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While Mr Mill was amending the Syllogistic theory so as to ensure for Formal Logic its legitimate place among the essentials of scientific procedure, Sir W. Hamilton was at the same time enlarging it on its technical side, in two modes which are highly esteemed both by himself and by others: 1. The recognition of two kinds of Syllogisms; one in Extension, the other in Comprehension: 2. The doctrine of the Quantification of the Predicate.—Both these novelties are here criticised by Mr Mill in chapter xxii., which we recommend the reader to peruse conjointly with Lectures 15 and 16 of Sir W. Hamilton on Logic.
Now whereas the main objection, by which the study of the syllogistic logic has been weighed down and discredited in modern times, is this, that it encumbers the memory with formal distinctions, having no useful application to the real process and purposes of reasoning—the procedure of Sir W. Hamilton might almost lead us to imagine that he himself was trying to aggravate that objection to the uttermost. He introduces a variety of new canons (classifying Syllogisms as Extensive and Intensive, by a distinction founded on the double quantity of notions, in Extension and in Comprehension) which he intimates that all former logicians have neglected—while it plainly appears, even on his own showing, that the difference between syllogisms, in respect to these two sorts of quantity, is of no practical value; and that 'we can always change a categorical syllogism of the one quantity into a categorical syllogism of the other, by reversing the order of the two premises, and by reversing the meaning of the copula' (Lect. xvi. p. 296); nay, that every syllogism is already a syllogism in both quantities (Mill, p. 431). Against these useless ceremonial reforms of Sir W. Hamilton, we may set the truly philosophical explanation here given by Mr Mill of the meaning of propositions.
'All judgments' (he says—p. 423), 'except where both the terms are proper names, are really judgments in Comprehension; though it is customary, and the natural tendency of the mind, to express most of them in terms of Extension. In other words, we never really predicate anything but attributes; though, in the usage of language, we commonly predicate them by means of words which are names of concrete objects—because' (p. 426)—'we have no other convenient and compact mode of speaking. Most attributes, and nearly all large bundles of attributes, have no names of their own. We can only name them by a circumlocution. We are accustomed to speak of attributes, not by names given to themselves, but by means of the names which they give to the objects they are attributes of.' 'All our ordinary judgments' (p. 428) 'are in Comprehension only; Extension not being thought of. But we may, if we please, make the Extension of our general terms an express object of thought. When I judge that all oxen ruminate, I have nothing in my thoughts but the attributes and their co-existence. But when by reflection I perceive what the proposition implies, I remark that other things may ruminate besides oxen, and that the unknown multitude of things which ruminate form a mass, with which the unknown multitude of things having the attributes of oxen is either identical or is wholly comprised in it. Which of these two is the truth I may not know, and if I did, took no notice of it when I assented to the proposition, all oxen ruminate; but I perceive, on consideration, that one or other of them must be true. Though I had not this in my mind when I affirmed that all oxen ruminate, I can have it now; I can make the concrete objects denoted by each of the two names an object of thought, as a collective though indefinite aggregate; in other words, I can make the Extension of the names (or notions) an object of direct consciousness. When I do this, I perceive that this operation introduces no new fact, but is only a different mode of contemplating the very fact which I had previously expressed by the words, all oxen ruminate. The fact is the same, but the mode of contemplating it is different. There is thus in all Propositions a judgment concerning attributes (called by Sir W. Hamilton a Judgment in Comprehension) which we make as a matter of course; and a possible judgment in or concerning Extension, which we may make, and which will be true if the former is true.'
From the lucid explanation here cited (and from a following paragraph too long to describe p. 433), we see that there is no real distinction between Judgments in Comprehension and Judgments in Extension; that the appearance of distinction between them arises from the customary mode of enunciation, which custom is here accounted for; that the addition to the theory of the Syllogism, for which Sir W. Hamilton takes credit, is alike troublesome and unprofitable.
The like may also be said about his other innovation, the Quantification of the Predicate. Still more extensive are the changes (as stated by himself) which this innovation would introduce in the canons of Syllogism. Indeed, when we read his language (Appendix to 'Lectures on Logic,' pp. 291—297) censuring generally the prior logicians from Aristotle downwards, and contending that 'more than half the value of logic had been lost' by their manner of handling it—we may appreciate the magnitude of the reform which he believed himself to be introducing. The larger the reform, the more it behoved him to be sure of the ground on which he was proceeding. But on this point we remark a serious deficiency. After laying down, with appropriate emphasis, the valuable logical postulate, to state explicitly what is thought implicitly, on which, Sir W. Hamilton says,
'Logic ever insists, but which logicians have never fairly obeyed—it follows that logically we ought to take into account the quantity, always understood in thought, but usually, and for manifest reasons, elided in expression, not only of the subject, but also of the predicate, of a judgment.'—('Discussions on Philos.,' p. 614.)
Here Sir W. Hamilton assumes that the quantity of the predicate is always understood in thought; and the same assumption is often repeated, in the Appendix to his 'Lectures on Logic,' p. 291 and elsewhere, as if it was alike obvious and incontestable. Now it is precisely on this point that issue is here taken with Sir W. Hamilton. Mr Mill denies altogether (p. 437) that the quantity of the predicate is always understood or present in thought, and appeals to every reader's consciousness for an answer:—
'Does he, when he judges that all oxen ruminate, advert even in the minutest degree to the question, whether there is anything else that ruminates? Is this consideration at all in his thoughts, any more than any other consideration foreign to the immediate subject? One person may know that there are other ruminating animals, another may think that there are none, a third may be without any opinion on the subject; but if they all know what is meant by ruminating, they all, when they judge that every ox ruminates, mean precisely the same thing. The mental process they go through, as far as that one judgment is concerned, is precisely identical; though some of them may go on farther, and add other judgments to it.'
The last sentence cited from Mr Mill indicates the vice of Sir W. Hamilton's proceeding in quantifying the predicate, and explains why it was that logicians before him declined to do so. Sir W. Hamilton, in this proceeding, insists on stating explicitly, not merely all that is thought implicitly, but a great deal more;[14] adding to it something else, which may, indeed, be thought conjointly, but which more frequently is not thought at all. He requires us to pack two distinct judgments into one and the same proposition: he interpolates the meaning of the Propositio Conversa simpliciter into the form of the Propositio Convertenda (when an universal Affirmative), and then claims it as a great advantage, that the proposition thus interpolated admits of being converted simpliciter, and not merely per accidens. Mr Mill is, nevertheless, of opinion (pp. 439-443) that though 'the quantified syllogism is not a true expression of what is in thought, yet writing the predicate with a quantification may be sometimes a real help to the Art of Logic.' We see little advantage in providing a new complicated form, for the purpose of expressing in one proposition what naturally throws itself into two, and may easily be expressed in two. If a man is prepared to give us information on one Quaesitum, why should he be constrained to use a mode of speech which forces on his attention at the same time a second and distinct Quaesitum—so that he must either give us information about the two at once, or confess himself ignorant respecting the second?
