ON VARIOUS POINTS OP THE ONYMATIC SYSTEM. 



473 



junction of contranominals is, in every one of its four cases, excluded from separate enunciation 

 by the main principle of this system. If Hamilton had expressly started on the principle 

 of allowing every Aristotelian proposition, every possible junction, and every disjunctive 

 denial, with simple conversion, he would have come very near a system. 



The syllogisms of this system are, when it is fully taken, — 1. The 32 forms with two 

 single premises each. 2. Eight universal forms with double premises and double conclusion, 

 being those I have called syllogisms of terminal precision; and l6 opponents, having one 

 disjunctive premise and a disjunctive conclusion. 3. Various forms in which a single 

 universal — or a double one, which gives only a strengthened form with the same conclusion, — 

 with a double particular, give a double particular. 4. Various forms in which premises one 

 or both of which ai'e more than single give only a single conclusion. On these it is not neces- 

 sary to dwell : any case is resolved at a glance by any one familiar with my notation. 



I cannot undertake, in the present paper, to give a full account, in relation to aggre- 

 gation' and composition, of the distinction of extent and intent. I shall therefore confine 

 myself to what I expect will be a termination of my controversy on this point, followed by a 

 brief account of what I hold to be the true logical foundation of the distinction. 



No part of Hamilton's system has received a more ready assent from his followers than his 

 mode of making the distinction — I say his substitute for the distinction — which Aristotle 

 announced when he divided genus in species — attribute in attribute — , from species in genus 

 — class in class. I shall not, after what is said in my third paper, oiFer any further proof 

 that there is a substitution. It will be enough here to quote (VI. 642*) his governing* 

 principle — " the predicate of the predicate is, with the predicate, affirmed or denied of the 

 subject" — which ushers in the form of depth, or comprehension, " All X is some Y", as 

 distinguished from that of breadth, or extension, " Some Y is all X", When we say, says 



' This distinction is not yet seen, nor, I fear, will it be 

 seen until the logician is restricted to puddings which are only 

 aggregates, and not compounds. It is remarkable that we have 

 no word of pure Knglish which designates the part as a com- 

 ponent: element, constifvent, ingredient, component, material, 

 are all foreign. Shakspeare's witches talk of ingredients ; but 

 they were scientific characters: the word can be distinctly 

 shown to have been limited to medicines, charms, &c. What 

 would a housewife of the time of Elizabeth have said, when 



she told her servant not to forget the — for one of those 



puddings which I would withhold from the logician. The 

 things or the stuff will suggest themselves ; but they only 

 prove the aljsence of the truly distinctive word. For things 

 may be aggregants as well as components : and stuff is the 

 proper term when there is but one kind of material; though, 

 for want of better, it occurs in such words as garden-stuft", 

 kitchen-stuff. And the word applies equally to aggregants 

 and components. 



' The word predicate is here loosely used. The first time 

 it occurs it means ' predicate affirmed': in the two other cases 

 it means * predicate affirmed or denied*. Hamilton's readers 

 must be cautioned as to the very positive way in which he 

 puts forward bran new principles as though they were gene- 

 rally received, and convicts those who deny them of mistake, 

 by appeal to the principles themselves. For example, (vi. 

 642») :— " Tliis suffices to show how completely Mr De Mor- 

 gan mistakes the great principle: — The predicate of the predi- 



cate is, with the predicate, affirmed or denied of the subject." 

 Would not any one suppose it to be notorious that this great 

 principle had been previously announced by others ? Be this 

 as it may — I assert no negative, but I cannot find it— I had 

 denied this principle, in effect, though I had never heard it, by 

 proceeding on principles repugnant to it. When I say a horse 

 has four legs, I ought to be taken as denying the great princi- 

 ple of bipedality, not as counting each leg twice in an attempt 

 to apply it. In the point before us the Port Royal logicians 

 have repugned the 'great principle' as well as myself, and to 

 all appearance with no more knowledge of its existence than 

 myself; and Hamilton proves his knowledge of their opinion 

 by citing them — very correctly, I believe, — as the restorers of 

 the distinction of extension and intension. I may slightly 

 mention another point. Hamilton thinks it sufficient to an- 

 swer his opponent's meaning by fixing another meaning on 

 his opponent's words. I designated a proposition of his as 

 spurious, referring to a page of my own book for my own tech- 

 nical use of that word. Hamilton (yi. 039*) begins his answer 

 thus, " Spurious in law means a bad kind of bifstard:" and 

 on this definition he easily convicts me of absurdity. If, under 

 a definition of my own, I had called his proposition goniome- 

 trical instead of spurious, he might well have impeached my 

 Greek ; but it would have been of coequal absurdity if he had 

 answered me by solemnly proving that he had not enunciated 

 a theodelite. 



60—2 



