154 THE PRINCIPLES OF SCIENCE. 



effects of the crystal upon light, heat, electricity, &c., 

 varying in all directions. But when we pursue induction 

 into the intricacies of its application to Nature we really 

 enter upon the subject of classification which we must 

 take up again in a later part of this work. 



Complete Solution of the Inverse or Inductive Logical 



Problem. 



It is now plain that Induction consists in passing back 

 from a series of combinations to the laws bv which such 



*/ 



combinations are governed. The natural law that all 

 metals are conductors of electricity really means that in 

 nature we find three classes of objects, namely 



1 . Metals, conductors ; 



2. Not-metals, conductors ; 



3. Not-metals, not-conductors. 



It comes to the same thing if we say that it excludes the 

 existence of the class, 'metals not-conductors.' In the 

 same way every other law or group of laws will really 

 mean the exclusion from existence of certain combinations 

 of the things, circumstances or phenomena governed by 

 those laws. Now in logic we treat not the phenomena 

 and laws but, strictly speaking, the general forms of the 

 laws ; and a little consideration will show that for a finite 

 number of things the possible number of forms or kinds 

 of law governing them must also be finite. Using general 

 terms we know that A and B can be present or absent in 

 four ways and no more thus 



AB, A6, aB, ab ; 



therefore every possible law which can exist concerning 

 the relation of A and B must be marked by the exclusion 

 of one or more of the above combinations. The number 

 of possible laws then cannot exceed the number of selec- 

 tions which we can make from these four combinations, 



