ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



485 



silent. Another appeal, relating to what Hamilton had orally taught, of a pointed and per- 

 sonal character, brought out Mr Baynes on the whole question, with assertions which are 

 — if he should see any plausibility^ in my reasoning — to be substantiated so soon as 

 my most appropriate opportunity of discussing them shall have passed away. These things 

 speak for themselves : I fully anticipate that any attempt to invalidate my conclusion will 

 speak more plainly still. Something I have got ; I have extracted the defence which is to 

 be set up: namely, that the new sense of "some" is to be asyllogistic. Should any one 

 point out to me, publicly or privately, any passage in Hamilton's writings on his sense 

 of ' some' which expresses or implies that this was the case in his mind, or even agrees 

 better with this supposition than with its contradiction, I will discuss that passage when I 

 next take up the subject. In the mean time, I cannot too distinctly affirm that the most 

 attentive consideration'' has not enabled me to detect such a passage. 



I now come to a proof which I cannot claim as one of my original grounds, for I never 

 noticed it until after this addition had been dated and signed. I can easily understand how 

 I came to miss it. I always read Hamilton's paper (VI.) in the Discussions as his defence of 

 himself: 1 gave it comparatively little of sharp scrutiny as his attack on me. I recommend to 

 every one who has to read a mixed polemical argument to give separate readings, some treat- 

 ing it solely as attack without reference to defence, some treating it solely as defence without 

 reference to attack. The article (VI.) was written against my second paper. In that paper 

 I had no notion^ whatever tiiat Hamilton had any other sense of ' some' than that of the 

 logicians ; this will be very apparent. I state that six of his propositions agree with those 

 of the old school ; which is not true of any one; I add that the remaining two are " peculiar 

 propositions." I set out the list of syllogisms symbolically : I point out the differences between 

 Hamilton's system and my exemplar derivation from it ; especially the failure of the canon of 



made to four persons, was not on a question of opinion, but 

 on a question of fact; namely, as to what sense of "some" 

 Hamilton tauglit from his chair: this question could bedecided 

 only by testimony. 



' Since the bulk of this addition was written, Blr Baynes 

 (Dec. 20) has given an unconditional assurance that he will 

 attempt to substantiate his statements. It was drawn out by 

 a letter of mine {Dec. 13) in which I administered what I call 

 a rebuke, and he calls a personality, upon the tone of his pre- 

 ceding letter. Here I need only say that I think my remark 

 was richly deserved, and that I know it was meant to be directly 

 personal. I have much reason to be pleased with the result, 

 namely, the withdrawal of the condition which left Ulr Baynes 

 at liberty to attempt proof of his statements, or to leave it 

 alone, as should seem fit. 1 expect good from the discussion, 

 which is really that of the question, argued upon an instance, 

 whether one who is not of a mathematical turn can safely at- 

 tempt to meddle with the forms of logic. Sly opponents— all 

 St least who follow Hamilton— will hold lliat the word in 

 Italics ought to be omitted ; and I readily accept this as the 

 issue, should it please them to take it. 



' The latest account which Hamilton gave of the proposi- 

 tions furnished by his own 'some' is in the Discussions 

 (VI. fi31»): to me it is also the clearest. After distinctly re- 

 legating the old system, indefinite definitude, to subsequent 



pages, he proceeds to explain his diagrams, in which parallel 

 straight lines denote coextension so far as they run together, 

 and cocxelusion so far as they separate. Letters stand for 

 terms, as usual : D and A for coextensives ; Z and Q for total 

 coexclusives; B and C for includent and included; C and K 

 for partially co-including and co-excluding ; and something I 

 am not sure I understand for ' Some — is not some — '. This I 

 must explain to show that he is really symbolizing his own 

 peculiar forms. Then follows " the rationale of the letters is 



manifest; "; it is so, and it is manifest that, so far as the 



different letters are distinctively symbolic, they typify circum- 

 stances peculiar to Hamilton's own system. The sentence then 

 runs on thus: "and it is likewise manifest, that this principle 

 of notation may be carried out into syllogistic." Here is an 

 express reference to syllogism in connexion with the new sense 

 of 'some.' Any one who denies that the new propositions are 

 meant to be applied to syllogism must rebut, from elsewhere, 

 the presumption which this passage raises. 



^ "But Sir William Hamilton is the first who published 

 the idea of taking all phases of usual quantification, and 

 making them the basis of a system of syllogism " (J 4 of my 

 second paper. Vol. IX. p. 1). The word usual implies anti. 

 thesis, not to any other meaning of 'some,' but to the numerical 

 quantification. 



