vn.] 



INDUCTION. 



135 



of possible laws then cannot exceed the number of selec- 

 tions which we can make from these four combinations. 

 Since each combination may be present or aljsent, the 

 number of cases to be considered is 2 x 2 x 2 x 2, or sixteen ; 

 and these cases are all shown in the following table, in 

 which the sign o indicates absence or non-existence of the 

 combination shown at the left-hand column in the same 

 line, and the mark i its presence : — 



Thus in column sixteen we find that all the conceivable 

 combinations are present, which means that there are no 

 special laws in existence in such a case, and that the 

 comljinations are governed only by the universal Laws of 

 Identity and Difference. The example of metals and 

 conductors of electricity would be represented by the 

 twelfth column; and every otlier mode in which two 

 things or ([ualities might present themselves is shown in 

 one or other of the columns. More than half the cases 

 may indeed be at once rejected, because they involve the 

 entire absence of a term or its negative. It has been 

 shown to be a logical principle that every term must have 

 its negative (p. iii), and wiien this is not the case, incon- 

 sistency between the conditions of combination must exist. 

 Thus if we laid down the two following propositions, 

 " Graphite conducts electricity," and " Graphite does not 

 conduct electricity," it would amount to asserting the 

 impossibility of graphite existing at all ; or in general 

 terms, A is B and A is not B result in destroying alto- 

 gether the combinations containing A, a case shown in the 

 fourth colunm of the above table. We therefore restrict 

 our attention to those cases which may be represented in 

 natural phenomena when at least two combinations are 

 present, and which correspond to those columns of tlie 



