S»6 Mr DE morgan, ON THE SYLLOGISM, No. Ill, 



Misrepresentation. In my second paper, speaking of complete quantification, I presumed 

 that, as had been done by various writers who quantify the predicate, the words some and all 

 would be made the words of quantity : so that, when quantity is expressly given, " No X is Y" 

 would become " All X is not all Y," and the like. Not that I complained of this awkward 

 language : on the contrary, though I called it forced in order and phraseology, hard to make 

 either English or sense of, I said that in its place in the system alluded to, the uncouth expres- 

 sion helps to produce system, and the perception of uniform law of inference. So I thought, 

 and so I think still. The entrance of the exemplar any into the negatives, while all is used in 

 the affirmatives, appears to me a symbolic blemish, though no doubt it is a grammatical 

 propriety. 



But as the system really does not proceed as I said it did, there is misrepresentation. My 

 affair with it now is to shew that I had presumptive grounds for making the statement in my 

 second paper. They were as follows : 



In the prospectus of a work on logic, not yet* published, which prospectus appeared in 

 1846, my critic describes universal quantity as an extensive maximum undivided, and universal 

 quantity is called definite. Now the maximum of extension, undivided, and definite, is all; 

 the word any both indicates division, and is indefinite. No hint is given that in negatives the 

 universal is represented by a maximum of extension divided by a word of indefinitely selective 

 import. 



In my work on logic (p. 302), forming the system from conjecture, I attributed the phrases 

 afterwards repudiated by my critic ; and this part of my work I knew to have been seen by 

 himself. Opportunity of correction subsequently offered itself in the statement of the system 

 furnished to Dr Thomson, for the second edition of his Laws of Thought (1849). But no 

 such correction was made ; the explicit propositional forms were not given ; and the only hint 

 on the subject which this work contains is the hint in the notation, more fully spoken of 

 immediately, in reference to another work. 



In July 1850, just after the last revise of my second paper had been sent to Cambridge, 

 but in time to have recalled it, I received Mr Baynes's New Analytic. I looked at all parts 

 of this, at once, with a view to correction. I found no propositional forms, but only such an ac- 

 count of the syllogistic notation as would allow no other phraseology except what I had used. 

 We are told, in more places than one (pp. 76, 151, 155) the last in a note by Hamilton himself, 

 that the colon (:) denotes all, and no other rendering is given. Thus " there is denoted by the 

 sign [:j all" and "the colon (:) to denote 'all' (definite quantity)" and "the colon denotes 



universal quantity 'all.'" In the notation, A: :B is intended to be read "All A is 



all B," and A : h— : B, the symbol -4— denoting negation, cannot, according to directions, be 

 read in any other way than " all A is not all B." Most of the instances in the body of the 

 work are material, and common words and elisions are employed. I did afterwards find a 

 negative form (I believe such a thing occurs only once) thus — 'No C is any B:' but even had 



• It is to appear under the editorship of the Rev. H. L. logic had been worn and torn until they were almost unintelli- 



Mansel, but I am afraid the state in which the papers were left j gible. Hamilton's remarltable power over language gave some 



will cause some delay. I understand that all which relates to | new life to almost every subject he touched : and logic will, I 



quantity is left in a scattered state. The technical phrases of i believe, not be found among the exceptions. 



