PART II—
SYMBOLS, COMPUTERS, AND THOUGHTS

Chapter Four—
Symbols—An Analysis

The preceding chapter has brought us to a crucial juncture in assessing the merits of the Computational Theory of Mind. The criticisms raised by Searle and Sayre point to some potentially serious problems for computationalism. But the exact nature and force of the problems cannot be judged without first undertaking an analysis of the notion of symbol, which figures prominently both in the claims made by computationalists and in the criticisms leveled by their opponents. In particular, we must ask what it is to be a symbol and how symbols may be said to have syntactic and semantic properties. This chapter will present answers to these questions, and will offer a rich set of terminology for talking about symbols, syntax, and semantics.

The terminology makes two important kinds of distinctions. First, the ordinary usage of the word 'symbol' as a sortal term is ambiguous. Sometimes the word is used precisely to denote utterances or inscriptions that have semantic interpretations—things that syrnbolize something. But in other contexts the word is used to denote things which do not have semantic properties: there are purely formal symbol games, for example, in which the tokens have syntactic but not semantic properties, and there are even symbols such as letters on eyecharts which have neither syntactic nor semantic properties. To distinguish these different senses of the word 'symbol', three sortal terms will be developed. The term 'marker' will be used to capture the road usage of 'symbol' which includes letters on eyecharts. To be a marker is just to be a token of a conventional type, and does not have any necessary semantic or syntactic consequences. The

term 'signifier' will be used to denote markers that have semantic interpretations. An object is a signifier just insofar as it is a token of a marker type which has an interpretation. The term 'counter' will be used to pick out markers on the basis of their syntactic features within some language game. To be a counter is to be a token of a marker type which has a particular set of conventionally determined syntactic properties in a particular language game.

The terminology developed in this chapter will also reflect a second, and equally important, distinction. For there are several different senses in which an object may be said to be a marker, a counter, or a signifier. For example, if we say that a marker token "has an interpretation," we might mean one of four things: (1) that there is a linguistic convention that associates the marker's type with that interpretation, (2) that the author of the marker meant it to have that interpretation, (3) that someone who apprehended the marker took it to have that interpretation, or merely (4) that there is an interpretation scheme available in principle that associates that marker's type with that interpretation. The terminology developed in this chapter disambiguates expressions like 'is a signifier' or 'has semantic properties' by offering different locutional schemas for each of the four legs of the ambiguity. In the four cases above, for example, the marker token would be said, respectively, to be (1) interpretable (under convention C) as signifying X , (2) intended (by its author S) as signifying X , (3) interpreted (by some Y) as signifying X , and (4) interpretable-in-principle as signifying X . These locutions point to four modalities under which an object may be said to have properties dependent upon conventions or intentions, and these modalities also apply to the sortals 'marker' and 'counter', as well as 'signifier', in ways that will be made clearer in the course of the chapter. The result is a terminology that reflects four different ways in which an object may be said to be a marker (a symbol in the barest sense), four ways a marker may be said to take on syntactic properties, and four ways it may be said to take on semantic properties. The remainder of this chapter will be devoted to a more detailed development of these distinctions.

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.

4.2—
Markers, Signifiers, Counters

I propose to use three existing words in new and technical ways in order to supply the necessary sortal terms. I propose to use the word 'marker' to replace the term 'symbol' in its broadest sense, the usage that can be applied to letters and numerals and carries no syntactic or semantic connotations. There are marker types (e.g., the letter P ) and marker tokens (a particular inscription of the letter P ). Marker types such as letter types and numeral types are a particular class of conventionally established types. And so an object is a marker token just insofar as it is a token of such a conventional type . Sometimes markers are used in such a fashion that they carry semantic values. The complex marker type 'dog', for example, has a conventional interpretation in English, but does not have one in French. Insofar as an object is a marker that carries a semantic value, it will be called a signifier . Finally, markers can be employed in symbol games in such a fashion that they have syntactic properties. The lower-case letters, for example, take on no syntactic properties when they are used on an eyechart, but take on one set of syntactic properties when used as proposition letters in the propositional calculus, and take on a different set of syntactic properties when used as variable letters in the predicate calculus. The syntactic rules of a symbol game serve to partition the markers employed in that game according to the syntactic positions they can occupy. These syntactic types will be called counter types, and a marker will be said to be a counter just insofar as it takes on syntactic properties within a symbol game .

These three sortal terms—'marker', 'signifier', and 'counter'—will play a significant role in the discussion of the nature of symbols and symbolic representation that is to follow. Although this book does not undertake to develop a thoroughgoing semiotics, it will prove helpful to undertake a brief discussion of each of these three terms.

4.3—
Markers

The first and most basic of the three sortal terms is 'marker'. Thus far the development of the term 'marker' has consisted of the citation of a few paradigm examples (letters, numerals, characters employed in musical notation) and a negative claim to the effect that being a marker has

nothing to do with syntax or semantics. To come to a better understanding of markers, it will be useful to employ a thought experiment.

4.3.1—
The "Text from Tanganyika" Experiment

Suppose that the noted Victorian-age explorer and linguist Sir Richard Francis Burton, while traversing central Africa in search of the source of the Nile, comes upon a lost city. There he finds a clay tablet on which there are inscriptions of unknown origin and meaning. One line of the script reads as follows:

What assumptions can Burton reasonably make about the inscription? First, he can probably proceed upon the assumption that what he has come upon is an inscription in a written language, which he dubs "Tanganyikan." He can assume that, like other written languages, Tanganyikan will employ symbols, that it will have a syntactic structure, and that at least some of the symbols will be used meaningfully. At this point, however, he most emphatically does not know what any of the symbols mean. Nor does he even know what symbolic units are meaningful . What he encounters may be a phonetically based script like that used in written English, in which case few if any of the individual characters will be meaningful. On the other hand, it might be an ideographic notation like that employed in written Chinese, in which case individual ideogram types are correlated with specific interpretations. Or it might be like Egyptian or Coptic script, in which characters can function as ideograms in some contexts and function as indications of phonemes in others. (If English were to be represented in a similar way, for example, we might have a character   to represent the word 'heart, and then represent the word 'hearty' by the string   -y .) And of course it could be the case that what he sees is not writing at all, but mere ornamentation or doodlings.

Now there is a great deal that Burton can do without an interpretation scheme for this writing. Notably, he can begin by making a list of the atomic characters employed, and on the basis of this he can do such things as compare them with characters used in other African languages to see if Tanganyikan may be related to any of these. For example, if the writing found at Timbuktu contains a character  , then Burton might postulate that the symbol   found in Tanganyikan script is a variant of  ,

and that Tanganyikan is related to Timbuktuni. And he can do all of this without knowing anything about the syntax or semantics of Tanganyikan. Indeed, even if it turns out that what he has found are a child's handwriting exercises or an ancient eyechart—in which case what he sees does not have either syntactic structure or semantic interpretation—his conclusions about the character type need not be imperiled. And the reason for this is that the characters themselves can be understood as falling into types quite independently of the linguistic uses to which they are put.

Once Burton has made this observation, he begins to realize that it is not only atomic graphemic character types that can be studied apart from their syntactic and semantic properties. On the one hand, strings of characters that function together can be treated as a single unit, and hence Burton can make some guesses about what sequences of characters make up words.^[1] On the other hand, graphemic characters are not the only tokens whose membership in a type can be understood apart from syntax and semantics. The very same kind of analysis can be applied to nonvisual units, such as phonemes, Morse code units, or ASCII units in computer storage locations. If, for example, Burton had a tape recording of someone speaking Tanganyikan, he might undertake a very similar analysis of the phonemes employed in the language, even without knowing where the breaks between words fall or what anything in the language means. Or, if he were in a position to intercept an electronically transmitted message such as a transmission in Morse code, he might be able to figure out the basic units (e.g., dots and dashes) and how they were instantiated in a telegraph wire or through modulations of radio waves. In light of these realizations, of course, he would come to realize that he could no longer employ the term 'character' to cover all of the relevant cases, and would be in search of a suitably neutral term: for example, the term 'marker.'

4.3.2—
What Is Essential to the Notion of a Marker?

