66 THE PRINCIPLES OF SCIENCE. 



the propositions are of the form 



A = AB 



B = c; 

 whence, by substitution, 



A = Ac. 



Inference of a Partial from Two Partial Identities. 



However common be the cases of inference already 

 noticed, there is a form occurring almost more frequently, 

 and which deserves much attention because it occupied a 

 prominent place in the ancient syllogistic system. That 

 system strangely overlooked all the kinds of argument we 

 have as yet considered, and selected as the type of all 

 reasoning one which employs two partial identities as 

 premises. Thus from the propositions 



Sodium is a metal (i) 



Metals conduct electricity, (2,) 



we may conclude that 



Sodium conducts electricity. (3) 



Taking A, B, C, respectively to represent the three terms, 



the premises are of the form 



A = AB (i) 



B = BC. (2) 



Now for B in (i) we can substitute its description as 



given in (2), obtaining 



A = ABC, (3) 



or, in words, from 



Sodium = sodium metal (i) 



Metal = metal conducting electricity, (2) 



we infer 



Sodium = sodium metal conducting electricity, (3) 

 which in the elliptical language of common life becomes 



Sodium conducts electricitv. 



