67 



A part of B 

 A part of not-B 

 Not-A part of B 

 Not-A part of not-B. 



Other apparent varieties, such as B part of not- A, will be 

 found equivalent to one or other of the above, equivalent laws 

 being those which lead to the same possible combinations. 



The remaining two selections of combinations are found 

 to correspond to the general form of law A=B expressing 

 the coincidence of the classes A and B, as, for instance, the 

 coincidence between equilateral and equiangular triangles. 

 This form is capable of only one other logically distinct 

 variety, that expressing the coincidence of A with the class 

 not-B. Thus the solution of the inverse logical problem of 

 two terms leads us to the conclusion that only two forms of 

 relation can exist between two classes, namely, the relations 

 of partial and complete coincidence, but these relations may 

 exist in six different ways altogether, capable of expression 

 in a still greater number of difierent propositions. 



The inverse problem of three terms is a far more complex 

 matter, since the possible combinations are eight in number, 

 and the selections of such combinations, the eighth power of 

 two, or 256. Many of such selections involve self-contra- 

 diction, but there appears to be no mode except exhaustive 

 examination of ascertaining how many. By methods of 

 inquiry fully described in the paper, it is shown that there 

 cannot exist more than fifteen general types or forms of 

 logical conditions governing the combinations of three 

 classes of objects. Some of these forms of law, for instance 

 A=:ABC, expressing the inclusion of A in the class BC, are 

 capable of as many as 24 variations; other forms of law 

 admit 12, 8, or 6 variations. A remarkable and unique form 

 is discovered in the proposition 



A = BC or not-B not-C, 