If 'marker' is to serve as a generic term for phonemes, graphemes, units of Morse code, and other such entities, it is worth asking just what is involved in being an entity of one of these kinds. And the best way of answering is by making a series of observations.

(1) Markers are tokens of types . The type-token distinction is applicable to all markers—to letters, numerals, Morse code units, ASCII code units, phonemes, and so on.

(2) Marker types are conventional . To say that a graphite squiggle on

a sheet of paper is a letter P is to say that it is a token of a particular type that is employed by particular linguistic communities. To say that it is a rho is to say that it is a token of a different particular type employed by a different community. And to claim that a particular squiggle is a P is not the same thing as to claim that it is a rho, even if it is the case that an object has the right shape to count as a P if and only if it has the right shape to count as a rho. This is because the claim that the squiggle is a P (or a rho) makes reference to more than the shape of the object: it makes reference to specific conventions of a specific linguistic community as well. Likewise, the claim that the squiggle is a P (or a rho) is not equivalent to a claim about its shape—for example, that it is composed of a vertical line on the left and a half-oval attached to the right side of the upper half of the line.

When I say that marker types are conventional, what I mean is merely that marker types are established by the beliefs and practices of language users. In particular, I wish to emphasize that marker types are not natural kinds . To be sure, sounds and squiggles may also fall into natural kinds on the basis of physical patterns present in them, such as their waveforms or their shapes: a sound wave is a sine wave at 440 kHz just because of its physical characteristics, and an inscribed rectangle is a rectangle just because of the distribution of graphite on paper. But when we say that an object is a marker—for example, an inscription of the letter P or an utterance of the word 'woodchuck'—we are not picking it out just by its sound or its shape, but by the way it fits into established linguistic practices in some community of language users. To determine what marker types an object falls into, we need to know more than what patterns are present in the object: we need to know what marker types there are as well, and what kinds of objects can count as tokens of those types. And to answer those questions, we need to know what linguistic communities there are and what shared understandings and practices members of those communities have about using sounds and inscriptions communicatively. An object can only be a P-token if there is a letter type P , and there can only be a letter type P if there is some community of language users who have a set of shared beliefs and practices to the effect that there is a marker type whose tokens are shaped in certain ways and may be employed in certain activities. So when I say that marker types are conventional, I mean that the existence of the type is determined by the beliefs and practices of language users.

(3) The conventions that establish marker types involve criteria gov -

erning what can count as tokens of those types . So while the assertion that a squiggle is a rho involves more than claims about its shape, it does entail things about the shape of the squiggle as well. The letter type rho is established by the conventions employed by writers of Greek, but part of what is involved in those conventions is a set of criteria governing what a squiggle has to look like in order to count as a rho.

(4) The criteria governing what can count as a token of a marker type pick out a set of (physically instantiable) patterns such that objects having those patterns are suitable to count as tokens of that type . In the case of letters, numerals, and other graphemes, the patterns are two-dimensional visible spatial patterns. In the case of phonemes, they are acoustic patterns distinguishable by the human auditory system. In the case of Morse code and computer data storage they are abstract patterns made up, respectively, of dots and dashes or binary units which can be instantiated in various ways in different media. One can also have complex marker types that are formed from arrangements of simple marker types: written words, for example, are complex markers composed of sequences of atomic markers (letters).

(5) The criteria for a marker type may be flexible and open-ended, and need not be subject to formulation in terms of a rule . This is clearest in the case of graphemic symbols. As Douglas Hofstadter (1985) has argued, letter types seem to permit an indefinite number of stylistic variations. A reader who has not foreseen these can nonetheless quickly recognize them as such when presented with them. It is by no means clear that one could provide a rule (e.g., in the form of a computer program) that could, for example, distinguish all of those patterns that a person could recognize as stylistic variants of the letter P from those patterns which a person would not recognize as such.

(6) Marker types are often found in groups or clusters that are employed in the same symbol games . Thus we speak of different sets of graphemic characters such as "the letters," "the numbers," "the punctuation symbols," and so on.

(7) Criteria for marker types may overlap, both within groups and across groups . Thus the same squiggles that count as letter o's can count as zeroes and omicrons as well. And indeed, as anyone who has had trouble reading another person's handwriting knows, handwritten letters are often interpretable in a number of different ways.

(8) Language users possess a repertoire of marker types, which can be used in various ways . Mathematicians, for example, are in the busi-

ness of developing new symbol games. In doing so, they commonly employ existing marker types such as letters and numerals whose origins may be traced to various linguistic communities. Mathematicians use existing marker types, but put them to new uses in new symbol games. Similarly, one can use one's knowledge of phonemes and the rules for combining them into words in one's language in order to coin a new word if one is needed.

(9) Marker types can be added to or deleted from an individual's repertoire . That is, a person can learn marker types and also forget them.

(10) Marker types can be added or deleted from the repertoire of a linguistic group . New words (complex markers) are coined, new atomic markers are invented (as in the case of the integration sign used in the calculus or the missionary St. Cyril's invention of the Cyrillic alphabet) and imported (as in the case of Europe's adoption of the Arabic numerals). Markers also disappear from usage. Many of the complex markers (Middle English words) one finds in Chaucer's writings, for example, are no longer in use; and the Old English letter thorn has survived only in the guise of a y on the signs of anglophilic innkeepers.^[2]

(11) The boundaries of a "linguistic group" and the extent to which conventions are shared within a group are highly flexible . In the case of natural languages, for example, there are often significant differences in dialect and idiolect which involve differences in the conventions for pronunciation, inscription, and so on. It is not always fully clear when one should say that one is faced with separate linguistic groups and when one is faced with a variety of practices within a single group. Moreover, there may be groups within groups: all topologists may observe certain notational practices, but topologists who work in a particular topological specialty (e.g., surgery theory) may all observe an additional set of practices not shared by other topologists, and an individual mathematician who has developed his own techniques for a particular problem may be the only person employing his new conventions. Similarly, an individual may find the need for a new word in a natural language and may therefore choose a phonetic sequence (a complex marker type) that is not currently used in his language and then employ it as a marker type. The new marker type is conventional in the sense that it is established by a human convention and not simply by a natural pattern, even though the convention that establishes it is not (yet) a convention of English, but merely a convention within some individual's idiolect. (Of course, it can become a convention of English; new words are introduced into languages, and they all start out as someone's idiosyncrasies.)

4.4—
Signifiers

While the conventions that establish marker types function independently of the particular uses to which the markers are put in actual practice, it is nonetheless part of the nature of markers that they can be used meaningfully. So while there is nothing, for example, about the marker type consisting of the sequence of letters d-o-g that binds it to a particular meaning, the marker type—just by virtue of being a marker type—is the sort of thing that can be associated with a meaning in such a fashion that its tokens can count as carrying or expressing that meaning. And within a linguistic community—such as the community of English speakers—there are conventions that set up an association between marker types and meanings. When we speak of something as a meaningful word in a natural language such as English, for example, we refer to it as a token of a marker type (be it typified phonetically, graphemically, or both) that is associated with a meaning by English semantic conventions, and we pick it out both by its marker type and by the associated meaning.^[3] (Hence we can distinguish between different words with the same spelling but different meanings, and vice versa.) Similarly, when we speak of a written number, we refer to a marker string and to its associated meaning. The marker string 1-1-0-1 can be used in the representation of various numbers: thirteen in base-2 notation, thirty-seven in base-3 notation, and so on. In the technical terminology introduced in this chapter, insofar as an object is a marker that is associated with a meaning, it may be called a signifier .

It will prove useful to think of symbols as things that can be examined at several different levels of analysis . Thus the inscription

dog

can be seen at several levels. First, it can be examined at what might be called the "marker level," at which it is a sequence of letters from the Roman alphabet, and also a complex marker employed in English. The atomic marker types are established by the conventions of a linguistic community, and the complex type is licensed for use in English by similar conventions. But the above inscription may also be examined at a second or "signifier level." At the signifier level, the inscription is a token of a signifier type employed in English. That signifier type is established by a linguistic convention that associates a complex marker type with a meaning.

