38 



'all 03 is some y' provided we understand ' some ' to mean 

 some at least, possibly all. But this is not to 'quantify the 

 predicate ' in the Hamiltonian sense. 



Mr. Murphy appears to think that when we interpret a 

 proposition in extension, we necessarily quantify the pre- 

 dicate, and that it is only when we interpret it in compre- 

 hension that we do not quantify the predicate. He appears 

 also to hold that Boole's literal symbols represent not 

 classes but qualities of things, and that because Boole's 

 notation is thus to be interpreted intensively, therefore the 

 doctrine of the quantification of the predicate finds no place 

 in Boole's system. This is a view which I cannot adopt. I 

 admit that before we can quantify the predicate, we must 

 interpret in extension, for quantity relates to extent; it 

 says, how much, the whole or part only. But I do not 

 admit that when we interpret in extension we necessarily 

 quantify the predicate. We may write the proposition ' x 

 is y' in the form ' x is part of y,' if by ' part ' we under- 

 stand part at least, possibly the whole ; and we may express 

 the proposition symbolically by the equation, x=y—p, if it 

 be granted that o is a possible value oi p. But this is not 

 to quantify the predicate. 



Boole expressly stipulates that his literal symbols, x^ y, 

 &c., shall stand for either classes or qualities of things ; in 

 other words, that they shall admit of interpretation either 

 in extension or in comprehension. Mr. Murphy appears to 

 limit them to the latter interpretation, while, curiously 

 enough, a recent writer on the Algebra of Logic (Miss Ladd, 

 now Mrs. Fabian Franklin) says of one of Boole's forms, " It 

 is suited only to a logic of extension, and it would be diffi- 

 cult to interpret it intensively" ("Studies in Logic," by 

 members of the John Hopkins University, p. 50). The 

 truth is that Boole's symbols may be interpreted either in 

 extension as classes, or in comprehension as quaKties, or 

 without reference to either classes or qualities, extension or 



