vii.] INDUCTION. 125 



definite combinations, we are required to point out the 

 laws which govern those combinations. Any laws being 

 supposed, we can, with ease and certainty, decide whether 

 the phenomena obey those laws. But the laws which may 

 exist are infinite in variety, so that the chances are im- 

 mensely against mere random guessing. The difficulty is 

 much increased by the fact that several laws will usually 

 be in operation at the same time, the effects of which 

 are complicated together. The only modes of discovery 

 consist either in exhaustively trying a great number of 

 supposed laws, a process which is exhaustive in more 

 senses than one, or else in carefully contemplating the 

 effects, endeavouring to remember cases in which like 

 effects followed from known laws. In whatever manner 

 we accomplish the discovery, it must be done by the more 

 or less conscious application of the direct process of 

 deduction. 



The Logical Alphabet illustrates induction as well as 

 deduction. In considering the Indirect Process of Inference 

 we found that from certain propositions we could infallibly 

 determine the combinations of terms agreeing with those 

 premises. The inductive problem is just the inverse. 

 Having given certuln combinations of terms, we need to 

 ascertain the propositions with which the combinations are 

 consistent, and from which they may have proceeded. 

 Now, if the reader contemplates the following combina- 

 tions, 



ABC abC 



BC abc, 



he will probably remember at once that they belong to the 

 premises A = AB, B = BC (p. 92). If not, he will require 

 a few trials before he meets with the right answer, and 

 every trial will consist in assuming certain laws and 

 observing whether the deduced results agree with the data. 

 To test the facility with which he can solve this inductive 

 problem, let him casually strike out any of the combina- 

 tions of the fourth column of the Logical Alphabet, (p. 94), 

 and say what laws the remaining combinations obey, 

 observing that every one of the letter-terms and their 

 negatives ought to appear in order to avoid self-contradic- 

 tion in the premises (pp.74, in). Let him say, for 

 instance, what laws are embodied in the combinations 



