INDUCTION. 



161 



the combinations of three terms, forming the premises 

 of fifteen essentially different kinds of arguments. The 

 following table contains a statement of these conditions, 

 together with the number of combinations which are 

 contradicted or destroyed by each, and the number of 

 logically distinct variations of which the law is capable. 

 There might be also added, as a sixteenth case, that case 

 where no special logical condition exists, so that all the 

 eight combinations remain. 



There are sixty-three series of combinations derived from 

 self-contradictory premises, which with the above 192 series 

 and the one case where there are no conditions or laws at 

 all, make up the whole conceivable number of 256 series. 



We learn from this table, for instance, that two pro- 

 positions of the form A = AB, B = BC, which are such 

 as constitute the premises of the old syllogism Barbara, 

 negative or render impossible four of the eight combi- 

 nations in which three terms may be united, and that 

 these propositions are capable of taking twenty-four vari- 

 ations by transpositions of the terms or the introduction 



M 



