THE THEORY OF SYLLOGISM, ETC. 



99 



These difficulties* lie on the surface; and the first objector is sure to seize them. I expect 

 a powerful consideration of them in Sir William Hamilton's forthcoming work, from the known 

 learning and acuteness of the author, with some weight given to his assertion that his system 

 has been " adequately tested and matured." And I should not be surprised at a successful 

 explanation : for, though I cannot give one myself, as long as the system stands on its in- 

 ventor's ground, yet I can prevent the appearance of the objections by shifting that ground. 



The occurrence of eight forms, corresponding in their modes of quantification with those 

 which I had obtained, and by coincidence which did not arise from any sameness in the path 

 of investigation, struck me as exceedingly remarkable. I could not entirely declare against 

 the possibility of sufficient reason for a system which, independently of the habitual ac- 

 quaintance of its promulgator with the logician's mode of thinking in every age, had, as we 

 shall see, strong symbolic claims to being something. Symbolic language gives the expression 

 of the laws of thought in their purest forms : and it has never deceived those who were 

 willing to be its servants before they claimed to be its masters. In the present case, there 

 seemed something resembling a system of algebra with a singular form in it. Formal Logic 

 must teach how to enunciate all definitely conceivable truth and falsehood, just as symbolic 

 algebra must teach how to enunciate all definitely expressible quantity : and • some ATs are not 

 some Fs' appeared to partake very much of the indeterminateness of ^. An algebraist has not 

 profited by the history of his science, if he dogmatically reject what appears incapable of 

 interpretation in connexion with the rest of its system. Thinking on this, I tried whether 

 there might not be some view of predication which would make Sir William Hamilton's eight 

 forms self-consistent : that is, make them contradict each other four and four. The thing 

 required is that )), ((, ).), (.(, ).(, and ( ) should remain related to each other as at present : 

 and that )( and (.) should be a double universal and a double particular, destructive each of 

 the other. 



We might put this question to any person, When you say ' every man is an animal,' do 

 you speak of all men, or of one man, of as many animals as there are men, or of one animal ? 

 Is your proposition cumular, or what I will call exemplar ? I apprehend the general first 

 answer would be in favour of the cumular view, but not the universal one. Some would say, 

 I speak of one man, being any one I can select, and of one animal, but not any one I please, 

 for upon what man I select, depends what animal I select. Some would say that the article 

 an, which denotes one animal, confines the subject to one man : how else can every man be an 

 animal ? And in truth they are etymologically right, for every is each, not all, in meaning. 



* Sir William Hamilton is, I have no doubt, the first 

 advocate of the form (•) : but it, and the peculiar syllogism 

 derived from it (with two particular premises) have been seen 

 and rejected, by myself at least, probably by others. I men- 

 tion the following as a curious coincidence. Sir William 

 Hamilton states that he had in his own mind arrived at the 

 form, ' most Ys are Zs, most Fs are Xs, therefore some Xs are 

 Zs' before me, and thrown it away, unpromulgated, as a 

 cumbrous and useless subtlety. He had thu9 made the ap- 

 proach of a single instance towards the numerically definite 

 syllogism. Now I, on my part, had made and published, as a 



true inference, but not within the forms of predication, one syl- 

 logism in the new part of Sir William Hamilton's system ; in 

 the following words : " The weakest syllogism from which such 

 an inference [particular negative] can be drawn would then 

 seem to be as follows. Some Xs axe Ys, some Zs are not Fs, 

 therefore some Zs are not Xs....But here it will appear on a 

 little consideration, that the conclusion is only thus far true, 

 that those Xs which are Ys cannot be those Zs which are not 

 Fs. ...(First Notions of Logic, 1839, reprinted (with slight 

 alteration) as the introductory chapter of F. L.) 



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