ON VARIOUS POINTS OF THE ONYMATIC SYSTEM, 



479 



which all quantification of the predicate is proved superfluous. Another notion, under the 

 name of quantification, has stirred up controversy. I say nothing here about the mere 

 question whether the quantity of the predicate should be expressed. The explicit demand for 

 this expression was first made by Hamilton : it is a great step ; and the logical world is 

 pretty well agreed that its merit is quite distinct from the merit or demerit of the particular 

 mode of quantifying which he adopted. 



What is quantification ? It means, or should mean, the giving or expressing of quantity ; 

 and as quantity is essentially a more or a less, the giving of quantity cannot exist without 

 the giving of a more or a less. But the quantity of the predicate, be it more or less, is always 

 the quantity of the subject, or its complement, as well in negatives as in affirmatives ; that 

 is, so far as it is more or less. I postulate that a proposition is only a proposition, a pro- 

 pounder, a challenger of assent or denial, in so far as, and with reference to, its assertion of 

 what might have been deniable, or its denial of what might have been assertable. For 

 example, in ' Every X is Y', it is a clear matter of affirmation, and so intended, that each X 

 is X, and each X not more than one Y: but these are not put forward as parts of the propo- 

 sition, because they are not distinctive parts. In propositions, as in terras, all that belongs 

 to the whole universe of propositions is to be tacitly rejected : I claim to make the rejection 

 explicit, because it is sometimes tacitly refused. This being conceded, if I say ' Xs are Ys' 

 it is clear that the number of Ys spoi<en of is the same as the number of Xs : if that number 

 be ten at most, then ten (or fewer) Xs are ten (or fewer) Ys. If I say ' Xs are not Ys', what 

 I deny is that the ten (or fewer) Xs are any ten (or fewer) Ys : I do not mean to deny 

 that the ten are nine or eleven ; for that I can deny by the form of thought, let X and Y 

 be what they may. If I say 'Everything is either X or Y' neither X nor Y has quantity 

 until quantity is assigned to the other : in a universe of 100 instances, if 40 Xs go to the veri- 

 fication of this proposition, the number of Ys required for the same purpose is 60. 



In treating the numerical syllogism, it appears that ' m Xs are found among n Ys' is a 

 proposition importing no more and no less than ' m Xs are Ys\ Also that ' m Xs are 

 not found among n Ys\ Xs and Ys being x and y in number, is spurious — that is, true inde- 

 pendently of which are Xs and which are Ys — if m + n be less than y or less than x ; and 

 otherwise, of the same import as ^m + n — y Xs are not Ys' and m + n — at Ys are not Xs. 



Neither is the predicate of an affirmative more or less definite than the subject, as to 

 quiddity^, to revive an old term. If I say ' All Xs are Ys', I only fail to know whether 



' This word, which was but badly replaced by essentia, has 

 been selected as a joke against the old logicians ; but quantity 

 and qunlity are in honourable use. The joke may be retorted 

 upon a discerning public, which, while treating the word with 

 ridicule, fell into the error of theory which it may be supposed 

 to favour, to every extent short of the absolute maximum. All 

 we know of quid is derived from quantum and quale : if man- 

 kind had discarded quiddity on this ground, the race would 

 have vindicated reason against philosophy with honour to 

 itself, or at least would have shown an appearance of it. But, 

 on the contrary, men in general assume a knowledge of things, 

 res ipste, entities, essences, substances, natures, &c. ; and they 



Vol. X. Part II. 



claim to assert much about quiddity upon any the least know, 

 ledge of quantity and quality. One exception, indeed, their 

 modesty does reserve; it is admitted, enforced, and made 

 pulpit doctrine, that the Almighty is known only by his 

 attributes, in a manner which implies that his creatures can be 

 otherwise known. There was a time when educated persons, 

 in numbers, had never heard of attributes in any other way ; 

 some may still be left. When a boy, I remember hearing mur- 

 mured charges of irreverence against a person in company who 

 spoke of the attributes of the vegetable world : my impression 

 was that some of those present had a vague idea that the speaker 

 miglit be a worshipper of leeks and onions. 



61 



