’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?