286 PROCEEDINGS OF TIIE AMERICAN ACADEMY 



Owing to its double character, analogy is very strong with only a 

 moderate number of instances. 



§ 4. Formal Relations of the above Forms of Argument. 



If we take an identical proposition as the fact to be explained by 

 induction and hypothesis, we obtain the following formulae. 



By Induction. 

 S, S', S" are taken at random as being 31, 



S, S 1 , S" have the characters common to S, S', S". 



.*. Any 31 has the characters common to S, S 1 , S". 



By Hypothesis. 

 31 is, for instance, P, P', P". 



Whatever is at once P, P', and P" is P, P, P". 



.-. Whatever is at once P, P', and P" is 31. 



By means of the substitution thus justified, Induction and Hypoth- 

 esis can be reduced to the general type of syllogism, thus : — 



Induction. 

 S, S 1 , S" are taken as 31, 



S, S', S" are P; 



.-. Any 31 is P. 



Reduction. 

 S, S 1 , S" are P ; 



Almost any M has the common characters of S, S', S' . 



.•. Almost any 31 is P. 



Hypothesis. 

 31 is, for instance, P, P", P", 



S is P, P", P" ; 



.-. S is 31. 



Reduction. 



Whatever is, at once, P, P', P" is like 31, 



S is P',P",P"; 



.*. S is like 31. 