The conventionality of signifier types is again a matter of there being

certain shared understandings and practices within a linguistic community. Individual inscriptions of the word 'dog' mean dog because they are tokens of a particular signifier type employed in English. That signifier type exists by virtue of a convention: in this case, a shared understanding among speakers of English that tokens of the complex marker type d-o-g can be used to express the meaning dog, and a shared practice of using tokens of that complex marker type to express that meaning.

There are thus at least two levels of conventionality involved in being a signifier token. First, anything that is a signifier must also be a marker, and marker types are established by conventions. Second, signifier types are established by conventions that associate marker types with interpretations. The first kind of conventionality appears at the marker level, the second connects the marker level to the signifier level. It is by virtue of marker conventions that objects bearing patterns can count as markers, and it is by virtue of signifier conventions that markers can count as signifiers.

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.

4.6—
The Relationship of the Marker, Signifier, and Counter Levels

Since marker types are independent of the syntactic and semantic properties that their tokens can take on in different symbol games, while counter and signifier types presuppose the existence of marker types, there is a hierarchic relationship between the marker level and the signifier and counter levels. Analyzing a complex of sounds or squiggles as counters presupposes dividing them into markers, and so both the counter and signifier levels are dependent upon the marker level.

There is not, however, any absolute dependence between the counter and signifier levels. One can, for example, assign interpretations to marker types without situating them within a syntactically structured symbol game, and one can concoct "purely formal systems" for which there is no interpretation scheme. This does not mean, however, that syntax and semantics are absolutely independent, either. The semantic values of some marker complexes, such as sentences, are dependent upon the syntactic structure of the complexes as well as the interpretations of the signifying terms. Such structures are subject to compositional analysis . But there is no absolute dependence of either the counter or the signifier level upon the other in the way that both are dependent upon the marker level.

The marker level is similarly related to lower levels of analysis. An entity's ability to count as a marker, after all, depends not only upon conventions but upon the fact that it bears a physically instantiated pattern satisfying the criterion for its type. One might see such patterns as abstract physical features that are literally present in objects, and one might thus speak of a "pattern level" which is connected to the marker level above it by marker conventions and to other physical descriptions below it by various kinds of abstraction. These abstractions bracket those features of an object that are not relevant to its having a pattern, rendering it suitable to count as a token of a marker type. We might represent the resulting structure of levels of analysis graphically as in Figure 5, with the nodes representing the objects appearing at a level and the arrows

[Full Size]

Figure 5

between nodes representing what relates the objects appearing at one level to those appearing at the next.

Now it is important to note that the sortal terms 'marker', 'signifier', and 'counter' designate conventional rather than natural kinds, and that they can pick out the same objects under different aspects. Indeed, any object that is a signifier or a counter must also be a marker, and objects that are markers may very well be signifiers and counters as well. The need for the sortal terms arises not because there are three mutually exclusive classes of particulars, but because there are different sorts of questions about symbols that call for classifications based on different features. (There are, for example, questions about orthography, syntax, and semantics.) The distinction between markers, signifiers, and counters is also useful for discussing certain aspects of language, such as ambiguity, homonymy, homophony, and certain kinds of performance errors. One kind of ambiguity occurs, for example, when one has marker strings that admit of multiple semantic interpretations. Homonymy occurs when a single graphemic marker string is associated by different signifier conventions with two or more meanings. Homophony occurs when a single auditory marker string is associated with multiple meanings. Performance errors such as slips of the tongue, malapropisms, and spoonerisms are ways of producing a marker token that is not compatible with the semantic interpretation that one intended one's utterance to have.

The different sortal terms also license different kinds of inferences about the objects they pick out. From the fact that an object is a counter in some language game, it follows that it is a marker and that it has syntactic properties. Nothing follows, however, about whether it has semantic properties. Similarly, if an object is a signifier, it follows that it is a marker and that it has semantic properties; but nothing follows about whether it is used in a syntactically structured symbol game. And from the fact that an object is a marker, nothing follows about whether it has either syntactic or semantic properties.

4.7—
Four Modalities of Conventional Being

This concludes the first part of the disambiguation of the notion of symbol —the separation of 'symbol' into three separate sortal terms. But there is also a need for a second disambiguation, a disambiguation of the senses in which a thing can be said to "be" a symbol. And the ambiguity that is of concern here is reflected in the technical terms 'marker', 'signifier', and 'counter', as well as the original term 'symbol'. I intend to present a case that, because each of these categories is convention-dependent, there are four ways in which an object can be said to be a token of one of the types, corresponding to four ways it can be related to human conventions and intentions. Once again, the distinctions are best motivated by a series of thought experiments.

4.7.1—
Case 1—The Optometrist

A man named Jones goes to an optometrist for an eye examination. The examination involves a test which requires the patient to look through a device containing a number of movable lenses. The device is pointed at an eyechart, and is so positioned that just one character on the chart can be seen through the eyepiece. The examination begins with the device being pointed at the single character on the uppermost line of the chart, in this case a letter P . Jones looks into the eyepiece and sees the following image:

P

The optometrist asks Jones, "What letter do you see?" Jones responds, "The letter P ." For purposes of this example, assume that Jones has correctly identified the character. One of the things that Jones has accomplished is the successful identification of a physical particular as a token

of a particular conventionally sanctioned marker type. To do this, Jones need not impute any syntactic or semantic properties to the marker token he sees. Indeed, if the doctor were to ask Jones "What does that symbol mean?" or "What is its truth value?" or "What are its syntactic properties?" Jones would likely perceive the questions as very queer indeed. Letters on eyecharts simply do not have syntactic or semantic properties. Moreover, it would be possible for Jones to learn to identify the symbol correctly even if he had never used the Roman letters in the representation of meaningful discourse, much as he might learn to distinguish Chinese ideograms without learning their meanings or the syntactic rules for Chinese—and even without learning that the ideograms were used by the Chinese as a form of writing. Even with such a poverty of competence with written language, Jones could still be said to have recognized and identified what he saw as a token of the type P .

4.7.2—
Case 2—The Bilingual Optometrist

Yet if we adjust the circumstances in the right ways, it quickly becomes more difficult to characterize what Jones has and has not accomplished. Suppose that Jones goes to a second optometrist, Dr. Onassis. Dr. Onassis lives and works in a Greek neighborhood and has a number of clients who speak and read only Greek, and so he has two sets of eyecharts—one with Greek letters, one with English letters. When Jones looks through the eyepiece of Dr. Onassis's instrument, he sees the following pattern:

P

Dr. Onassis asks Jones, "What letter do you see?" And Jones responds, "The letter P ." At this, however, Dr. Onassis casts Jones a very puzzled look. He then looks at the eyechart and laughs. "Oh, I see," he says. "I made a mistake, and put up the Greek eyechart instead of the English one, and then I was puzzled, because the English chart begins with the letter Q and does not even contain a letter P . What you see, by the way, isn't a P but a rho."

This example differs from the first in that our natural intuitions about what Jones has and has not accomplished no longer serve us as well as they did in the first case. Indeed, they may tend to lead people towards two opposite extremes. To continue the story: Jones, upon being told that what he is looking at is not a P at all, becomes quite indignant. "Of course it's a P ," he says. "I know what a P looks like, and I can see this one as

plain as day, and it's a P if ever I've seen one!" This, however, is taken by the doctor as a challenge to his professional competence. "Look here," he says, "I made this chart myself, so I know darned well what the letters are. I made it for my Greek patients, and meant this symbol to be a rho, so a rho is what it is!"

Jones and the doctor are each partially correct in their claims, and each is partially mistaken as well. The most important thing to see, however, is that they are both making the implicit assumption that there is just one univocal meaning to the locutional schema 'is a P ' (or 'is a rho'), while in fact there are several ways a particular may be said to be a token of a conventional type. The necessary distinctions are easily missed, however, because the same English locution can be used to express each of the several ways. Yet the distinctions may be formulated out of fairly ordinary English locutions, and are easily mastered if one attends to the nature of the situation rather than the form of the ordinary locutions.

4.7.3—
Interpretability

First, consider Jones's line of reasoning: Jones is a competent user of the letters employed in the representation of English. (Here they will be called "the Roman letters.") The pattern he sees meets the spatial criteria for counting as a token of the marker type P . Under the conventions governing the Roman letters, the pattern Jones sees can count as a P , and cannot count as a token of any of the other marker types which form the set of Roman letters. There is thus a sense of "being a P " which does apply to the mark on the eyechart.

