72 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



KINDS OF SYMBOLS 



Some symbols are more directly pictorial than others. 

 Images, for example, are more directly representative than 

 verbal descriptions, and models convey information about 

 their referents more directly than do mathematical equa- 

 tions. Hence one may conveniently arrange symbols on a 

 scale according to their mirroring capacities. At the one ex- 

 treme will be that type which Peirce calls an icon. This is 

 defined by him as any symbol which "may represent its 

 object mainly by its similarity." Illustrations of icons are 

 to be found in images "which partake of simple qualities"; 

 diagrams "which represent the relations, mainly dyadic, or 

 so regarded, of the parts of one thing by analogous relations 

 in their own parts"; 1 and metaphors which represent through 

 parallelism. "It is a familiar fact that there are such repre- 

 sentatives as icons. Every picture (however conventional its 

 method) is essentially a representation of that kind. So is 

 every diagram, even although there be no sensuous resem- 

 blance between it and its object, but only an analogy between 

 the relations of the parts of each." 2 At the other extreme 

 will be those which are not primarily pictorial. Here will be 

 found practically all words 3 and probably most mathe- 

 matical symbols other than the direct representation of 

 spatial figures. 4 These symbols which have only a remote 

 pictorial value may be called, for want of a better term, 

 characterizing symbols, since they point to their referents by 



1 C. S. Peirce, Collected Papers (Cambridge: Harvard University, 1932), Vol. II, 

 par. 2.276 and 2.277. 



2 Ibid., par. 2.279. 



3 One must say practically all words, for there are many which retain their pic- 

 torial character in their sounds, such as "pitter-patter," "bow-wow," and similar 

 onomatopoetic words, and others which retain their pictorial character in their 

 appearance, such as Egyptian hieroglyphics. 



4 Peirce considers mathematical symbols to be icons. " A distinguishing property 

 of the icon is that by the direct observation of it other truths concerning its object 

 can be discovered than those which suffice to determine its construction. Thus, by 

 means of two photographs a map can be drawn, etc. Given a conventional or other 

 general sign of an object, to deduce any other truth than that which it explicitly 

 signifies, it is necessary, in all cases, to replace that sign by an icon. This capacity of 

 revealing unexpected truth is precisely that wherein the utility of algebraical for- 

 mulae consists, so that the iconic character is the prevailing one." Ibid., par. 2.279. 



