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 T 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 at least of the 

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

 B. We might represent our former example thus. 



Mammalia = Mammalian vertebrata. 

 This proposition asserts identity between a part (or it may 