Notice, however, that the exposition of how the character Jones sees can be said to be a P has required an appeal to several things in addition to the mark and the marker type—notably, it has required an appeal to (a ) a community which employs a certain set of marker types which includes P , and (b ) conventions within that community which govern what can count as a token of that marker type. The sense of "being a P " that is operative here, then, turns out to be more complex than is suggested by the locution used to express it. To put it differently, the predicate indicated by this usage of the locutional schema 'is a P ' is more complex than one might assume. To spell out entirely the sense in which Jones might be right in saying that what he sees is a P , one would have to say something like the following: "This mark t has a pattern p_i which is a member of the set P of patterns suitable for tokening the marker type T employed by linguistic community L ."

We may capture and codify this sense of "being a symbol" by coining the technical expression 'is interpretable as a token of type T ' (e.g., 'is interpretable as a rho'). The rules for the application of this predicate may be articulated as follows:

(M1) An object X may be said to be interpretable as a token of marker type T iff

(1) there is some linguistic community L which employs marker type T ,

(2) the conventions in L which govern what can count as a token of type T allow any object having any pattern p_iÎP :{p₁ , . . . , p _n } to be suitable to count as a token of type T ,

(3) X has a pattern p _j , and

(4) p_jÎp .

This sense of "being a P " points to a relationship between (1) a physical particular, (2) a pattern present in that particular, (3) a convention linking that pattern to a marker type, and (4) a linguistic community using that marker type and employing that convention. An object X related in such a fashion to a marker type T will be said to be interpretable as a (marker) token of type T (under convention C) (for linguistic group L) . The parentheses are used here to separate a short form of the new technical term—'interpretable as a token of type T '—from its complete form. In many cases it will prove unnecessary to allude specifically to a convention or a linguistic group, and so the shortened locution 'interpretable as a token of type T ' can purchase some measure of simplicity with little cost in terms of exactitude. The items in parentheses, however, are not optional —any claim that a physical pattern is interpretable as a token of a marker type involves at least implicit reference to a convention and to a linguistic community, even if these are not specified.

It is, of course, quite possible for a single object X to be interpretable as a token of a number of different marker types {T 1, . . . , T_n }. In each of the optometrist examples, the object Jones sees is interpretable under the conventions for Roman letters as a P and interpretable under the conventions for Greek letters as a rho. It may be subject to interpretation as a token of other marker types as well. There is no inconsistency in saying that a mark is interpretable as a token of a variety of different types. Such illusion of an inconsistency as there may be is quickly dispelled if one looks at the long way of describing interpretability. If one says "X

is interpretable as a token of type T " and "X is interpretable as a token of type U ," the long versions of the two statements will always reveal additional differences which will explain how it is that X is multiply interpretable. These will be differences in what linguistic community's conventions are involved (as in the case of the bilingual optometrist), or differences in the particular conventions of a single community which are operative in the different cases (as in the case of the numeral zero and the letter o in our community), or differences in what pattern in each particular mark is relevant to its interpretability as a marker of that type.^[4]

4.7.4—
Intentional Tokening and Authoring Intentions

If Jones has something of a point, the doctor does as well. The doctor's line of argument is that he drew the eyechart himself, and as a consequence he is in a special position to say what the characters are. Indeed, he might go so far as to say that he is in a position to stipulate what they are. The mark on the chart was, after all, made with the intention that it be a token of a particular marker type—in this case that it be a token of the Greek letter rho. There is thus a sense in which it seems right to say that the doctor inscribed a rho. And in this sense it would not be correct to say that he inscribed a P , because he did not intend it to be a P .

Hence, in distinction with the interpretability of a particular object X as a token of type T , one may also develop another technical locution:

(M2) An object X may be said to have been intended (by S) as a token of marker type T iff

(1) there is some linguistic community L that employs marker type T ,

(2) there is a language user S who is a member of L (or is otherwise able to employ the conventions in L governing marker type T ),

(3) S inscribed, uttered, or otherwise "authored" X , and

(4) S intended what he authored to count as a token of type T by virtue of conventions in L governing marker type T .

Several clarifications and caveats are immediately in order. First, the term 'intended' is meant very broadly here. Notably, it need not imply that the author of the mark must have a conscious, linguistically formulated characterization of what he is doing in producing the marker.

When someone writes a sentence without any explicit awareness of making marks with a pen, he would, according to this usage, "intend" his marks to be letters of particular types.^[5] This use of 'intend' is also meant to allow a great deal of latitude in how direct a causal chain there is between the intention of the author of the marker and its ultimate production. Notably, it is intended to be broad enough to cover at least some instances of the printing of stored representations of text by a computer. The explanation of how the marks on a printed page—a page of a book, for example—are said to count as letters (and how conglomerations of them are to count as words, sentences, statements, and arguments) will need to appeal in part to the intentions of the author. (It may also need to appeal to the intentions of the various engineers and programmers who designed the hardware, software, and coding schemes which mediate the process which begins with the author's striking keys on a keyboard and ends with the production of a printed page.)

A second clarification which needs to be made is this: the author of a marker token may intend it to be a token of more than one type. Within the story about the bilingual optometrist, one should say that the mark which Jones saw was interpretable as a P and interpretable as a rho, but that it was intended as a rho and not intended as a P . In devising the two scenarios used in this thought experiment, however, the visible pattern that was chosen—namely,

P

—was deliberately chosen precisely for its susceptibility to multiple interpretations. One could devise more complex enterprises which turn upon such ambiguities, such as acrostics which make sense in two languages, or which make sense in one language vertically and another horizontally. (In spoken language, puns might well fall into this category. Take for example the case of Lewis Carroll's "We called him the Tortoise because he taught us, " which works in British but not American English because the expressions 'tortoise' and 'taught us' sound the same in British English, but different in American English.)

From these two clarifications a third emerges—namely, that there is room for some very different ways of intending an utterance or inscription to count as a token of more than one type. Here are a few exampies: (1) In devising the P /rho example, the intention was to find an inscription that could clearly count as a token of either of two marker types which might be presumed to be familiar to those likely to read these pages. (2) In legal, political, and diplomatic enterprises, it is often deemed

prudent to choose what one says or writes so that it has multiple interpretations—in particular, so that it has one natural interpretation that is likely to appeal to the hearer or reader, and another more exacting interpretation which can be offered as what was "really meant" at a later date. (For example, promising "no new taxes" does not, strictly speaking, involve promising that existing taxes will not be raised by 10 percent or even 1000 percent.) This kind of intentional ambiguity is most important on the semantic level, but could occur at the level of marker interpretability as well. (3) A slightly different form of ambiguity is present when what is said or written is intended to be interpretable in more than one way, all of which are intended to be understood by the hearer or reader, who then chooses which leg of the ambiguity to treat as operative. An expression of interest in doing business together in the future, for example, can be treated as an opening move in negotiations to do business or as a mere expression of good will. Properly used and properly understood, such ambiguous expressions can allow two parties to explore one another's interests without risk of "losing face." (This practice is reportedly expected by Japanese in business dealings to a degree seldom appreciated by American businessmen.)

4.7.5—
Actual Interpretation

In addition to the interpretability of a marker token and its intended interpretation, one may identify two additional relationships between a particular marker token and a marker type. The first of these is (actual) interpretation of the figure as a marker of some particular type. In both of the optometrist examples, Jones interprets the figure he sees as a letter of a familiar type—he identifies each as a P -token. One might want to say there is a sense in which he was right in so identifying each (because each is interpretable under English conventions as a P ) or that there is a sense in which he was wrong in his identification of the second figure (because its author intended it to be a rho and did not intend it to be a P ). But neither of these facts alters one fact about what Jones did: namely, he placed an interpretation upon a figure he saw; he interpreted it as or took it to be a P -token.

Once again, the new terminology has hidden references to marker types, conventions governing what can count as tokens of the types, and linguistic communities which use the types. To interpret a figure as a token of type T is to be familiar with marker type T employed by some linguistic community L , which in turn involves understanding (not nec-

essarily perfectly) how to apply the criteria for interpretability as a token of that type (though the "understanding" does not necessarily involve the ability to form or consciously articulate a rule for what can and cannot count as a P , but is better understood as a kind of competence ).

