282 PROCEEDINGS OP THE AMERICAN ACADEMY 



premise is, by enumeration, true. Whence we have, as a valid demon- 

 strative form of inference, 



."• Any S is HP; 



where U' P' denotes the conjunction of all the characters of M, if 

 the conclusion and first premise are true, the second premise is true by 

 definition ; so that we have the demonstrative form of argument. 



Any 31 is n' P', 



Any S i^ U P ; 



:. Any S is 3L 



This is reasoning from definition, or, as it may be termed, formal 

 hypothesis. 



One half of all possible propositions are true, because every prop- 

 osition has its contradictory. Moreover, for every true particular 

 proposition there is a true universal proposition, and for every true 

 negative proposition there is a true aifirmative proposition. This 

 follows from the fact that the univer.-al affirmative is the type of all 

 propositions. Hence of all possible propositions in either of the forms, 



X S is 31, and 31 is n' P', 



one half are true. In an untrue proposition of either of these forms, 

 some finite ratio of the /S"s or P's are not true subjects or predicates. 

 Hence, of all propositions of either of these forms which are partly 

 true, some finite ratio more than one half are wholly true. Hence, if 

 in the above formulce for formal induction or hypothesis, we substitute 



