4.5—
Counters

Markers can, of course, take on syntactic as well as semantic properties. But like semantic properties, syntactic properties are extrinsic to the marker type. That is, there is nothing about the marker type P that implies anything about the syntactic properties of P -tokens. P 's can be used in symbol games without syntactic rules—for example, on eyecharts. They can also be used in games that have syntactic rules, such as written English, written French, algebraic topology, and predicate logic. Just what syntactic properties a P -token can take on depends on what symbol game it is used in, what syntactic categories are involved in that symbol game, and which syntactic slots can be occupied by P -tokens.

Now all of this implies that there is more to syntax than marker order—that the syntactic properties of a marker token are intimately connected with the role it plays in larger linguistic activities, and are not just a matter of the marker's combinatorial properties. One could, of course, use the word 'syntax' so broadly as to include all arrangements of markers—or, indeed, to include all arrangements of objects, since all objects can, in principle, serve as markers. But the word 'syntax' has some paradigm uses in which it is applied to specifically linguistic structures, and there is arguably a great deal about linguistic structure that falls under the rubric of syntax that goes beyond combinatorial features. There is, for example, a sense in which we should say that a sentence has a syn-

tactic structure while the order found in other entities (e.g., the sequence of cars in a traffic jam, the sequence of philosophy courses taken by an undergraduate major) is not plausibly regarded as syntactic.

Let us briefly inquire as to how the syntactic structure of a string of markers is dependent upon the symbol game in which it is employed. Consider, for example, the marker string

Fad

What is the syntactic structure of this sequence of markers? The answer depends entirely upon the symbol game that is operative. If the letters appear on a line of an eyechart, one would be inclined to say that the string of markers has no syntactic structure: there is an order to the markers, to be sure, but it is not a syntactic order. But if the markers make up the English word 'fad' with a capitalized f , the story is quite different. It has both internal syntactic structure, since spelling rules can plausibly be called "syntactic" (even if spelling is not the kind of syntax that comes most quickly to mind). It also has external or relational syntactic properties, since the word 'fad' is of a grammatical type that can occupy certain slots in English sentence structure, but not others. For example, sentence (1) is grammatically permissible in English, while sentence (2) is not:

(1) The hula hoop was a fad.

(2) ^* The hula hoop fad was.

The string F-a-d could also be used as an expression in the predicate calculus, with F being a predicate letter and a and d its arguments. Here once again the string would have both internal and relational syntactic properties, but very different ones from the previous case. The difference, of course, lies in the fact that the same marker string can be used in several different language games, but those games have different syntactic rules, and the role that the markers play in the different games is correspondingly different. Moreover, the kinds of syntactic categories in terms of which one can analyze a marker string are closely related to kinds of symbol games. Natural languages have nouns, verbs, adjectives, and so on. Some natural languages also have syntactic features that others do not: articles, plural suffixes, case indicators, privative prefixes, and so on. (Greek has all of these features; Chinese has none of them.) Technical languages may have very different categories: predicate logic, for example, has no nouns or verbs but does have quantifiers, predicate letters,

variable letters, and connectives, while the propositional calculus has only sentence letters and connectives.

When we are interested precisely in the syntactic role that a marker or marker string plays in a particular symbol game, it is useful to be able to refer to it precisely as an object of a type distinguished by its syntactic role in that symbol game (as a predicate letter, for example, or as a count noun). Each symbol game has some set of syntactic categories. (It may be the empty set, as in the case of the eyechart.) These are established by the conventions governing the symbol game—that is, the set of beliefs and practices, shared by those who have mastered the game, that govern how symbols may be combined within the game. These conventions also govern what markers and marker strings can be employed in the symbol game, and which syntactic slots they may occupy.

Sometimes, as in the case of the predicate calculus or the Fortran programming language, the stock of markers is set up from the very beginning to fall into categories such that one can tell from the marker type itself what syntactic roles it can play. In the predicate calculus, capital letters can be predicate letters but not variables, while lower-case letters can be variables but not predicate letters. In Fortran, variables with names beginning with the letter i can only store integer values, while variables with names beginning with the letter n can only store floating-point values. But other symbol games are more complicated. In English, the marker string h-o-u-s-e can be used either as a verb or as a noun, and one cannot tell just from the string of symbols which it will be in a given instance. The language has conventions establishing both 'house' the noun and 'house' the verb; and there is no reason that the marker string could not be used as an adjective as well. Likewise, in the computer language Pascal, virtually any string of ASCII characters can be used as a the name for a variable that can store any kind of value. One simply has to specify elsewhere what kind of variable it is, and that will have consequences for its syntactic properties. (A variable that stores a boolean value, for example, cannot appear immediately before a slash indicating division.)

The word 'counter', as it is being developed here, will be used to indicate a marker as it takes on particular syntactic properties in a specific language game. Thus, for example, 'house' the noun and 'house' the verb are of separate counter types; for while they employ the same marker string, they have different syntactic properties in English. When we are attending specifically to syntax, we may say that we are working at the counter level. Like the marker and signifier levels, the counter level has

its uses. Notably, the study of formal systems, for example, takes place almost exclusively at the counter level, since it brackets semantics and treats differences in what markers are employed as "notational variants." Likewise, much of computer science is devoted to work at the counter level.