This notion of actual interpretation may once again be expressed by a more technical definition:

(M3) An object X may be said to have been interpreted (by H) as a token of marker type T iff

(1) there is some linguistic community L which employs marker type T ,

(2) there is a language user H who is a member of L (or is otherwise able to employ the conventions in L governing marker type T ),

(3) H saw, heard, or otherwise apprehended X , and

(4) H construed X as a token of type T .

Now it is important to see the distinction between authoring intentions and mere interpretations. For while authoring intentions do, in a sense, involve interpretation, the author of a marker's intention is not "just another interpretation." There is a significant difference between Dr. Onassis's original interpretation of the figure on his eyechart—the one that was involved in its authoring—and Jones's interpretation of it, and this leads to our strong intuition that there is a sense in which the figure "is a rho" and "is not a P ." The difference between intended interpretation, or authoring interpretation, and other interpretations of the same figure also applies to Dr. Onassis's own later interpretations of what he has inscribed. The author of a marker token is certainly likely to be in a unique epistemic position with regard to what the token was meant to be, even long after he has brought it into being, and hence he is usually accorded unique authority in clarifying any ambiguities which might be spotted. But the reason for this is precisely that he is believed to know better than anyone else what he intended to write or utter, and it is what he intended that determines "what it is" in one sense—namely, in the sense captured by the technical locution 'intended to be a token of type T .' (Note, for example, that the author's [current] interpretation of his words and actions is not accorded the same respect if its fidelity to his original intent is in question—if he is a defendant in a libel suit, for example, or if he has suffered a loss of memory.)^[6]

4.7.6—
Interpretability-in-Principle

There is one way of "being a symbol" that is yet to be discussed. It is most easily developed for signifiers—and will be shortly—but can be developed for markers as well, albeit with less intuitive appeal. Again let us perform a thought experiment. Assume that there is a sandstone cliff in the Grand Canyon that bears certain dark patterns against a lighter background. Let us assume, moreover, that there are no actual orthographic conventions, past or present, by virtue of which these patterns would be interpretable as marker tokens. The patterns are not now interpretable as marker tokens. But consider the future. It could be the case that some future culture will develop an orthography whose conventions will be such that the patterns on the sandstone cliff would then be interpretable as markers in that orthography. It could even be that members of that culture would naturally perceive the cliff as bearing a meaningful message in their language. Let us call this scenario "Future A ." Now of course it could also be the case that such a culture will not arise—that it will never be the case that there is a culture anywhere that will employ conventions by virtue of which the patterns on the cliff face would be rendered interpretable as marker tokens. Call this scenario "Future B ."

Now it would seem to make some sense to say that the patterns on the cliff face are already suitable to count as markers, given the existence of the right sorts of conventions. It seems right to say that, if only the right sorts of conventions were adopted—for example, the conventions that are eventually adopted in Future A but not in Future B —those patterns would then be interpretable as markers. To put it slightly differently, we might say that, while those patterns are not in fact interpretable (under any actual conventions) as markers, they are nonetheless interpretable-in-principle as markers under conventions that could be (or could have been) adopted, and their being so interpretable-in-principle is independent of which future—A or B —actually comes about.

This notion of interpretability-in-principle can be developed more exactly as follows:

(M4) An object X may be said to be interpretable-in-principle as a token of a marker type T iff

(1) a linguistic community could, in principle, employ conventions governing a marker type T such that any object having any pattern p_iÎP :{p₁ , . . . , p_n } would be suitable to count as a token of type T ,

(2) X has a pattern p _j , and

(3) p_jÎp .

That is, for any object X one might consider, if X has some pattern that could, in principle, be used as the criterion for a marker type, then X is interpretable-in-principle as a marker. (One could, for example, establish a convention whereby spherical objects could count as markers of a particular type, and hence globes, oranges, and planets are interpretable-in-principle as markers.)

Now it should be immediately evident that this notion of interpretability-in-principle is extremely permissive. For while the range of patterns that human beings can easily employ for marker types is rather limited, and the range of patterns they do in fact employ is more limited still, this is more a consequence of the nature of our bodies than of the nature of markers. The patterns we use for markers are chosen for the ease with which we can perceive and implement them. Thus until very recently marker types were confined largely to those distinguished by patterns that could be easily seen or heard. With the aid of instruments, however, humans can deal with markers that are distinguished by patterns of voltage levels in a wire or across a field of circuits, or by patterns of magnetic activity, or by various other kinds of patterns. And there is no reason why a being with very different powers and senses could not use very different sorts of things as markers. (To take an extreme example: an all-powerful God might use configurations of stars as criteria for marker types employed in storing messages for very large angels, and use patterns of electron activity in a single atom as criteria for marker types used to send messages to very small angels.) As a consequence, it would seem that everything whatsoever is interpretable-in-principle as a marker token.

4.7.7—
The Four Modalities

The expression 'is a marker' has been replaced by four locutional schemas that have been given technical definitions:

—'is interpretable (under convention C of linguistic group L ) as a marker of type M '

—'was intended (by its author S ) as a marker of type M '

—'was interpreted (by some H ) as a marker of type M '

—'is interpretable-in-principle as a marker'

To these four locutional schemas correspond what might be called four modalities of conventional being, or four ways in which an object can be related to a conventionally established type (though in the case of interpretability-in-principle, the conventions and the type need not be actual). These four modalities can be applied not only to markers, but to other conventionally established types as well, as we shall see presently. These locutional schemes, moreover, are intended to capture and distinguish four different senses in which one might speak of an object "being" a marker (e.g., a letter or a Morse code dot) or "being" of one of the other conventionally established types. These different senses are, to some extent, already operative in ordinary and technical uses of the word 'symbol', but existing terminology is not subtle enough to distinguish the different senses.

4.8—
Four Ways of Being a Signifier

Just as it is important to distinguish four senses of "being a marker," it is likewise important to distinguish four different senses in which a marker may be said to "have" or "bear" semantic properties, and hence four ways in which a marker may be said to be a signifier. In order to clarify these four senses, we shall employ another thought experiment. The great detective Sherlock Holmes has been called in to solve a murder case. The victim, a wealthy but unpleasant lawyer, has been poisoned. Before dying, however, he managed to write a single word on a piece of paper. The inscription is

PAIN

Inspector Lestrade of Scotland Yard has concluded that the deceased was merely expressing the excruciating agony that preceded his death. Holmes, however, makes further investigations and discovers that the victim's French housekeeper is also his sole heir. It occurs to Holmes that 'pain' is the French word for bread, and upon inquiring he discovers that the housekeeper did indeed do the baking for the household. Perhaps, reasons Holmes, the deceased was poisoned by way of the bread, and has tried to indicate both the means by which the poison was conveyed and the identity of his murderess by writing the French word for bread.

Which was inscribed on the dead lawyer's stationery—the English word 'pain' (meaning a particular kind of sensation) or the French word 'pain' (meaning bread)? To put it differently, what does the inscription mean —pain or bread? It should immediately be evident that this ques-

tion is very much like the question about the figure on the bilingual optometrist's eyechart. First, there is a sense in which what is on the paper is interpretable (under English conventions) as meaning pain . In this very same sense the mark on the paper is interpretable (under French conventions) as meaning bread . That is, the sequence of Roman letters on the stationery is used by English speakers to carry one meaning and used by French speakers to carry a different meaning.

Yet there is also a sense in which the inscription can be said to mean one thing and not the other, provided that one assumes that the victim intended what he wrote to mean one thing rather than the other. If Holmes's hypothesis is correct, for example, the lawyer meant to write the French word for bread and did not mean to write the English word for pain. Assuming that this was the case, there is a sense in which the inscription can be said to mean bread but not to mean pain.

This distinction between two ways a marker token can be related to a meaning should seem familiar, as it parallels the first two ways an object could be said to "be" a marker token—namely, interpretability and intended (or authoring ) interpretation .

