430 



Mr DE MORGAN, ON THE SYLLOGISM, No. V. AND 



fore addressed two letters to the Jthenceum journal (published July IS and August 17, 1861) 

 in which I exposed a curious apparent blunder relative to Aristotelian logic, and also one 

 of the paralogisms above alluded to. I gave two months for denial, with notice that, if 

 no denial were attempted, I should myself point out grounds of ewtenuation. I fully 

 expected that editors, or pupils, or other disciples, would dispute my conclusions : but 

 nothing whatever appeared. I accordingly wrote two other letters (published Nov. 2 

 and Dec. 28, 1861), in which I pointed out how hurry, illness, and halting between two 

 systems, deprived the errors, which I then assumed to be undeniable, of the very gross 

 and illiterate character which would have attached to them had they been deliberate. Further 

 account of them will appear in the proper places. [Having waited more than a year, 

 I again called the attention of the logical world to a point which nothing but testimony could 

 settle, naming those from among whom I expected an answer. This plan was successful; 

 and an account of the defence made will be found in an Addition. I have allowed the body 

 of the paper to stand as it was written. December, 1862.] 



My knowledge of Hamilton's system is derived from the following sources. I. A 

 prospectus of the intended New Analytic issued in 1846, with Requirements for a prize 

 Essay ; both reprinted, the first with some omissions, in the Lectures on Logic. II. My 

 correspondence with Hamilton in 1846-7, printed by him in 1847, with notes and additions, 

 as part of our personal controversy. III. Mr T. Spencer Baynes's Essay on the new 

 Analytic, the prize Essay of 1846, published in 1850, with additions, including a note by 

 Hamilton himself. IV. A review of Hamilton, myself, and others, afterwards acknowledged 

 by Mr Mansel, in the North British Review of May, 1851. V. A letter of Hamilton, 

 dated August 7» 1850, forthwith published in the Athenceum, and reprinted in the Discussions. 

 VI. An article' in the Discussions (1852) inserted probably at the last moment, under 



sion I care not to avoid; and the discussion, I hope, may 

 have its uses." The last words of this paper are — "So much 

 for Mathematical Logic; so much for Cambridge Philosophy." 

 I neither claim to represent the University, nor do I admit 

 the alternative on which Hamilton risked himself: but, 

 when I found I must prove that my opponent, though well 

 knowing his alphabet, spelt new words incorrectly, I thought 

 it right that the Society and the University should not give 

 that faint appearance of sanction which this publication in- 

 volves, until denial from Hamilton's followers had been chal- 

 lenged. 



' This hurried article, as I shall sometimes call it, contains 

 those quantities which are one and the same quantity, but of 

 which the greater the one the less the other, and the apparent 

 assertion that "some at least" is "possibly none." It seems to 

 show excitement: its sarcastic photographs have stronger lights 

 than those of preceding writings. As Hamilton had had the 

 last word in the Athenceum journal eighteen months before, 

 this is presumption of some new call to action. 1 surmise, 

 from a stray sentence at the end, that the writer was roused, 

 when his work was all but published, by information of 

 the effect which my objections had produced south of the 

 Tweed. After comparing a mathematician to an owl by day- 

 light and a dram-drinker, Hamilton says, — "For a time, I 

 admit, Toby Philpot may be the Champion of England." 



Those who examine the whole discussion in time to come, will 

 note the manner in which his instinct made him feel that ma- 

 thematics would destroy his fabric, unless he could first destroy 

 mathematics. 



Every proof of hurry in this article is an act of charity : 

 the following is worth notice. Hamilton knew well (ix. i. 43) 



that in respect of "irrefragable certainty" "Logic and 



Mathematics stand alone among the sciences, and their pecu- 

 liar certainty flows from the same source." He knew just as 

 well that the contest between him and me turned wholly on 

 the "forms of intelligence" — the necessary laws of thought — 

 of an exact science. How then came he to object to me that 

 a mathematician in "contingent matter" is like an owl by 

 daylight? How came he thus to assert, by implication, that 

 he and I had been arguing contingent matter? How came he 

 to imply that the logical half of exact science is contingent? 

 Except under this implication his assertion, supposing it true, 

 would not help him. The answer is that he was in a great 

 hurry, and pelted the mathematician with whatever came up- 

 permost. 



There is also hurry in Hamilton's appeal for help to War- 

 burton's remark, that in his time the oldest mathematician in 

 England was the worst reasoner in it. The person alluded to 

 was Whiston: and no man of letters, writing very deliberately, 

 would have taken Warburton as sufficient authority against 



