HI.] PROPOSITIOXS. ■ 41 



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

 fusion exists between this sense of the verb and tliat 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 projDosed to avoid tlie 

 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 ])redicate 

 is identical with the subject. Some, is an indeUrminate 

 adjective; it implies unknown qualities by which we might 

 select the part in cpiestion 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. Tims, taking the special symbol V = Some, the 

 general form of a partial identity would be A = YB, and ni 

 Booles Logic expres.^ions of the kind were much used. 

 But I believe that indeterminate symbols only introdui.e 

 complexity, and destroy the beauty and simple universality 

 of tlie system M'hich may be created without their us;e. A 

 vague rt'ord 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 noplace it by the special description, ^^'e do not 

 know whether some colour is red. yellow, blue, or wnat 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 sul)Stituting one of the other terms. To express the 

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

 A = \'B, 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 

 cUins B, it implies the inclusion of the class A in tli;;t of 

 B. We mi;j,ht represent our fornier example thus, 



Mammalia = Mammalian vertebrata. 

 This proposition asserts identity between a part (or it may 



