296 PROCEEDINGS OF THE AMERICAN ACADEMY 



2° : Symbols which also independently determine their objects by 

 means of other term or terms, and thus, expressing their own objective 

 validity, become capable of truth or falsehood, that is, are propositions ; 

 and, 



3° : Symbols which also independently determine their interpretants, 

 and thus tlie minds to which they appeal, by premising a proposition 

 or propositions whicli such a mind is to admit. These are arguments. 



And it is remarkable that, among all the definitions of the proposition, 

 for example, as the oratio indicativa, as the subsumption of an object 

 under a concept, as the expression of the relation of two concepts, and 

 as the indication of the mutable ground of appearance, there is, per- 

 haps, not one in which the conception of reference to an object or 

 correlate is not the important one. In the same way, the conception 

 of reference to an interpretant or third, is always prominent in the 

 definitions of argument. 



In a proposition, the term which separately indicates the object of the 

 symbol is termed the subject, and that which indicates the ground is 

 termed the predicate. The objects indicated by the subject (which 

 are always potentially a plurality, — at least, of phases or appearances) 

 are therefore stated by the proposition to be related to one another on 

 the ground of the character indicated by the predicate. Now this re- 

 lation may be either a concurrence or an opposition. Propositions of 

 concurrence are those which are usually considered in logic ; but I 

 have shown in a paper upon the classification of arguments that it 

 is also necessary to consider separately propositions of opposition, if 

 we are to take account of such arguments as the following: — 



Whatever is the half of anything is less than that of which it is 

 the half; 



A is half of B: 



.'. A is less than B. 



The subject of such a proposition is separated into two terms, a 

 "subject nominative" and an "object accusative." 



In an argument, the premises form a representation of the conclu- 

 sion, because thc^y indicate the interpretant of the argument, or repre- 

 sentation representing it to represent its object. The premises may 

 afford a likeness, index, or symbol of the conclusion. In deductive 

 argument, the conclusion is represented by the premises as by a 

 general sign under which it is contained. In hypotheses, something 



