142 



THE PRINCIPLES OF SCIENCE. 



[chap. 



when we attempt to apply the same kind of method to 

 the relations of lour or more terms, the labour becomes 

 impracticably 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^^ 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 types of laws which may govern the com- 

 binations of only four things, and but a small part of such 

 laws would be exemplified or capable of practical appli- 

 cation in science. The purely logical inverse problem, 

 whereby we pass from combinations to tlieir laws, is 

 solved in the preceding pages, as far as it is likely to be 

 for a long time to come ; and it is almost impossible that 

 it should ever be carried more than a single step 

 further. 



In the first edition, vol i. p. 158, I stated that I had not 

 been able to discover any mode of calculating the number 

 of cases in which inconsistency would be implied in the 

 selection of combinations from the Logical Alphabet. The 

 logical complexity of the problem appeared to be so great 

 that the ordinary modes of calculating numbers of com- 

 binations failed, in my opinion, to give any aid, and 

 exhaustive examination of the combinations in detail 

 seemed to be the only method applicable. This opinion, 

 however, was mistaken, for both Mr. 1\. B. Haywanl, of 

 Harrow, and Mr, W. H. Brewer have calculated the 

 numbers of inconsistent cases both for three and for four 

 terms, without much difficulty. In the case of four 

 terms they find that there are 1761 inconsistent selections 

 and 6i,']'J^ consistent, which with one case where no 



