DEDUCTIVE REASONING. 77 



Our principle of inference then includes the rule of nega- 

 tive premises whenever it is true, and discriminates correctly 

 between the cases where it does and does not apply. 



The paralogism, anciently called Undistributed Middle, 

 is also easily exhibited and infallibly avoided by our 

 system. Let the premises be 



Hydrogen is an element, (i) 



All metals are elements. (2) 



According to the syllogistic rules the middle "term element 

 is here undistributed, and no conclusion can be obtained ; 

 we cannot tell then whether hydrogen is or is not a 

 metal. Represent the terms as follows 

 A = hydrogen 

 B = element 

 C = metal. 

 The premises then become 



A = AB (i) 



C = CB. (2) 



The reader will here, as in a former page (p. 75), find 

 it impossible to make any substitution. The only term 

 which occurs in both premises is B, but it is combined 

 with different letters. For CB we cannot substitute the 

 equivalent of AB. We have no right to decompose 

 combinations ; and if we adhere rigidly to the rule given, 

 that if two terms are stated to be equivalent we may 

 substitute one for the other, we cannot commit the 

 fallacy. It is apparent that the form of premises given 

 above is the same as that which we obtained by trans- 

 lating two negative premises into the affirmative form. 



The old fallacy, technically called the Illicit Process of 

 the Major Term, is more easy to commit and more diffi- 

 cult to detect than any other breach of the syllogistic rules. 

 In our system it could hardly occur. From the premises 

 All planets are subject to gravity, (i) 



Fixed stars are not planets, (2) 



