PROPOSITIONS. 51 



Spalding d distinctly says that the proposition * all metals 

 are minerals' might be described as an assertion of partial 

 identity between the two classes. Hence the name which 

 I have adopted for the proposition. 



Limited Identities. 



A highly important class of propositions have the 

 general form 



AB = AC, 



expressing the identity of the class AB with the class AC. 

 In other words, ' Within the sphere of the class of things 

 A, all the B's are all the C's/ or The B's and C's, which 

 are A's, are identical/ But it will be observed that nothing 

 is asserted concerning things which are outside of the 

 class A ; and thus the identity is of limited extent. It is 

 the proposition B = C limited to the sphere of the class A. 

 Thus if we say ' Plants are devoid of locomotive power/ 

 we must limit the statement to large plants, since minute 

 microscopic plants often have very remarkable powers of 

 motion. When we say ' Metals possess metallic lustre,' we 

 mean in their uncombined state. 



A barrister may make numbers of most general state- 

 ments concerning the relations of persons and things in 

 the course of an argument, but it is of course to be under- 

 stood that he speaks only of persons and things under the 

 English Law. Even mathematicians make statements 

 which are not true with absolute generality. They say 

 that imaginary roots enter into equations by pairs ; but 

 this is only true under the tacit condition that the 

 equations in question shall not have imaginary coefficients. 6 



d ' Encyclopaedia Britannica,' Eighth Ed. art. Logic, sect. 37, note. 

 8vo reprint, p. 79. 



e De Morgan ' On the Boot of any Function.' Cambridge Philosophical 

 Transactions, 1867, vol. xi. p. 25. 



E 2 



