4.1—
Symbols: Semantics, Syntax, and Tokening a Type

It should come as no surprise that the word 'symbol' is used in widely differing ways by writers with different research interests. When a linguist studying the development of the set of graphemic characters used

to represent English words speaks of the graphemes as "symbols," he will very likely mean something different from what a Jungian psychologist means when he expresses an interest in finding out what "symbols" are important to a patient. But even if we restrict our attention to the linguistic notion of symbol that is relevant to the analysis of natural, technical, and computer languages, there are still ambiguities that need to be unraveled.

First, the word 'symbol' is sometimes used precisely to indicate objects that symbolize something else. An object is a symbol in this sense just in case it has a semantic interpretation . This usage of the word 'symbol' is found quite frequently in discussions of computation and the philosophy of mind. Fodor, for example, uses the word 'symbol' in this way in the introduction to RePresentations, where he repeatedly glosses the word 'symbol' with the phrase "semantically interpreted object[s]" (Fodor 1981: 22, 23, 30) and claims that the objects of propositional attitudes "are symbols . . . and that this fact accounts for their intensionality and semanticity" (ibid., 24). Haugeland likewise uses the word 'symbol' in this way when he writes, "Sometimes we say that the tokens in a certain formal system mean something—that is, they are 'signs,' or 'symbols,' or 'expressions' which 'stand for,' or 'represent,' or 'say' something" (Haugeland 1981: 21-22).

But not all writers who discuss the tokens employed in formal systems follow Haugeland's practice of applying the word 'symbol' only to objects having semantic interpretations. Pylyshyn, for example, distinguishes between "a system of formal symbols (data structures, expressions)" and a scheme of interpretation "for interpreting these symbols" (Pylyshyn 1984: 116). Here Pylyshyn uses the word 'symbol' in a way which clearly and explicitly does not have semantic overtones, since the "symbols" of which he speaks are purely "formal" and are only imbued with meaning through the additional imposition of a scheme of interpretation. Logicians interested in formal systems likewise use the word 'symbol' to denote the characters and expressions employed in those systems, even though by definition semantics falls outside of the purview of formal systems.

Such a practice is also justified by ordinary usage: it is quite acceptable, for example, to use the word 'symbol' to refer to graphemic characters such as letters, numerals, punctuation marks, and even to such characters as those employed in musical notation. To merit the application of this use of the word 'symbol', an object need not have any semantic interpretation. For example, individual letters employed in

inscriptions in a natural language seldom have semantic values, and yet there is nothing strange about referring to them individually as symbols.

Here it might seem tempting to follow Haugeland's terminological practice and to contrast "symbols" (things with interpretations) with "formal tokens"—or, alternatively, to join Pylyshyn in using the expression 'formal symbols' when referring to such entities as character strings without reference to their semantic properties. But to do so would be to risk running afoul of a further distinction. For the word 'formal' has weaker and stronger uses. In its weaker use, it means "not semantic"; in its stronger use, it means "syntactic." This distinction is important because entities such as letters and phonemes fall into types quite independently of their syntactic properties . The same set of letter types, for example, is employed in the written forms of most of the European languages, and the same letters take on different syntactic properties in different languages. Now if letter types were determined by the syntactic positions that their tokens could occupy in a symbol game, then symbol games with different syntactic rules would, by definition, have to be construed as employing different symbol types. For example, given that the spelling rules of English and French allow different combinations of letters to occur, one would have to say that English and French employ different letters. But surely such a conclusion would be misguided: there is good reason to say that written French and written English employ the same symbol types (i.e., the same letter types), but that symbols of the same types take on different syntactic properties when used in inscriptions in different languages. It is surely more natural, for example, to say that the letter y can stand alone as a word in French but not in English than to say that French and English have distinct symbol types which happen to look alike, just because the English y can occur only within a larger word while the French y can occur alone. Or, to take a different example, it seems natural to say that base-2 notation and base-10 notation both employ the numerals zero and one, even though those numerals take on different combinatorial properties in the two systems. (This is trivially true, since the digits 0 and 1 can be combined in base-10 notation with digits that are not employed in base-2 notation.)

We thus stand in need of three separate sortal terms to play the different roles played by the ordinary term 'symbol'. First, we need a term that designates objects like letters and numerals quite apart from any considerations about what syntactic or semantic properties they might take on in a particular context. Second, we need a term that designates objects just insofar as they are assigned a semantic interpretation. Finally,

we need a term that designates objects just insofar as they are of a particular syntactic type.