434 



Mr DE morgan, ON THE SYLLOGISM, No. V. AND 



common language is 'all the rest'. The hypothesis was truly and consistently applied to 

 every form of enunciation except one: and in that one, by a curious forgetfulness, the second 

 side of the double partition remained unnoticed. According to Hamilton, ' Some X is not 

 some Y' quadrates (VI. 632*) with all the other forms, is useful only to divide a class, and 

 (IX. ii. 283) is consistent with all the other negatives ; which is true of non-partition or 

 single partition ; but is false of double partition. It is a singular commentary on Hamil- 

 ton's assertion of his system as actually in thought that his ' Some X is not some Y', sys- 

 tematically interpreted, is an equivalent of the Aristotelian 'Some X is some Y' being the 

 simple contradiction of ' Any X is not any Y.' This I must prove at length. 



Remembering that all Hamilton's propositions are simply convertible, and that his ' some' 

 is both affirmative and negative, we see in ' Some X is not some Y' that all the other ' Some X 

 is some Y', that ' Some Y is not some X', and that all the other 'some Y is some X'. 

 Now all these four assertions are true when X and Y are' equivalents, when X is part of Y, 

 when Y is part of X, and when X and Y have each part, and part only, in common with 

 the other. Consequently ' Some X is not some Y' is true except only when X and Y are 

 wholly external each to the other, and then false : it is therefore the simple contradiction of 

 ' Any X is not any Y', and consequently the equivalent of the usual ' Some X is some Y'. 



It would have caused but little alteration in the details of my criticism if this oversight 

 had not been made. I now proceed to write down the forms of Hamilton's system, on all 

 the three suppositions : the doubly partitive case being closely taken from himself (VI. 631*, 

 632*) in what appears to be his latest exposition. 



Hamilton's forms, 



AfBrmatives. 



Toto-totaP All X is all Y 



Toto-partial All X is some Y 



Parti-total Some X is all Y 



Expressed in Aristotelian forms, 



is Yl 

 isXj 



when doubly partitive. 

 Every X is Y 

 Every Y 



Every X is Y 1 

 Some Y is not Xj 



Every Y is X 1 

 Some X is not YJ 



Parti-partial Some X is some Y Some X is Y "1 



Some X is not Y) 

 Some Y is not X' 



when singly partitive. when non partitive. 



Every X is Yl Every X is Yl 

 Every Y is XJ Every Y is Xj 



Every X is Y \ Every X is Y. 

 Some Y is not Xj 



Every Y is X 1 Every Y is X. 

 Some X is not Yj 



Some X is Y Some X is Y. 



' Take notice that the mere application of this ' some ' de- 

 nies that its term is singular. 



' This proposition was objected to by me as being only a 

 compound of the toto-partial and the parti-total: this was 

 when I supposed the partition to be wholly vague. Mr Mansel 

 (iv. 116) declared "all X is all Y" to be a simple act of 

 thought; and Hamilton (vi. 633*) supports this view. I now 

 quote Hamilton's cooler thoughts, written without an opponent 

 in the field (ix. ii. 292). " For example; if 1 think that the 

 notion triangle contains the notion trilateral, and again that 



the notion trilateral contains the notion triangle ; in other 

 words if I think that each of these is inclusively and exclu-/ 

 sively [or perhaps includedly should have been invented] 

 applicable to the other; I formally say, and, if I speak as I 

 think, must say — all triangle is all trilateral." This is all I 

 want: here is one proposition compounded of two. Hamilton 

 remarks that when 1 declare this last to be compound (vi. 

 633*) I do not attempt to explain how all should be compound 

 and some simple. I never said this, nor thought it : what I 

 said was that the proposition X{| Y is a compound of two pro- 



