formed-first, that some are; secondly, that some (others of the class) are not. It seems to me that we must, first of all, work out logical principles on the indefinite meaning of some at least. This is the primary requisite and meaning of affirmation-the least possible-in dealing with a class. Some only, as appears to me, is a secondary and derivative judgment. Still this need not interfere with the recognition of the meaning in propositions. Nor does it make it less a single judgment, after the process of formation has been completed. It is then no more a double judgment than all are; and, like it, may appear as a single premiss in a reasoning.

§ 388. There can be no doubt of the common use of this definite meaning of some in ordinary thought and speech. When I say, some of the men in the ship were drowned, I naturally mean only some; I oppose this definite particularity to all,—all the men in the ship were drowned. I should not,

in this connection, naturally say, some of the men in the ship were not drowned. The positive element in the occurrence is that to which I should naturally refer, and in wishing to express that all were not, I should say some were,—that is, only some were.

(a) "I saw some of your children to-day." These words, according to Mill, do not mean that I saw some only. But we are led to infer that they do, because it is most likely, if I had seen them all, that I should have said so; “and it is further presupposed that I must have known whether the children I saw were all or not." Any tyro in Logic would say in reply to this, that if I say I saw some, I must mean not all, but only some, in whatever way I may have come to know this. Logic begins with the assertion made, and demands its explicit meaning. Is it conceivable that even Mill could have imagined that some, said of what had been seen, might mean more than the some seen? or that the some expressed did not exclude all?

(b) In Greek we have a means of distinguishing the some and some. In the case of an individual object, say in space, we have one part of the object distinguished from the other by a definite form of expression. Thus, if we only mean to speak of the middle market-place, we should say μéon ȧyopá; but if of the middle of the market-place, we should Bay, ἡ ἀγορὰ μέση. So τὸ ἔσχατον ὄρος means the outmost mountain, but EXаTOV TO Õрos means the outmost part of the mountain.-(Clyde's Greek Syntax, p. 21.) This is simply the some and some, or the some and some not of the logical conception & μev δ δε, These may ex

δ

press opposition; they also often express different or divided parts of the same thing-portions of the same class-the one, the other, hic and ille -as this species and that species of the same class-in logical form some and some (other) (of organisms)

"In English, as in Greek, the attributive formula marks a distinction of persons and things, whereas the predicative formula marks a distinction of conditions in the same person or thing. The stone is soft here, Téτpa uaλaký čoτi évтavba, is predicative; the soft stone is here, ἡ μαλακή πέτρα ἐστὶν ἐνταῦθα, is attributive-marking a difference in the kind of stone. I see the mountains white (predicative); I see the white mountains (attributive)." (Clyde's Greek Syntax, p. 19.)

(c) Laurentius Valla, long ago, vindicated the practical use of the bi-particular proposition (propositio biparticularis)—some is not some. "Non totus orbis," he said, "paruit Alexandro," i.e., "pars orbis paruit, pars non paruit." So "tota Græcia non paruit Alexandro," i.e., "non tota Græcia," This was a distinct and formal anticipation, as well as vindication, of the necessity for thought and expression of the some and the some not in reference to the same class.-(See Dialectica, c. xxvi.)

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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 treethat 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 I 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

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 position 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.

pro

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.