286 PROCEEDINGS OF THE 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 formulce. 



By Induction. 

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



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



.: Any J/ has the characters common to S, S', S". 



By Hypothesis. 

 ilf 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 : — 



Ifiductio)i. 



S, S', S" are taken as M, 

 S, S', S' are P; 

 .-. Any 31 is P. 



Reduction. 

 S, S', S" areP; 



Almost any il/has the common characters of S, S', S' . 



.'. Almost any 31 is P. 



Hypothesis. 

 31 IS, for instance, P, P", P", 



S is P, i?", P" ; 



.-. S is 31. 



Reduction. 

 Whatever is, at once, P, F", P"' is hke 31, 



S is P, P", P" ; 



.-. S is like 31. 



