264 PROCEEDINGS OF THE AMERICAN ACADEMY 



which, taken as a premise along with all the others, will again justify 

 the final conclusion. In either case, it follows that every argument 

 of more than two premises can be resolved into a series of arguments 

 of two premises each. This justifies the distinction of simple and 

 complex arguments. 



§ 5. Of a General Type of Syllogistic Arguments. 



A valid, complete, simple argument will be designated as a syllogis- 

 tic argument. 



Every proposition may, in at least one way, be put into the form, 



Sis Pi 



the import of which is, that the objects to which S or the total subject 

 applies have the characteristics attributed to every object to which P 

 or the total predicate applies. 



Every term has two powers or significations, according as it is sub- 

 ject or predicate. The former, which will here be termed its breadth, 

 comprises the objects to which it is applied ; while the latter, which 

 will here be termed its depth, comprises the characters which are 

 attributed to every one of the objects to which it can be applied. This 

 breadth and depth must not be confounded with logical extension and 

 comprehension, as these terms are usually taken. 



Every substitution of one pi'oposition for another must consist in 

 the substitution of term for term. Such substitution can be justified 

 only so far as the first term represents what is represented by the 

 second. Hence the only possible substitutions are — 



1st. The substitution for a term fulfilling the function of a subject 

 of another whose breadth is included in that of the former ; and 



2d. The substitution for a term fulfilling the function of a predicate 

 of another whose depth is included in that of the former. 



If, therefore, in either premise a term appears as subject which does 

 not appear in the conclusion as subject, then the other premise must 

 declare that the breadth of that term includes the breadth of the term 

 which replaces it in the conclusion. But this is to declare that every 

 object of the latter term has every character of the former. The 

 eliminated term, therefore, if it does not fulfil the function of predi- 

 cate in one premise, does so in the other. But if the eliminated term 

 fulfils the function of predicate in one premise, the other premise 

 must declare that its depth includes that of the term which replaces 

 it in the conclusion. Now, this is to declare that every character of 



