90 THE PRINCIPLES OF SCIENCE. [CHAP. 



required class or term as regards the terms involved in the 

 premises. 



2. For each term in these alternatives substitute its 

 description as given in the premises. 



3. Strike out every alternative which is then found to 

 break the Law of Contradiction. 



4. The remaining terms may be equated to the term in 

 question as the desired description. 



Mr. Venn's Problem. 



The need of some logical method more powerful and 

 comprehensive than the old logic of Aristotle is strikingly 

 illustrated by Mr. Venn in his most interesting and able 

 article on Boole's logic. 1 An easy example, originally got, 

 as he says, by the aid of my method as simply described 

 in the Elementary Lessons in Logic, was proposed ill 

 examination and lecture-rooms to some hundred and fifty 

 students as a problem in ordinary logic. It was answered 

 by, at most, five or six of them. It was afterwards set, 

 as an example on Boole's method, to a small class who 

 had attended a few lectures on the nature of these 

 symbolic methods. It was readily answered by half or 

 more of their number. 



The problem was as follows : " The members of a board 

 were all of them either bondholders, or shareholders, but 

 not both ; and the bondholders as it happened, were all on 

 the board. What conclusion can be drawn ? " The con- 

 clusion wanted is, " No shareholders are bondholders." 

 Now, as Mr. Venn says, nothing can look simpler than the 

 following reasoning, when stated ; " There can be no 

 bondholders who are shareholders ; for if there were they 

 must be either on the board, or off it. But they are not 

 on it, by the first of the given statements ; nor off it, by 

 the second." Yet from the want of any systematic mode 

 of treating such a question only five or six of some 

 hundred and fifty students could succeed in so simple a 

 problem. 



1 Mind ; a Quarterly Review of Psychology and Philosophy ; 

 October, 1 876, vol. i. p. 487. 



