iv.] DEDUCTIVE REASONING. 65 



The old fallacy, technically called the Illicit Process of 

 the, Major Term, is more easy to commit and more difficult 

 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) 



we might inadvertently but fallaciously infer that, " Fixed 

 stars are not subject to gravity." To reduce the premises 

 to symbolic form, let 



A = planet 

 B = fixed star 

 C = subject to gravity ; 

 then we have the propositions 



A = AC (I) 



B = Ba. (2) 



The reader will try in vain to produce from these premises 

 by legitimate substitution any relation between B and C ; 

 he could not then commit the fallacy of asserting that B is 

 not C. 



There remain two other kinds of paralogism, commonly 

 known as the fallacy of Four Terms and the Illicit Process 

 of the Minor Term. They are so evidently impossible 

 while we obey the rule of the substitution of equivalents^ 

 that it is not necessary to give any illustrations. When 

 there are four distinct terms in two propositions as in 

 A = B and C = D, there could evidently be no opening for 

 substitution. As to the Illicit Process of the Minor Term 

 it consists in a flagrant substitution for a term of another 

 wider term which is not known to be equivalent to it, 

 and which is therefore not allowed by our rule to be 

 substituted for it 



