in.] PROPOSITIONS. 41 



that men form a part of the class mortal ; but great con- 

 fusion exists between this sense of the verb and that in 

 which it expresses identity, as in " The sun is the centre of 

 the planetary system." The introduction of the indefinite 

 article a often expresses partiality ; when we say " Iron is 

 a metal" we clearly mean that iron is one only of several 

 metals. 



Certain recent logicians have proposed to avoid the 

 indefiniteness in question by what is called the Quanti- 

 fication of the Predicate, and they have generally used the 

 little word some to show that only a part of the predicate 

 is identical with the subject. Some is an indeterminate 

 adjective ; it implies unknown qualities by which we might 

 select the part in question if the qualities were known, but 

 it gives no hint as to their nature. I might make use of 

 such an indeterminate sign to express partial identities in 

 this work. Thus, taking the special symbol V = Some, the 

 general form of a partial identity would be A = VB, and in 

 Boole's Logic expressions of the kind were much used. 

 But I believe that indeterminate symbols only introduce 

 complexity, and destroy the beauty and simple universality 

 of the system which may be created without their use. A 

 vague word like some is only used in ordinary language by 

 ellipsis, and to avoid the trouble of attaining accuracy. 

 We can always employ more definite expressions if we 

 like ; but when once the indefinite some is introduced we 

 cannot replace it by the special description. We do not 

 know whether some colour- is red, yellow, blue, or what it 

 is ; but on the other hand red colour is certainly some 

 colour. 



Throughout this system of logic I shall dispense with 

 such indefinite expressions ; and this can readily be done 

 by substituting one of the other terms. To express the 

 proposition " All A's are some B's " I shall not use the form 

 A = VB, but 



A = AB. 



This formula states that the class A is identical with the 

 class AB ; and as the latter must be a part a.t least of the 

 class, B, it implies the inclusion of the class A in that of 

 B. We might represent our fprmer example thus, 



Mammalia = Mammalian vertebrata. 

 This proposition asserts identity between a part (or it may 



