OP ARTS AND SCIENCES: MAY 14, 1867. 297 



like the conclusion is proved, that is, the premises form a likeness of 

 the conclusion. Take, for example, the following argument : — 



31 is, for instance, P', P", P", and P'^ ; 



S isP', P", P'", andPi^: 



.-. S is M. 



Here the first premise amounts to this, that " P P", P", and P'^ " 

 is a likeness of M, and thus the premises are or represent a likeness 

 of the conclusion. That it is different with induction another example 

 will show. 



S', S", S'", and /S'^ are taken as samples of the collection M; 



S', S", S"',and S'^ areP: 



.-. All 31 is P. 



Hence the first premise amounts to saying that " S', S", S'", and S''' " 

 is an index of 31. Hence the premises are an index of the conclu- 

 sion. 



The other divisions of terms, propositions, and arguments arise 

 from the distinction of extension and comprehension. I propose to 

 treat this subject in a subsequent paper. But I will so far anticipate 

 that, as to say that there is, first, the direct reference of a symbol to 

 its objects, or its denotation ; second, the reference of the symbol to 

 its ground, thx'ough its object, that is, its reference to the common 

 characters of its objects, or its connotation ; and third, its reference to 

 its interpretants through its object, that is, its reference to all the syn- 

 thetical propositions in which its objects in common are subject or 

 predicate, and this I term the information it embodies. And as every 

 addition to what it denotes, or to what it connotes, is effected by means 

 of a distinct proposition of this kind, it follows that the extension 

 and comprehension of a term are in an inverse relation, as long as 

 the information remains the same, and that every increase of informa- 

 tion is accompanied by an increase of one or other of these two quan- 

 tities. It may be observed that extension and comprehension are 

 very often taken in other senses in which this last proposition is not 

 true. 



This is an imperfect view of the application which the conceptions 



VOL. VII. 38 



