iv.] DEDUCTIVE REASONING. 55 



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 to represent the three terms respectively, 

 the premises are of the forms 



A = AB (i) 



B = BC. (2) 



Now for B in (i) we can substitute its expression 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 electricity." 



The above is a syllogism in the mood called Barbara l in 

 the truly barbarous language of ancient logicians ; and the 

 first figure of the syllogism contained Barbara and three 

 other moods which were esteemed distinct forms of argu- 

 ment. But it is worthy of notice that, without any real 

 change in our form of inference, we readily include these 

 three other moods under Barbara. The negative mood 

 Celarent will be represented by the example 



Neptune is a planet, (i) 



No planet has retrograde motion ; (2) 



Hence Neptune has not retrograde motion. (3) 



1 Aii explanation of this and other technical terms of the old logic 

 will be found in my Elementary Lessons in Logic, Sixth Edition, 

 1876 : Macmillan. 



