ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



441 



of mathematical habit : and I confidently predict that it will often be cited as such 

 when the number of those who stow both logic and mathematics in one head shall be 

 greater than it now is. So far I have not produced a single hint of double partition. 

 When I examined the late Professor Spalding's work (1857) I could not trace a phrase 

 which was not perfectly reconcileable with the Aristotelian sense, or at most with single 

 partition. On re-examining my copy for the purposes of the present paper, I found inserted 

 a number of the Edinburgh Weekly Review (July 18, 1857) containing an account of Mr 

 Spalding's work, and citing' him as among the chief objectors to Hamilton's junction of 

 " some at least " and " some at most." 



Lastly, I mention myself, who might have been expected to have read the whole riddle 

 at once in the publication (VI.) of 1852. But I, at that time, had good reason to feel 

 estopped, as the lawyers say, from all interpretation of Hamilton's meaning : the reason is 

 described in the Appendix to my third paper. I found that, in spite of the most distinct 

 assertions, as well on the part of Hamilton as of his expositors, that ' all ' is the exponent 

 of universal quantity, I was wholly in the wrong for not divining that 'any'' must be 

 used in every ^ negative proposition (V. passim). The sarcastic pictures caused the article 

 (VI.) to be to me, so long as its author lived, a joke and nothing else ; I mean that whenever 

 I sat down to read in earnest I was always captured by the fun. And when, at last, I gave 

 it serious examination, my disinclination to interpret was augmented. When I saw that 



MrDe Morgan refuses to quantify [Mr M&nsel means partitive- 

 ly] ihe predicate in a single affirmative proposition. Accordingly, 

 the universal affirmative, all X is Y, may form part of two 

 complex propositions, either ' all X is Y, and all Y is X', or 

 ' All X is Y, and some Y is not X'. Hence a syllogism in 

 Barbara which, in Sir W. Hamilton's system, would be ex- 

 pressed in the form 'All X is some Y, all Y is some Z, there- 

 fore all X is some Z', becomes in Mr De Morgan's hands the 

 following complex reasoning [a hasty word ; expression must 

 be meant: for Hamilton's syllogism contains all this reasoning; 

 and this by the partitive force of ' some ' ]. 



All X is Y, and some Y is not X. 



All Y is Z, and some Z is not Y. 

 Therefore, All X is Z, and some Z is not X. 



The reader who is desirous of further details must seek 

 them in Mr De Morgan's own work. Those who will take 

 the trouble of comparing his fourth and fifth chapters with the 

 system we are about to describe, will, we are convinced, dis- 

 cover abundant grounds to justify our preference for the latter. 

 We have followed Mr De Morgan through a tedious journey, 

 during which we have more than once had occasion to express 

 our respect for his talents, and our regret at their perversion. 

 We take leave of him in the words of an eminent logician and 

 mathematician: — ^' Enimvero quae confuse tantum cognoscun- 

 tur, ea ssepius confunduntur, ut adeo casus similes videantur 

 quae sunt dissimiles, et secundum ideam confusam qui agit, 

 facile omittit quibus vel maxime fuerat opus. Atque ideo 

 logica naturali instructus in applicatione saspissime aberrat. 

 Exemplo nobis sunt illi qui, in mathesi cum laude versati, 

 methodum mathematicam extra eandem perperam applicant, 

 etsi sibl rem acu tangere videantur.' (Wolf, Philosophia Ratio- 

 nalis, Proleg. § 19)." I suspect that the text of the last two 



sentences is corrupt: and I propose conjectural emendations. 

 Remember that all that relates to quantity is mathematical ; 

 for naturali read sine mathematica, for cum laude read mimta, 

 for extra eandem read inscitia naturali. 



' " Unless indeed objection be taken, as is done by some 

 of them [his disciples], and particularly by Professor Spald- 

 ing, to Sir William's employment of both the alternative 

 meanings of the word 'some', as 'some at least' and 'some at 

 most'. There seems good reason for suspecting that the ac- 

 ceptance of the latter interpretation would again open the door 

 [how is this possible?] to extralogical considerations." I 

 again examined the work: and again without success. I then 

 remembered that Mr Spalding himself had sent me this review, 

 as written by a friend of his own : and I suppose his friend had 

 mixed up reminiscences of conversation with those of the printed 

 pages. I conclude that Mr Spalding did object to the doubly 

 partitive system, but showed his objection only by suppres- 

 sion. 



' Hamilton's editors have judiciously ignored the whole 

 controversy. But on one point they have made an indirect 

 reference, seemingly intended to intimate that any one who 

 lays down 'all' as the symbol of universal quantity, does in 



fad lay down '■ant/' as its substitute in negatives. They say 



"The comma (,)denotes some; the colon (:)aH"; which is all that 

 is given in explanation of the symbols of quantity. They then 

 say — " Thus ; — C : — , A is read all C is some A. C : -K : D 

 is read, iVo C is onjr D." (ix. ii. 277, 278.) The word /Ams 

 implies exemplification. To read ' No C is any D ' may be 

 permitted : but he who thuses this reading of ' C : m- : D' upon 

 "the colon denotes all" reminds me of my old French master, 

 an unhorsed hussar of 1815, who gravely taught that "All the 

 French words are derived from the Latin : thus '■ Seigneur ', 

 which is 'Lord,' comes from the Latin 'Dominus'." 



56—2 



