ON VARIOUS POINTS OP THE ONYMATIC SYSTEM". 



439 



5. Some X is some Y : X partipartially inclusive of Y : X a complex particular {For- 

 mal Logic, p. 66) of Y : or X (•()■) Y, conjoined of X ( • ( Y, X ( ) Y, X ) . ) Y. The contra- 

 diction is * Either X )) Y, or X).(Y, orX((Y', denoted by X)); ((Y, 



These enunciations constitute the system • at which Hamilton was aiming, but which 

 permutations of « some' and ' all' did not and could not reach. I do not think it worth 

 while to set out all the syllogistic forms : these are best obtained by resolution into simple 

 pairs of premises. I shall presently have occasion to exhibit a more perfect completion. 



I now proceed to inquire how this system was received in the time preceding the 

 publication of Hamilton's Lectures. The day will come when, but for such hints as 

 I now give and the explanations which they will directly or indirectly produce, an in- 

 quirer into the early history of the expressed quantification of the predicate would be in 

 serious difficulty. From 184.7 to I860 he will trace a stream of eulogy and controversy, 

 of which Ilamilton's quantification is the subject : but not a direct word does either 

 advocate or opponent let fall about this quantification containing a very striking departure 

 from Aristotle and his followers. Hamilton himself gives no information until 1852, when 

 he announces his plan in terms which, to the inquirer I am supposing, will appear as clear 

 as any terms could be : but still neither friend nor foe seems to know more about it than 

 before. It is not until after i860, when those remains were published which had for eight 

 years been known by nearly sufficient extract, that all Hamilton's admirers are suddenly 

 and publicly challenged to show that his reaP system does not lead to mere paralogism: 

 which not one of them undertakes to do. What does all this mean ? Is it reserve ? 

 Is it misapprehension ? 



Previously to 1852, Hamilton did not indicate intention to depart from Aristotle in 

 the meaning of the quantifying designations. In his Prospectus (1846) he announces that 

 he is to put the key-stone on the Aristotelic arch : not a hint is given that the but- 

 tresses are to be changed. In his correspondence with me, not a word of so much, as 



' It is clear that Hamilton never examined the syllogism 

 upon the doubly partitive hypothesis. To my mind by far the 

 most probable hypothesis is that, after the attack of illness 

 which he never wholly recovered, he really believed that he 

 had examined the syllogism : a sudden interruption of this 

 kind often has strange effects in the way of confusion between 

 what had been done and what was to be done. This supposi- 

 tion receives some confirmation from the note at the end of the 

 table of propositional relations — ' The preceding table may not 

 be quite accurate in details' (ix. ii. 284, vi. 637»;. Such a 

 memorandum in a private paper is for personal use: it was 

 copied into the hurried article (vi.), which means that no deli- 

 berate examination had taken place up to 1852, even of the 

 table of propositional forms. Now it is cleat that a minute 

 verification of the cases of syllogism must have either ended in, 

 or been preceded by, such examination of the table of enuncia- 

 tions as would have led to the erasure of the note. 



' There is another point, which I cannot decide. Hamilton 

 taught his own system publicly from 1840 downwards. What 

 use of 'some' did he adopt? Neither he himself, nor Mr 

 Baynes in his New Analytic, nor Bishop Thomson in his 



Vol. X. Part II. 



Outlines, nor Mr Mansel in his edition of the Lectures on 

 Logic, give any information on the point. I put the question 

 in my letters to the AthencEum, but no reply was made. I 

 cannot bring myself to think that my acute opponent actually 

 taught, year after year, a system of syllogism containing a 

 cluster of paralogisms. I lean strongly to the supposition that 

 he retained the Aristotelian sense, or made no further departure 

 than the singly partitive meaning : but if this be the fact, what 

 hinders those who can from establishing it? 1 repeat the ques- 

 tion again, and I trust that, if the point can be cleared up, 

 those who have the means will not allow me to be the only 

 person who shows interest in Hamilton's literary fame. For the 

 honour of Scotland, a land noted for the logical turn of its 

 sons, the question should be settled. Should judgment at last 

 go by default, the decision must be that for sixteen years un - 

 detected paralogisms formed a third part of the system of syl- 

 logism taught in the University of Edinburgh as the "key- 

 stone of the Aristotelic arch." [Mr Baynes replied satisfacto- 

 rily on this point, as will appear in the Addition. I leave this 

 note as showing what I thought on the subject when this paper 

 was communicated. December, 1862.] 



56 



