this does not tell me that I am speaking of the whole of the subject, and the proposition is not the convertible equivalent of all man is some mortal. It is simply a narrower proposition, and at the utmost a puerile verbal inference from it, which depends on the wider proposition.

But if the some in the predicate means some only, which it might do, the attempted equation of the two propositions is even ludicrous. All men are (only some) mortal, cannot be translated into all men are men mortal,-for this does not in the least tell me what I said originally that all men do not exhaust the class mortal, but are only a part of it. And to put men mortal for the predicate all men, is merely to repeat the blunder already exposed.

The formula becomes even more inappropriate when the subject and predicate are each universally quantified. We may say, all the men at the bar are all the rioters. This, according to the formula, should be, all the men at the bar are the men at the bar-rioters. And this paltry tautology is actually to be regarded as representing the statement made in the original proposition!

Again, let us take such a proposition as some stars are all the planets. Here, according to the formula, we ought to mean some stars are star-planets-which is pretty well nonsensical, and certainly not in the least the equivalent of the original proposition.

§ 393. The criticism, indeed, proceeds on the confusion of the Comprehensive and Extensive Predicates.

(1.) In regard to concepts,-when we translate man is some mortal, into man is man mortal,—we pass from the predicate in extension to that in comprehension-from what has quantity to what has none, but is indivisible. The some mortal of the first proposition indicates the limited place of the subject in the class; the man mortal of the other clumsily indicates mortality as an attribute of man. Instead of saying this simply, we say man is man (the) mortal, or man is the (or a) subject which possesses the mark mortal. To pass from the comprehensive predicate to the extensive is natural and legitimate; to repass from the extensive to the comprehensive is arbitrary and wholly unnecessary, and it does not proceed on any equivalence of quantity; for we really pass from what has quantity to what has none-from extension to comprehension.

To take an individual subject:-Simon is a tanner—that is, one of the tanners or class. If, however, we thus quantify the predicate, we ought, on the principle stated above, to have this form-Simon is Simon tanner, as man is man mortal. Now this is not the equivalent of the original proposition at all. This means that of those named Simon, the one of whom I now speak is tanner, or the tanner, as opposed to Simon the miller or butcher, or some one else of the same name. He is marked, in fact, by an attribute as one of the Simons; whereas, when I say Simon is a tanner, or one of the class, I am not considering whether there are other Simons, but only that he is one or a part of a definite class. He is in the class, but does not necessarily exhaust the whole extension. The proposition, Simon is Simon (the) tanner, is in Comprehension as giving the mark of the individual; the proposition, Simon is a tanner, is in Extension, and gives the place of the subject in the class.

§ 394. Objections have been made to the scientific validity of certain of the Propositional Forms:

(1.) Toto-total affirmation.

It is objected by De Morgan

All is all. All X is all Y.

(1) This is complex. (2) It cannot be denied by a simple proposition.

(1.) It is complex; and all Xs are Ys is compounded of all Xs are some Ys, and some Xs are all Ys.

(a) All Xs are all Ys is not more complex than its alleged constituents-all Xs are some Ys, or some Xs are all Ys. One

All is

quantity cannot be more complex than another. not compound, while some is simple. The truth is that some is made up of several, as this, that, &c., just as all is made up of every one. It is the business of Logic to consider a judgment as a completed or finished product. The psychological complexity of the judgment is a wholly different point. Moreover, to admit that some is all-some figure is all triangle-is simple, renders it impossible to conceive that all is all, or all triangle is all trilateral, is compound. All and some are both made up of a plurality. The attempt has been made to show the composition in question, on the ground that the propositions which make up all X is all Y—viz., all X is Y, and all Y is X, are independent of each other; while the propositions which make up all X is some Y-viz., all X is Y, and some Y is X, are not, the one being inferrible from the other by conversion. But when we find that this proceeds on the assumption (1) that the predicate as predicate has no quantity, and (2) nevertheless, that in conversion the quantity acquired is particular when the convertend is affirmative, and universal when it is negative, we need not argue the point. If the predicate in the convertend had no quantity, and yet acquired it in the conversion, the acquisition was at once arbitrary and illogical.

$395. (b) All Xs are all Ys is said to be compounded of two propositions-viz., all Xs are some Ys, and some Xs are all Ys. In concrete language, all triangle is all trilateral, is said to be made up of all triangle is some trilateral—some triangle is all trilateral. But these are incompatible propositions. If either of them is true, the other is false. Nay, if either of these alleged generating propositions be true, the so-called product, all triangle is all trilateral, is false. Here some is used in the sense of some only. All triangle is (only some) trilateral is contradictory of (only some) triangle is all trilateral; and either of these is contradictory of all triangle is all trilateral. Nor can it be shown that this form AfA is made up of these two forms, even if we take some in the ordinary Aristotelic sense of some at least. Thus (a) all triangle is some at least trilateral; and (b) some at least of triangle is all trilateral. For the quantity of the predicate in (a) is wholly indefinite, and the quantity of the subject in (b) is wholly indefinite, and the two