124 PROF. W. STANLEY JEVONS ON THE 



of the problem then is that two terms admit only of six dis- 

 tinct logical relations, which again have only two essentially 

 different typical forms, namely, A= AB and A = B. These 

 laws express respectively partial and complete coincidence ; 

 the first is illustrated by the relation between metals and 

 elements, the metals coinciding with a part of the elements ; 

 the latter, by the complete coincidence between substance 

 possessing inertia, and substance possessing gravity, or 

 between crystals of the cubical system and crystals not 

 capable of doubly refracting light. 



The Inverse Logical Problem involving Three Terms. 



No sooner do we introduce into the problem a third 

 term C, than the investigation assumes a far more com- 

 plex character. There are now three terms, A, B, C, and 

 their negatives, a, b, c, which may be combined, according 

 to the Laws of Thought, in eight different combinations, 



namely, 



ABC, aBC, 



ABc, aBc, 



AbC, abC, 



Abe, abc. 



The effect of any logical conditions is to destroy one or more 

 of these combinations. Now we may make selections from 

 eight things in 2 8 , or 256 ways ; so that we have no less than 

 256 different cases to treat, and the complete solution is at 

 least fifty times as troublesome as with two terms. Many 

 series of combinations indeed are contradictory, as in 

 the simpler problem, and may be passed over. The test 

 of consistency is that each of the letters A, B, C, a, b, c 

 shall appear somewhere in the series of combinations ; but 

 I have not been able to discover any mode of calculating 

 the number of cases in which inconsistency would happen. 

 The logical complexity of the problem is so great that the 



