ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



483 



had made only "simple assertion", refused (Dec. 6, 1862) to give any support whatever to 

 what he admitted were his own unsupported assertions, until after the appearance of this 

 memoir. He then pledged himself to reply if I should support my case by " definite evi- 

 dence", by " anything like proof", by "anything indeed approaching to a plausible reason". 

 It would require, he said, " not only a detailed statement, but a number of extracts". I take 

 Mr Baynes as admitting that no single extract, and no two extracts put together, would make 

 a prima facie appearance of contradiction to my hypothesis. I fear I shall never see this 

 defence: the mode of proceeding does not promise much. In Mr Baynes's short opening 

 letter (Nov. 1, 1862), he thinks his reply "may be put into very moderate compass"; and 

 that it "may be easily shown that Prof. De Morgan's chief difficulties arise from a complete, 

 though perhaps not very unnatural, misunderstanding of Sir W. Hamilton's condensed form 

 of expression". Here the words " easily shown" can hardly have meant that all the showing 

 was to be assertion, without one single supporting reference to Hamilton's writings. But 

 when Mr Baynes finds that simple assertion will not be taken as showing anything, and that 

 substantiating references are called for, and when he is told that I shall handle his reply in 

 ti)is paper, the moderate compass becomes detailed statement too long for the journal, and the 

 tone becomes more sarcastic. In pointing this out I direct attention to all' that Mr Baynes 

 will allow to be shown : high confidence with good humoured condescension changing, on 

 demand for proof of statements, into what must be interpreted as confession of difficulty, 

 with disparagements and ironies which seem intended to avenge the difficulty upon him who 

 put it in the way. I am quite content that Mr Baynes's imitation of his great teacher's 

 tone of controversy shall continue, provided only that he will demand respectable references 

 from every statement which applies for admission. Should he really attempt to redeem his 

 conditional pledge, I shall be much pleased: for I confidently expect that my views will be 

 positively confirmed. , But should I and the public hear nothing more from him, which from 

 his recent retreat is too much to be feared, I must be content with the negative confirmation 

 which his silence will inevitably be taken to afford. But I hope better things. 



I now proceed to point out how I came to arrive at so strange a conclusion as that 

 Hamilton's own new propositional forms, emerging out of his own new use of " some", 

 were intended to be used, as well as the old ones, in his own new system of syllo- 

 gistic forms. In every book of logic the treatment of the proposition precedes that of the 

 svlloofism : and the forms of enunciation treated in the chapter on propositions are those 

 used in the chapter on syllogism. This of course; for usually there is but one system of 

 propositions. When, for the first time, we see two systems of propositional forms, of which 



' Perhaps not quite all. The assertions being dismissed 

 which are to be established "some" day at latest f perhaps 

 tlierefore never ? ) there remains the fact proved by fllr Baynes's 

 evidence, that Hamilton explained to his class the doubly par- 

 titive " some," and (ix. ii. 268) the immediate inference thence 

 arising. There is also the fact proved by Mr Baynes's silence, 

 that Hamilton did not therewith tell his hearers that the doubly 

 partitive enunciations would not validate the only syllogistic 

 forms which he had given them. In my mind this adds pro- 

 bability to the hypothesis that Hamilton had never tested the 



point: it was his habit to go on year after year without making 

 any alterations. If he began to explain doubly partitive 

 enunciation to his class, with an intention of soon proceeding 

 to investigate the syllogism belonging to it, there is good rea- 

 son to suppose that, though the execution of the intention were 

 delayed, he would still continue his imperfect statement. The 

 third Lecture on Logic has pages beginning with "I would 

 interpolate some observations which I ought, in my last Lec- 

 ture, to have made before leaving " These lectures were 



read for twenty years without the alteration being made. 



