224 



Mr DE morgan, ON THE SYLLOGISM, No. Ill, 



first knew the existence from Mr Baynes's New Analytic (1850, July). Ploucquet gave, ac- 

 cording to my critic, the following rule : Deleatur in premissis medius : id quod restat indicat 

 conclusion em (pp. 630*, 685); but in what work is not stated, nor whether Ploucquet used symbols. 

 My rule is : — Erase the symbols of the middle term ; the remaining symbols shew the infer- 

 ence. It is assumed that I derived this rule from Ploucquet. I answer that, in the second 

 appendix to my Formal Logic (p. 323) I gave what then* was " all I know of any attempt to 

 deal with the forms of inference otherwise than in the Aristotelian method." I had one borrowed 

 work of Ploucquet in my hands for a few weeks; the only one of that writer I ever saw : 

 I gave all I got from it. If the methodus calculandi described by me in page S3& be what-j- 

 was meant, it will be seen to have not even a remote resemblance to my method : if not, I never 

 saw what was meant. My quantum — very far from sufficit — of research in logical biblio- 

 graphy does not, at this moment, bear the most remote comparison to what some of my writings 

 prove as to mathematical bibliography : and in 1849 it was much less than now. 



Ignorance of elementary Logic. To the general charge my writings must reply. But 

 there are especial instances, which are quoted or referred to in three of the critic's writings. 

 I have never been able to find the source of more than one of these instances. In giving 

 an account of it, I cannot but express my conviction that the author of the imputation had lost 

 some of his habit of deliberate reading, and that the misinterpretation of my meaning, and the 

 indisposition to refer back, are to be attributed to ill-health. 



The assertion is that I had confounded the middle term of a syllogism with its conclusion. 

 The ground of this assertion is the following sentence in my Statement in Answer Stc. : the 



had never used it. Many must know that when the older 

 German paper is marbled, the leaves stick together at the edges 

 in such manner that not the smallest crevice can be found for 

 the end of a paper knife : and liberties which may be taken 

 with an oyster must not be taken with a borrowed book; which 

 put very serious difficulties in the way, and prevented even 

 a cursory glance at all parts which I did not open. When 

 1 borrowed the book for the second time, after seeing Mr 

 Baynes's work, I found that all the part on probabilities had 

 never been opened. Had I opened this portion the first time, I 

 could have learnt nothing more than the Society had published 

 by reading more than a year before, and by printing six months 

 before: but it would have been my duty to have stated what I 

 had found. 



* I add, so far as notes or recollections serve, what I have 

 arrived at since. First, it is stated by Hamilton that From- 

 michen gave the numerical quantification of the middle term : 

 but whether from Lambert, or independently, is not stated. 

 Secondly, George Bentham, in his Outlines of a new system of 

 Logic, (1827) made a universal quantification : but it is clear 

 that he misunderstood some of its forms. A discussion arising 

 out of this work, between Mr Warlow of Haverfordwest, the 

 promoter, Hamilton, Dr Thomson, Mr Baynes, and others, 

 took place in the AthentBum Journal (December 1850 — March 

 1851, Nos. 1208—1218). Thirdly, Mr Solly did the same, as 

 noted in my last paper. Fourthly, Christopher Sturm, in his 

 Universalia ^uc/irf^a... printed by Adrian Vlacq ( Hague, Ififil, 

 8vo. small) gave 12 forms of syllogism in which, the premises 

 being Aristotelian, the contrary of one of the terms in the pre- 

 mises is allowed to be the subject of the conclusion. Thus 

 from A)-(B and B)-(C he deduces c( -(A. 



I have already mentioned the Bemoullis. Their logical 

 papers are heads of theses, in which both, but especially 

 James Bernoulli, import the algebraical mode of thought into 

 logic. They both take the distinction of extension and com- 

 hension from the Port-Royal Logic, of which both were 

 readers. James Bernoulli compares the common attribute of 

 two notions to the common measure of two numbers, thus con- 

 firming my assertion that a mathematician would, of course, 

 compound attributes, and not aggregate them. ( Joh. B. Works 

 i. 79; James B. Works i. 177, 213, 228). 



Lastly, while writing this note, accident led me to a paper 

 by Louis Richer, in the volume for 17fiO-17f>l of the Turin 

 Memoirs (the one which contains Lagrange's celebrated paper 

 on sound). This paper contains, among others, the very sym- 

 bols I have used to distinguish propositions : but the object is 

 to symbolise the notions of metaphysics. Thus ( •) is necessity, 

 (• ) when positive, ( •) when negative; and (") is contin- 

 gency. 



t My opponent had not my work before him, by his own 

 act. He returned me the copy which I sent to him, in dis- 

 pleasure at my comments on his own accusation and its conse- 

 quences ; apparently denying, or at least not apprehending, 

 that the copies of controversial works which pass between 

 antagonist writers are no more favours than the gloves which 

 used to pass between combatants of another kind. From this 

 circumstance, and from internal evidence, I conclude that when 

 he (pp. 649', 704) pronounced me acquainted with the logical 

 writings of both Ploucquet and Lambert, he spoke from 

 vague recollection of my appendices, which were returned cut 

 open. 



