INDUCTIVE LOGICAL PROBLEM. 



121 





i. 



2. 



3- 



4- 



5- 



6. 



7- 



8. 



9- 



IO. 



II. 



12. 



* 



13- 



14. 



!5- 



* 



16. 



* 



AB 



o 

 o 

 o 

 o 



O 

 O 



o 

 I 



o 

 o 

 I 

 o 



o 

 o 

 I 

 I 



o 

 I 



o 



o 



o 

 I 



o 

 I 



o 

 I 

 I 



o 



o 

 I 

 I 

 I 



i 



o 

 o 

 o 



I 



o 

 o 

 I 



I 



o 

 I 



o 



I 



o 

 I 

 I 



i 

 i 



o 

 o 



I 

 I 





 I 



I 

 I 

 I 







I 

 I 

 I 



I 



A* 



«B 



ab 





Thus column 16 represents the case where all combina- 

 tions are present, and the only conditions are the laws of 

 thought. The example of metals and conductors of elec- 

 tricity would be represented in the 12th column; and 

 every other mode in which two things or qualities might 

 present themselves together or apart, is shown in one 

 column or another. But more than half the cases may at 

 once be rejected because they involve the entire absence 

 of a term or its negative. Thus, in the 1st column, no 

 combinations at all are represented as present. In column 

 2 there is only the negative combination ab. Now it is a 

 logical principle that when any term or its negative entirely 

 fails to appear, there must be some contradiction between 

 the conditions of combination. Thus the two conditions 

 A is B and A is not B, would result in altogether destroy- 

 ing the combinations containing A. We may therefore 

 restrict our attention to those cases where at least two 

 combinations are present, and they contain among them 

 each of the letters A, B, a, b ; these cases are represented 

 in the columns marked with the sign *. Among these 

 seven cases we find 



Four cases containing three combinations, 

 Two cases containing two combinations, 

 One case containing four combinations. 



It has already been pointed out that a proposition of the 

 form A is B, or, as it is more exactly represented in a 

 symbolic notation explained in the essays referred to, 

 A=AB, destroys one combination Ab, and thus accounts 

 for the 12th case. Let us consider in how many ways we 



