THE NATURE OF SYMBOLS 65 



This feature of a symbol is complex and involves (a) the 

 referential property or relationship, and (b) the entity which 

 is referred to. But these two features of the symbol do not 

 belong to it in the same sense. The referential property 

 must be given with the symbol; without it the symbol has no 

 meaning and is therefore not a symbol. But the referent 

 (as contrasted with the reference) need not be given in the 

 situation at the moment except under the form of another 

 symbol. To consider the example, the word "circle" must 

 have a referential character in order to be a symbol, i.e., it 

 must have the power to point to what would be identified as 

 a circle were it given; but no actual circle may be given, 

 though one may find himself aware of an image of a circle, 

 or of certain words such as "equality of radii," "conic sec- 

 tion," "two-dimensional plane figure," etc., and he may 

 believe that such a thing as these is the referent of the 

 symbol. It is the essential virtue of symbols that one can 

 use them in the absence of their referents, and, hence, as 

 substitutes for those events to which they refer. Just how 

 symbols refer to events is hard to say. It is convenient to 

 picture the referential property of a symbol by means of 

 an arrow ; this suggests in a vague sort of way certain of the 

 features of the reference. It suggests, for example, if the 

 arrow is properly drawn, that the reference somehow takes 

 its origin in the symbol itself as a mere event, and goes out 

 of and away from this source in the direction in which its 

 referent is to be found. It also calls attention to two of the 

 most important features of the reference, viz., its asymmetric 

 character, and its capacity to limit the range of possible 

 events referred to. For if the word "circle" refers to an 

 actual circle, the actual circle cannot refer to the word 

 in the same way. And through the word one is able to 

 know, in advance of seeing the actual circle in question, the 

 kind of event to which reference is made. Furthermore, the 

 arrow is a convenient mode of representing the referential 

 property because an arrow may point without pointing to 

 anything, i.e., it may have a general directional indication 



