164 PROFESSOR BOOliE S MATHEMATICAL THEORY 



being attached by bim to tlie predicate. But an affirmative judg- 

 ment is nothing else than an assertion, through immediate comparison, 

 of the identity of concepts. Suppose, therefore, that we are required 

 to express the judgment, " Some stones are precious." Let x denote 

 stones ; and y, precious. The proposition means, that some stones 

 are identical with some precious things. Consequently, its symbolical 

 expression [see (1)J is, 



vx = vy. 



If the judgment to be represented had been, " Some stones are not 

 precious," its expression would [see (6)] have been 

 vx =-v (J. — y). 



These examples in the meantime may suffice. More complicated 

 forms will present themselves afterwards. 



With the few simple preliminary explanations whieli have been 

 given, and which were necessary to render intelligible some of tbe 

 criticisms presently to be offered, we are now prepared to state the 

 view which our author takes of the science of Logic. Logic he re- 

 gards as the science of Inference ; and the problem which it seeks to 

 solve is this : Given certain relations among any number of concepts 

 {x, y, z, &c.), it is required to find what inferences can be drawn regard- 

 ing any one of these or regarding a given function of any one of them. 

 A properly constructed science of Logic would require to solve this 

 problem adequately, and by a definite and invariable method. Now, 

 Professor Boole claims that the view which he presents of the prob- 

 lem which Logic has to solve, is both deeper and broader than that 

 commonly taken ; and he claims at the same time that he has devised 

 an adequate method, different from all existing methods, for solving 

 this problem, and that his method is one of definite and invariable 

 application. 



The objections brought against the logic of the schools, that it is 

 neither sufficiently deep nor sufficiently broad, will probably take 

 our readers by surprise. It is not difficult to understand how a 

 question might be raised as to the practical utility of the scholastic 

 logic ; but most persons who have examined the subject will be ready 

 to admit, both that the scholastic logic is well founded, and that, 

 when properly developed from its first principles, it forms a complete 

 and perfect system. In the opinion of our author, however, it is so 

 defective in its foundation, and so incomplete in its superstructure, 

 as not to be entitled to the name of a science. " To what fiual con- 



