ON VARIOUS POINTS OF THE ONYMATIC SYSTEM, 481 



To the mathematician I assert that from the time when logical study was neglected by his 

 class, the accuracy of mathematical reasoning declined. An inverse process seems likely 

 to restore logic to its old place. The present school of mathematicians is far more rigorous 

 in demonstration than that of the early part of the century : and it may be expected that 

 this revival will be followed by a renewal of logical study, as the only sure preservative 

 against a relapse. 



A. DE MORGAN. 



University College, London, 



April 14, 1S62. 



%• This paper has been before the CouncU since May 19, 1862, though circumstances caused the deferment of tlie reading 



until May 4, 1863. 



ADDITION, 



. Since the communication of the preceding paper I have obtained some notice of my 

 criticisms from Mr T. Spencer Baynes, who I hoped might have been able to give evidence 

 from his own personal recollections of Hamilton's conversation and public teaching : this he 

 does only on one of the points, referring the others to Hamilton's printed works. Some 

 account of his remarks is necessary : they do not induce me to alter anything I have 

 written ; but, as noticed, I omit the detailed proof of the falsehood and incompleteness of 

 many of the syllogisms, because I find that no opposition will be made on this point. I 

 remain of opinion, and must so remain until further showing, of which I entertain no hope, that 

 Hamilton did leave one set of syllogistic forms as recipients of both senses of " some", the 

 old non-partitive sense, and his own doubly-partitive sense. That the neglect to make the 

 necessary comparisons was a consequence of illness ' I have no doubt. All the letters referred 

 to appeared in the Athenceum journal: the dates are those of publication. As stated in the 

 paper, I liad brought forward Hamilton's phrase "some at least (possibly therefore aW or 

 none)"', failing all attempt at defence, I had (Dec. 28, 1861) given my own method of 

 excusing its occurrence. Mr Baynes defends Hamilton (Nov. 22, 1862) : I' abide by my 

 explanation ; and the matter is now left to opinion. The phrase carries its own condemna- 

 tion with it ; to those who cannot see this I have really nothing to say. But as my object 

 in producing it was only to show the hurry of the article in which it appears ; and as it 

 belongs, not to Hamilton's system, but to his account of the old one ; and as I have omitted 



' Mr Baynes took no notice of my expressed conviction 

 (Nov. 2, 1861) that "as to his [Hamilton's] passing what 1 

 have called the Gorgon syllogism as valid inference, after actual 

 examination, there is no need to say that it was impossible he 

 should have done it." My whole position was that he had 

 allowed himself, without examination— and this probably 

 owing to his illness — to take the whole application to syllogism 

 for granted. I said (Nov. 2, 1861), "I have no doubt that 

 when he returned to his studies after the seizure, he imagined 

 that he had tested the whole system of syllogism upon his most 



recent definitions of the quantifying words." According to 

 Mr Baynes I have charged Hamilton with false reasoning : 

 the preceding quotations will show the sense in which the 

 charge was made. Be it remembered that these quotations are 

 no afterthoughts, but actual accompaniments of what is called 

 the " charge ". But 1 regret to say that the last proof of my 

 view of the subject, given near the end of this addition as very 

 recently discovered, shakes my coniidence in Hamilton's want 

 of examination, though I still hold that It is the more probable 

 hypothesis. 



61—2 