(S1) An object X may be said to be interpretable as signifying (meaning, referring to) Y iff

(1) X is interpretable as a marker of some type T employed by linguistic group L , and

(2) there is a convention among members of L that markers of type T may be used to signify (mean, refer to) Y .

(S2) An object X may be said to be intended (by S) to signify (mean, refer to) Y iff

(1) X was produced by some language user S ,

(2) S intended X to be a marker of some type T ,

(3) S believed that there are conventions whereby T -tokens may be used to signify Y, and

(4) S intended X to signify Y by virtue of being a T -token.

Two observations should perhaps be noted about these definitions. First, neither of them is intended to correspond precisely to what is meant by the vernacular usage of the words 'meaning' or 'reference'. Indeed, the whole enterprise of specifying new terms such as these is necessary only because ordinary usage is ambiguous and imprecise. In as-

suming that the inscription meant pain, Lestrade was probably (implicitly) assuming both that the inscription was interpretable under English conventions as carrying the meaning pain and that the deceased had intended the inscription to mean pain. But his assumption would be implicit in that he has probably never made the distinction under discussion. It is only when someone like Holmes notices that the ordinary assumptions do not always hold that distinctions can be made, and at such a point it is of little interest to the specialist (be he detective or philosopher) to argue about whether interpretability or authoring intention or the combination of the two best captures the "real" (i.e., the vernacular, precritical) use of the term 'meaning' (or 'reference'). It is the new, more refined terms that are needed. The determination of vernacular usage may be left to the descriptive linguist.

Yet there is most definitely no intention here to imply that ordinary usage is irrelevant in the pursuit of philosophy. Attention to ordinary usage can often be of great help in solving philosophical problems, especially when those problems are themselves caused by an impoverished understanding of language on the part of the philosopher. The point here is that language points to the phenomena to be studied, and sometimes it points too vaguely and indistinctly to serve the purposes of the theorist. When this happens, terminology must be refined to capture distinctions the specialist needs but the ordinary person does not. The enterprise is far more risky when the process proceeds in the opposite direction—that is, when ordinary terms are extended instead of refined . The application of the terms 'symbol' and 'representation' to the contents of intentional states is a case in point. (This entire book is an examination of what has gone wrong in the extension of such ordinary terms as 'symbol' and 'representation'.)

The second observation about these definitions is that the definition of authoring intention allows for the possibility that the speaker is wildly idiosyncratic in his use of language. If, for example, Jones believes that the word 'cat' is used to refer to newspapers, and utters "The cat is on the mat" to express the belief that the newspaper is on the mat, we may nonetheless say that Jones intended to signify the newspaper. In particular, he uttered a token of the marker type 'cat', which he believed could be used to signify newspapers, and intended to signify the newspaper by uttering the word 'cat'. Of course, there is no convention of English that allows the word 'cat' to be used to signify newspapers. (Utterances of 'cat' are not interpretable, under English conventions, as signifying newspapers.) But Jones nonetheless intended to refer to the newspaper by

uttering the word 'cat'. And of course there could be subgroups of English speakers who employ semantic conventions that are not conventions of English, but only of a dialect of English (as, for example, some Baltimoreans refer to street vendors as "Arabs" [pronounced ay -rabz], or Bostonians refer to submarine sandwiches as "grinders"). And indeed one might even wish to speak of idiolects in terms of the special semantic conventions of a linguistic subgroup consisting of one member, in which case Jones correctly believes that there is a convention licensing the use of 'cat' to refer to newspapers, but incorrectly believes that it is a convention of English rather than of his own idiolect. One might wish to use the term 'convention' in such a case because there are beliefs and practices that can govern how a marker may be used. These beliefs and practices are, in principle, public and shareable, even though in fact only one person possesses them. (Because they are essentially public, and the fact that they are possessed by only one person is merely incidental, Wittgenstein's concerns about a private language do not arise here.)

Third, it should be noted that the semantic features to which these definitions are relevant are meaning and reference. The truth value of a signifier is undetermined by the relationships between the token, linguistic conventions, and the intentions of its speaker or inscriber. (There are some exceptions, such as analytic truths, but here the interest is in a general characterization of ways objects can be said to have semantic properties.)

In addition to interpretability (under conventions employed by some linguistic group) and intended interpretation, one may distinguish two additional ways in which a thing may be said to carry a semantic value. These correspond to the two remaining ways that a figure could be said to count as a marker token: namely, actual interpretation (by someone apprehending the signifier) and interpretability-in-principle . Regardless of what the deceased lawyer intended his inscription to mean, it is nonetheless the case that it was interpreted by Lestrade as meaning pain and interpreted by Holmes as meaning bread. These actual acrs of interpretation are, indeed, independent of whether the lawyer intended his inscription to mean anything at all —they would be unaltered if, for example, he had been scribbling random letters. The notion of actual interpretation may be defined for signifiers as follows:

(S3) An object X may be said to have been interpreted (by H) as signifying (meaning, referring to) Y iff

(1) some language user H apprehended Y ,

(2) H interpreted X as a token of some marker type T ,

(3) H believed there to be a linguistic convention C licensing the use of T -tokens to signify Y , and

(4) H construed X as signifying Y by virtue of being a T -token.

Finally, it is notorious that any symbol structure (i.e., any marker, simple or complex) can be used to bear any semantic interpretation whatsoever. Haugeland, for example, writes of a set of numerical inscriptions he supplies as examples in Mind Design that "formally, these numerals and signs are just neutral marks (tokens), and many other (unfamiliar) interpretations are possible (as if the outputs were in a code)" (Haugeland 1981: 25). And Pylyshyn writes of symbols in computers,

Even when it is difficult to think of a coherent interpretation different from the one the programmer had in mind, such alternatives are, in principle, always possible. (There is an exotic result in model theory, the Lowenheim-Skolem theorem, which guarantees that such programs can always be coherently interpreted as referring to integers and to arithmetic relations over them.) (Pylyshyn 1984: 44)

In the terminology developed in this chapter, what this means is that there is nothing about markers that places intrinsic limits upon what interpretations they may be assigned, and so it is possible for there to be conventions which assign any interpretation one likes to any marker type one likes. Now there are two different ways in which we might wish to formulate this insight. One way of formulating it would be to say that, for any marker type T and any interpretation Y , it is possible for there to be a semantic convention to the effect that Y -tokens are interpretable as signifying T . In terms of a technical definition:

(S4) An object X may be said to be interpretable-in-principle as signifying Y iff

(1) X is interpretable-in-principle as a token of some marker type T, and

(2) there could be a linguistic community L that employed a linguistic convention C such that T -tokens would be interpretable as signifying Y under convention C .

That is, to say of some X and some Y that "X is interpretable-in-principle as signifying Y " is to say (1) that one could, in principle, have a marker convention whereby X would be interpretable as a marker of some type

T , and (2) that one could, in principle, have a semantic convention C whereby T -tokens would be interpretable as signifying Y .

One might, however, wish to characterize semantic interpretabilityin-principle in a different manner. All that is necessary for an object X to be interpretable-in-principle as signifying Y is the availability of an interpretation scheme that maps X 's marker type onto Y . And all that this requires is that X be interpretable-in-principle as a marker, and that there be a mapping available from a set of marker types to a set of interpretations that takes X 's marker type onto Y . In terms of a technical definition:

(S4^* ) An object X may be said to be interpretable-in-principle as signifying Y iff

(1) X is interpretable-in-principle as a token of some marker type T ,

(2) there is a mapping M available from a set of marker types including T to a set of interpretations including Y , and

(3) M(T) = Y .

Definitions (S4) and (S4^* ) are extensionally equivalent for real and counterfactual cases. Under either definition, for any object X and any interpretation Y that one might specify,^[7]X is interpretable-in-principle as signifying Y . First, we have already seen that every object is interpretable-in-principle as a marker token of some type T . Now, according to definition (S4), all that is additionally necessary for X to be interpretable-in-principle as signifying Y is that one could, in principle, have a convention licensing T -tokens as signifying Y . But one could, in principle, have such a convention for any type T and any Y . Similarly, according to definition (S4^* ), what is necessary for X to be interpretable-in-principle as signifying Y (over and above X 's being interpretable-in-principle as a marker of some type T ) is the availability of a mapping M from marker types to interpretations such that Y is the image of T under M . Such a mapping is merely an abstract relation between two sets, however, and there is such a mapping, for any type T and any Y , that maps T onto Y . So both (S4) and (S4^* ) license the conclusion that every object is interpretable-in-principle as signifying anything whatsoever. This conclusion may seem bland in and of itself, but it is important to distinguish this sense of "having a meaning" or "having a referent" from

other, more robust senses. It is all the more important to do so since computationalists seem at times to be interested in this sort of "having a meaning," but do not always make it adequately clear what role (if any) it plays in their accounts of semantics and intentionality for cognitive states.

