LOGIC 307 



truths the work contains, so that he will have no need 

 to study its various propositions, all of which he will 

 thus know without having once read them. Yet all the 

 propositions about circles, triangles, &c., in his "Euclid" 

 are implicitly contained in the definitions and axioms. 

 Although, then, a student may know that mass of geo- 

 metric truths implicitly (in knowing the definitions and 

 axioms) he does not for all that, really and actually 

 know them. In order that he may learn truly to 

 know them, he must go through those various processes 

 of " inference " by which the different truths implicitly 

 contained in Euclid's definitions and axioms are brought 

 to the student's knowledge explicitly. 



After this digression we will continue and conclude 

 our notice of the elementary rules of logic. 



One form of argument is termed a Swites. In it a 

 number of propositions are so heaped up together that 

 the predicate of the preceding proposition is always 

 taken as the subject of the following one, till the last 

 predicate is enunciated together with the first subject. 



Thus we may have : 



Peter is a man. 



All men are animals. 



All animals are living things. 



All living things are corporeal. 



All corporeal things are substances. 



Therefore Peter is a substance. 



This reasoning really consists of a series of syllogisms, 

 all the minor terms of which, except the first, and all 

 the conclusions, except the last, are left out. All the 

 majors, however, the first minor and the last conclusion, 

 have been retained, while the retained minor and the 

 first major have been transposed, the minor coming 



