440 



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



allusion. In my Formal Logic (1847) I published my suspicions of what the system was, 

 in which I made it clear that I supposed the non-partitive quantity to be the one adopted. 

 This was soon followed by Bishop Thomson's second edition (1849) and by Mr Baynes's 

 Essay (l850), the first containing information communicated by Hamilton himself, the second 

 a student's account crowned — and augmented — by Hamilton himself. But, though both 

 writers drop a sentence or two which seem to hint that their own system is the singly 

 partitive — most writers, as already noticed, occasionally use at least a singly partitive 

 phraseology in their preliminaries — not a doubly partitive syllable escapes from either. 

 In my second paper (1850) I made it still more apparent that I attributed only the 

 non-partitive sense. Hamilton made an indignant remonstrance (V.) against the use of " all" 

 which I attributed to him : but not a word about " some" : [it turns out (see Addition) 

 that he took me to be using ' some' in his own new sense, which first appeared in print with 

 his criticism on my supposed objections to it. He had forgotten his own previous silence.] 

 His editors (IX. ii.) say that his notation had a uniform^ import from 1839-40 onwards. 



Mr Mansel (IV. 113, ll6) gives evidence (1851) of having on his mind the impression 

 that Hamilton differs from Aristotle : but not a syllable is there in his article from which we 

 can infer more than single partition, or at most the double partition which single partition 

 forces out of the universal affirmative. I feel justified in so much use of our private 

 correspondence as to state that he has informed me that all his sources were in print. 

 He makes no allusion to Hamilton's pamphlet (II.), probably because he did not, any 

 more than myself, gain any knowledge of the system from this source. I rest perfectly 

 satisfied, until contradicted, that Mr Mansel had no complete idea of the double partition, 

 nor of its consequences. As one editor, indeed, he has given me and others the means of 

 arriving at knowledge of the whole case : but both editors, in their short preface, imply 

 a caveat against being supposed to agree with their principal in all points. Mr Mansel's 

 article is a valuable repertory^ of the non-mathematical logician's objections to the results 



' They say that "this" (p. 278) was his uniform import. 

 By the preceding sentence it appears that "this" is "the 

 meaning which the author attached to them [the symbols] on 

 the new doctrine." These symbols, therefore, never had more 

 than one meaning; but they certainly were doubly partitive at 

 last; therefore they were doubly partitive throughout. But 

 the diagrams on which (and on their explanation) the note is 

 made do not agree with the later diagrams (vi. 632»): the 

 partial negatives, for example, are not disjoined affirmatives; 

 and the whole gives more than a suspicion of the singly parti- 

 tive sense. 1 hope that the second edition will be more precise 

 on this point. 



In the text I give nothing but facts. My own belief is that 

 Hamilton neither publicly taught, nor privately communicated 

 to any of those who have since acknowledged communication, 

 any thing beyond the singly partitive system. If, as his 

 editors seem to suppose, — and not against any presumption 

 which I can bring forward — his double partition was elabor. 

 ated by 184S, I feel almost sure that he intentionally reserved 

 it. He had a perfect right to do so; the same right which 

 Titus Oates's fox had to carry a stone over the broolc to see if 

 the ice would bear, before he attempted to carry over the goose. 



But such reserve always brings perplexity into history : Hamil- 

 ton has made it easier to cook his goose than to write its 

 biography. 



The following gives a strong suspicion — even more^^f 

 reserve in 1850, abandoned in 1852. In (v.), he says, "The 

 language I use is that of the logicians ; only the quantity of 



the predicate, contained in thought, is overtly expressed ". 



In the reprint of this letter (vi.626*) he adds to the words 

 "some is not", the following in brackets — "[Some is should, 

 however, have been held its direct and natural result; for, as 

 we shall see, two particulars in the affirmative and negative 

 forms, ought to infer each other. Compare p. 635*, sq.]" [This 

 makes the forgetfulness above noted very strange.] 



2 I quote at length the chief point of reference : — " Before 

 quitting this part of our subject, we will describe the principle 

 of Mr De Morgan's complex syllogism, as that part of his 

 system which comes in some degree into rivalry with the 

 quantified predicate of Sir W. Hamilton, which we are about 

 to examine. When we say that the latter accomplishes all 

 the ends attained by Mr De Morgan, with a vast superiority 

 in clearness and simplicity as well as in accuracy of thinking, 

 we have said all that is necessary in the way of criticism. 



