1880.] expressing the common propositions of Logic, 45 



thrown out as little more than a hint. His view is this. The 

 sign (— ) is the sign of 'detraction,' i.e. abstraction, or the with- 

 drawal of an attribute from a notion ; and (oo ) is the sign of 

 identity. Now let L and P be two notions which have something 

 in common, but that when 8 is thrown out of the former the re- 

 mainder is P. This is expressed by L — SccP, and implies that 8 

 and P are distinct notions, or that No S is P. 'His own account 

 of the matter (I have changed some of the letters) is this. "Sit 

 L — S oo P. Dico 8 et P nihil habere commune. Nam ex defini- 

 tione detracti et residui omnia quoe sunt in L manent in P prater 

 ea quae sunt in S, quorum nihil manet in P ": so that no 8 is P. 



This particular suggestion is very brief, and seems to me 

 decidedly obscure, but it deserves mention, both historically and 

 as having possibly given occasion to the similar but much more 

 complete suggestions of Lambert. I proceed to their discussion. 



22. This scheme of Lambert's might at first sight be con- 

 sidered identical with that of Holland (No. 8), or rather with 

 the general propositional form of which that is a particular case ; 

 for the two expressions are formally the same. In reality, however, 

 they are in striking contrast with each other. With Holland, 

 the letters p and tt, in the denominators, really stood for numerical 

 factors. What he meant to signify was that ' some portion of 

 the extent (estimated by 1 -^p) of 8, is identical with some portion 

 (similarly estimated by 1 -f- tt) of that of P ' ; though he blundered 

 when he came to interpret this into a negative proposition. But 

 with Lambert, m and n have a better right to stand in the deno- 

 minator. They mark attributes, and division by ♦them stands 

 for abstraction, so that the proposition is interpreted here not in 

 respect of extent but of intent. His idea is this. Though S 

 and P are distinct as classes they must have some attributes in 

 common ; that is, they must both belong to some higher genus. 

 Abstract then certain attributes from each, as indicated in the 

 division respectively by m and n, and the remaining groups of 

 attributes will coincide. 



This is quite true, and highly ingenious, but what one does not 

 see is how this symbolic expression becomes a fitting represen- 

 tative of the universal negative proposition rather than of any 

 other. Whatever the relations of extent of two notions, 8 and P, 

 it will always hold good that some of the attributes in one are 

 different from some of those in the other. This points, I think, 

 to an essential defect in the attempt to interpret propositions 

 in respect of the intent of both their subjects and predicates ; 

 it gives us, for instance, no means of distinguishing between 'some 

 X is I',' and ' some X is not Y' or indeed for adequately charac- 

 terising any ' particular ' proposition whatever. 