4.9—
Four Modalities for Counters

The four conventional modalities are also applicable to counters. Returning to the optometrist examples, suppose that the optometrist's instrument is adjusted so that Jones can see more than one symbol at a time. Suppose, moreover, that what he sees is the following image:

p & q

Jones has just come from his logic class, and so, when asked what he sees, says "p and q ." The optometrist, however, is ignorant of the conventions of logic. To him, this is just a line of three characters: the letter p , an ampersand, and the letter q . As the doctor sees it, the symbols on the eyechart are not related to one another syntactically, because the "eyechart game" does not bare any syntactic rules .

Once again, both Jones and the doctor are partially right, and in much the same ways they were each partially right in the original examples. Jones has a point in that the figures he sees are interpretable as markers of familiar types (and are in this case intended to be of the types that Jones guesses), and he is furthermore right in seeing that they are arranged in a fashion that is interpretable, under the conventions he has been taught for the propositional calculus, as having a certain syntactic form in the propositional calculus. Yet the optometrist has a point as well: the chart at which Jones is looking was designed as an eyechart. (We may, if we like, assume once again that the doctor drew the chart himself, and knows quite well what he meant to draw.) It was not intended to contain formulas in the notation employed in propositional logic, and the fact that some symbols in the eyechart are interpretable as forming such a formula is quite accidental. Similarly, if a diagonal sequence of letters should be interpretable as a sentence in Martian, that fact would be quite accidental. When the author of the eyechart drew it, Martian language played no role in his activity, and neither did the propositional calculus. To use terminology developed earlier, syntactic relationships did not form part of the authoring intention with which the

[Full Size]

Figure 6

chart was created, and so the symbols in question would not rightly be said to have been intended to have a particular syntactic form.

It is, of course, possible that someone should devise an eyechart or some other display of symbols with more than one symbol game in mind. Someone who believed in subliminal suggestion, for example, might devise a display of symbols so that parts of it were interpretable under standard English conventions in a fashion that was not supposed to be consciously recognized by the reader. Thus a greedy optometrist might try to sell extra pairs of glasses by designing his eyechart like that shown in figure 6. In this case, the figures on the chart can be interpreted in two ways: (1) as characters on an eyechart, and (2) as letters forming English words that make up the sentence "Buy an extra pair now." As they are employed in the "eyechart game," the markers on the display do not enter into syntactic relationships, because syntactic relationships are always relative to a system with syntactic rules, and the "eyechart game" has no syntactic rules. As markers used in the formation of an English sentence token, however, they are counters having syntactic properties, because the English language does have syntactic rules. In this example, moreover, the markers on the chart are not only (a ) interpretable as syntactically unstructured tokens in the eyechart game and (b ) interpretable as syntactically structured tokens in a written English sentence, they are also (c ) intended as syntactically unstructured tokens in the eyechart game and (d ) intended as syntactically structured tokens in a written English sentence. Both "games" are intended by the author of the chart in this case—unlike the earlier case, in which the optometrist did not intend the line of symbols p-&-q to count as a formula structured by the rules of propositional logic, even though the line of symbols was nonetheless interpretable as such.

In that example, moreover, the line of symbols was also interpreted (by Jones) as a formula in propositional calculus notation, and was interpreted in such a fashion that Jones imputed to it a certain syntactic structure that is provided for by propositional logic. This interpretation is not affected in the least by the fact that the eyechart was not designed with it in mind, or even by the fact that the author of the chart was unfamiliar with propositional logic. Finally, as in the case of markers and signifiers, there is infinite latitude in the ways a display of markers could, in principle, be interpreted as counters of various sorts, because any given marker type can be employed in an indefinite number of systems characterizable by syntactic rules. For any arrangement of markers, one could, as Haugeland says, "imagine any number of (strange and boring) games in which they would be perfectly legal moves" (Haugeland 1981: 25).

It is now possible to provide definitions for the four ways of being a counter. These definitions will not be employed directly in the argumentation that follows, but are provided for the sake of exactitude and balance in the development of semiotic terminology. They may safely be skimmed over by the reader who is not interested in the definitions for their own sake, but only in their contribution to the main line of argument.

(C1) An object X may be said to be interpretable as a counter of type C iff

(1) X is interpretable as a marker of type T ,

(2) the marker type T is employed in some language game G practiced by a linguistic community L ,

(3) G is subject to syntactic analysis,

(4) there is a class C of markers employed in G sharing some set F of syntactic properties, and

(5) the conventions of G are such that tokens of type T fall under class C .

(C2) An object X may be said to be intended (by S) as a counter of type C iff

(1) there is a language user S who is able to apply the conventions of a language game G ,

(2) the marker type T is employed in G ,

(3) G is subject to syntactic analysis,

(4) there is a class C of markers employed in G sharing some set F of syntactic properties,

(5) the conventions of G are such that tokens of type T fall under class C ,

(6) S intended X to be a marker of type T ,

(7) S intended X to count as a move in an instance of language game G , and

(8) S intended X to fall under class C .

(C3) An object X may be said to be interpreted (by H) as a counter of type C iff

(1) some language user H apprehended X ,

(2) H interpreted X as a token of type T ,

(3) H is able to apply the conventions of language game G ,

(4) the marker type T is employed in G ,

(5) G is subject to syntactic analysis,

(6) there is a class C of markers employed in G sharing some set F of syntactic properties,

(7) the conventions of G are such that tokens of type T fall under class C ,

(8) H interpreted X as counting as a move in an instance of G , and

(9) H interpreted X as falling under class C in game G .

(C4) An object X may be said to be interpretable-in-principle as a counter of type C iff

(1) X is interpretable-in-principle as a token of marker type T ,

(2) there could be a language game G employing markers of type T ,

(3) that game G would be subject to syntactic analysis,

(4) these conventions would be such that there would be a class C of markers employed in G sharing some set F of syntactic properties, and

(5) the conventions of G would be such that tokens of type T would fall under class C .

4.10—
The Nature and Scope of This Semiotic Analysis

The preceding sections of this chapter have been devoted to the development of an analysis of symbols and their semantic and syntactic properties. In the ensuing chapters this analysis will be applied towards an assessment of CTM's claims about the nature of cognition. Before proceeding to that assessment, however, it is important to clarify the nature and status of the semiotic analysis that has been presented here.

The new terminology is intended to resolve perilous ambiguities in the uses of (a ) the word 'symbol' and (b ) expressions used to predicate semantic and syntactic properties of symbols (for example, 'refers to', 'means', 'is a count noun'). For purposes of careful semiotic analysis, the technical terms are meant to replace the ordinary locutions rather than to supplement them. Thus the sortal terms 'marker', 'signifier', and 'counter' do not name different species of symbol, nor do they signify different objects than those designated by the word 'symbol'. Rather, these terms serve collectively as a disambiguation of the word 'symbol' as it is applied to discursive signs, and each sortal term is designed to correspond to one usage of the word 'symbol'.

Similarly, the modalities of interpretability (under a convention), authoring intention, actual interpretation, and interpretability-in-principle have been referred to as "ways of being" a marker, signifier, or counter. But this does not mean that there is such a thing as just being a marker, signifier, or counter, and—over and above that—additional properties of being interpretable as one, being intended as one, and so on. For there is no such thing as simply being a symbol. Symbol is not a natural but a conventional kind, and to say that something "is a symbol" (a marker) is to relate it in some way to the conventions that establish marker types.

