INDUCTION. 



163 



premises corresponding to each. Such a table enables us 

 by mere inspection to learn the laws obeyed by any set of 

 combinations of three things, and is to logic what a table 

 of factors and prime numbers is to the theory of numbers, 

 or a table of integrals to the higher mathematics. The 

 table already given (p. 1 6 1 ) would enable a person with 

 but little labour to discover the law of any combinations. 

 If there be seven combinations (one contradicted) the law 

 must be of the eighth type, and the proper variety will be 

 apparent. If there be six combinations (two contradicted), 

 either the second, eleventh, or twelfth type applies, and a 

 certain number of trials will disclose the proper type and 

 variety. If there be but two combinations the law must 

 be of the third type, and so on. 



The above investigations are complete as regards the 

 possible logical relations of two or three terms. But 

 when we attempt to apply the same kind of method to 

 the relations of four or more terms, the labour becomes im- 

 practicably great. Four terms give sixteen combinations 

 compatible with the laws of thought, and the number of 

 possible selections of combinations is no less than 2 16 or 

 65,536. The following table shows the extraordinary 

 manner in which the number of possible logical relations 

 increases with the number of terms involved. 



Some years of continuous labour would be required to 

 ascertain the precise number of types of laws which may 

 govern the combinations of only four things, and but a 

 small part of such laws would be exemplified or capable 



M 2 



