NATURE AND AXIOMS OF THE SYLLOGISM. 299 



relations of subject to attribute. To this the laws of thought 

 make no explicit reference. Hence the need of Mediate Axioms, 

 which expressly recognize and state the function of this character 

 istic element These Mediate Axioms we shall now proceed to 

 examine. 



151. THE SYLLOGISTIC AXIOMS OF IDENTITY AND DIVERSITY. 

 We referred above (147) to a definition of the syllogism as 

 a mental process in which two concepts are compared with a third in 

 order thus to discover whether they agree or disagree with each 

 other. This definition or description notes a comparison which 

 is necessarily made in all possible forms of the syllogism. On 

 it are based two axioms, applicable, therefore, to all forms of 

 syllogistic reasoning. They may be stated as follows : 



1. If two ideas agree with a same third, they agree with each 

 other. Quae sunt eadem cum uno tertio sunt eadem inter se. 



2. If one of two ideas agrees, while the other disagrees, with 

 a same third, they disagree with each other. Quorum unum est 

 idem, et alterum non est idem, cum uno tertio, non sunt eadem 

 inter se. 



Instead of &quot; ideas &quot; [or &quot; concepts &quot;] some logicians prefer to 

 use the word &quot; terms,&quot; others, again, to speak of &quot; things &quot;. The 

 usage is optional, provided the proper view about the scope of 

 logic be retained behind whatever set of words we may employ 



(26). 



The two axioms just stated present an obvious and striking 

 analogy with the mathematical axioms that &quot; Two things which 

 are equal to the same are equal to each other, &quot; while &quot; Two things, 

 one of which is equal, the other unequal, to a same third thing, are 

 unequal to each other&quot;. But the axioms of the syllogism are 

 not mathematical : they have not to do with quantities, magni 

 tudes, numbers. They are logical axioms : they have to do with 

 ideas (109). It would be interesting to inquire, however, to which 

 side the extensive or the intensive of the meaning of the con 

 cepts compared, the logical axioms mainly refer. Primarily, it 

 would appear, to their extension 1 . But the concepts have in 

 tension as well as extension. Hence, though the axioms of 

 identity and diversity are simple and instructive so far as they 

 go, they do not rest upon any detailed analysis of syllogistic 

 reasoning. 



1 Cf. WELTON, op. cit,, i., pp. 282, 283. 



