INDUCTION. 



155 



and we arrive at this utmost number of cases by omitting 

 any one or more of the four. The number of cases to 

 be considered is therefore 2x2x2x2 or sixteen, since 

 each may be present or absent ; 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 

 combinations 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 other mode in which two 

 things or qualities 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 necessary logical principle that every term 

 must have its negative (p. 88), and where this is not the 

 case some inconsistency between the laws or conditions of 

 combinations 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 altogether the combinations containing A. 