But there are several ways in which an object can be related to such conventions: it can be interpretable as a token of a type by virtue of meeting the criteria for that type, it can be intended by its author as being of that type, it can be interpreted as being of that type, or it can simply be such that one could have a convention that would establish a type such that this object would be interpretable as a token of that type. The case is much the same for semantics and syntax: there is no such thing as a marker simply being meaningful or simply referring to an object. To say that a marker has a meaning, or that it refers to something, is to say something about interpretation and interpretive conventions. We can say that

the marker is of such a type that it is interpretable, under English semantic conventions, as referring to Lincoln. We can say that its author intended it to refer to Lincoln, or that someone who apprehended it construed it as referring to Lincoln. And we can say that one could, in principle, have a convention whereby it would be interpretable as referring to Lincoln. But there is no additional question of whether a symbol just plain refers to Lincoln. Expressions such as 'refers to Lincoln', 'is a marker', 'is a P ', or 'is an utterance of the word dog ' are ambiguous. The process of disambiguation consists of substituting the four expressions, 'is interpretable as', 'was intended as', 'was interpreted as', and 'is interpretable-in-principle as' for 'is'.

So, for example, if someone asks of an inscription, "What kind of symbol is that?" we should proceed by supplying four kinds of information: (1) We should provide a specification of how it is interpretable as a marker token by virtue of meeting the criteria for various marker types. For example, we might point out that it is interpretable under English conventions as a P or under Greek conventions as a rho. (2) If the mark was in fact inscribed by someone, we should say what kind of marker it was intended to be: for example, that it was intended as a P , or that it was intended as a rho, or that it was intended precisely to meet the criteria for both P and rho. (3) If someone has interpreted the inscription as a marker token, we should say who did the interpreting and what they took it to be. We might say, for example, that Jones took the symbol to be a P , while Mrs. Mavrophilipos took it to be a rho. (4) We should point to the fact that such a mark might be used in all kinds of ways—namely, that one could, for example, develop new marker conventions whereby that mark might count as a token of some new type.

Similarly, if someone asks what an inscription means, a full response would involve the following: (1) A list of the meanings that the inscription could be used to bear under the semantic conventions of various linguistic groups. (For example, English speakers use the marker string p-a-i-n to mean pain while French speakers use it to mean bread.) (2) A specification of what the author of the inscription intended it to mean. (The deceased lawyer in the thought experiment, for example, might have used it to mean bread, while I, the author of the example, intended precisely that it be interpretable as meaning either bread or pain.) (3) A specification of how anyone who apprehended the symbol interpreted it. (For example, Lestrade took it to mean pain and Holmes took it to mean bread.) (4) A reference to the fact that one could, in principle, use markers of that type to refer to anything whatsoever.

And similarly for counters, if one were to inquire as to the syntactic properties of an inscription such as 'p & q', a complete answer would require four kinds of information: (1) A list of ways that string could be interpreted as bearing a syntactic structure in different symbol games. (It could be a series of syntactically unrelated markers on an eyechart, for example, or a conjunction in the sentential calculus.) (2) A specification of how the inscription was intended by its author. (For example, the optometrist intended those markers as items on an eyechart, and did not intend them to bear any syntactic relation to one another.) (3) A specification of how such persons as apprehended the symbols took them to be syntactically arranged. (Say, Jones took them to constitute a propositional calculus formula of the form 'p and q', while Mrs. Mavrophilipos took them to just be individual letters.) Finally, (4) an allusion to the fact that one could devise any number of symbol games with quite a variety of syntactic structures such that this inscription would be interpretable as being of the syntactic types licensed by the rules of those games.

Now there are other uses of the term 'symbol'—for example, those employed in Jungian psychology and cultural anthropology. Similarly, there are other senses in which a marker might be said to "mean something." Holmes's companion Dr. Watson might, for example, inquire of Holmes, "What does the deceased attorney's inscription mean?" and Holmes might reply, "What it means, Watson, is that the housekeeper is a murderess." In this case, Watson's query, "What does it mean?" amounts to asking "What conclusions about this case can we draw from it?" and Holmes's answer supplies the relevant conclusion.

Yet it is important to emphasize that there is no general sense of "being a symbol" or "meaning such-and-such" over and above those captured by our technical terms. For suppose that someone were to ask what the first mark on the eyechart was, and we told him about how it was interpretable under various conventions, how it was intended by the doctor who drew it, how it was interpreted by various people who saw it, and pointed out, finally, that one could develop all sorts of conventions that could apply to marks with that shape. Suppose, however, that our questioner was not satisfied with this, but insisted upon asking for more. Suppose he said, "I don't want to hear what conventional types it meets the criteria for, or how it was intended, or how anyone construed it, or how it could, in principle, be interpreted. I just want to know what kind of symbol it is ." Suppose that it was clear from the way that he spoke that he thought that there was just some kind of brute fact about

an object that consisted in its being a marker of a particular type, quite apart from how it met the criteria for conventionally sanctioned types, how it was intended, and so on. How would we construe such a question?

There are, I think, two basic possibilities. The first is that the questioner is just confused, and does not realize that the relevant uses of the expression 'is a symbol' have effectively been replaced by our technical terminology. If this is the case, he would seem to be suffering from a misunderstanding of what is meant when we say that something is a rho, or a P , or a token of some other marker type. He is much like the person who misunderstands the use of the word 'healthy' when it is applied to food and demands of us that we tell him what "makes vitamin C healthy" without telling him how it contributes to the health of a body.

The second possibility is that the questioner has some special use of the expression 'is a symbol' in mind. He might, for example, be asking for an answer cast in the vocabulary of some particular psychological or anthropological tradition. (We might, for example, respond to a query about something on the wall of an Irish church in the following fashion: "This is the Celtic cross, a fine example of syncretic symbolism. In it one finds the Christian cross, the symbol of salvation through the death of Christ, cojoined with the Druidic circle, symbolizing the sun, the source of life and light.") Or he might have some more novel use of words in mind. He might, for example, just use the word 'symbol' in a way that did not make appeals to conventions. Allen Newell, for example, apparently identifies symbols with the physical patterns that distinguish them. Newell writes, "A physical symbols system is a set of entities, called symbols, which are physical patterns that can occur as components of another type of entity called an expression (or symbol structure)" (Newell and Simon [1975] 1981: 40, emphasis added). In another place, Newell (1986: 33) speaks of symbols systems as involving a physical medium and writes that "the symbols are patterns in that medium."

I shall discuss the proper interpretation of Newell's usage at length in chapter 5, but the basic point I wish to make may be summarized as follows: In characterizing symbols in this way, Newell is using the word 'symbol' differently from the way it is normally used in English, not unlike the way someone might just use the word 'healthy' to mean "full of vitamins." (By the same token, one could use the word 'symbol' to designate all and only objects that have odors pleasing to dogs. Why one should wish to abuse a perfectly good word in such a fashion, however, is quite another matter.) This kind of idiosyncratic use of words may be confusing, but it need not be pernicious so long as the writer (a ) does

not draw inferences that are based upon a confusion between his idiosyncratic usage of the word and its normal meaning (e.g., inferring that food that is healthy_v [i.e., full of vitamins] must be healthy [i.e., conducive to health]), and (b ) makes his own usage of the word adequately clear that his readers are not drawn into such faulty inferences. Thus there is nothing troublesome about using the word 'charm' to denote a property of quarks because (a ) physicists have an independent specification of the meaning of 'charm' as applied to quarks, and (b ) no one is likely to mistakenly infer that quarks would be pleasant guests at a soirée.

Similarly, it is possible to use words such as 'means' and 'refers to' in novel ways. One could, for example, become so enamored of causal theories of reference that one began to use sentences like "The word 'dog' refers to dogs" to mean something like "Tokens of 'dog' stand in causal relation R to dogs." This would, of course, be an enterprise involving linguistic novelty: the locutional schema 'refers to' is not generally used by English speakers to report causal relationships per se. But the idiosyncratic usage of the locutional schema might be an efficient way of expressing something that is important and for which there is no more elegant means of expression. So long as the writer makes his usage of words clear and does not make illicit inferences based on nonoperative meanings of words, his idiosyncrasy need not be construed as being pernicious. But if, for example, someone uses 'refers to' to mean "is larger than," he cannot draw an inference like that below from (A) to (B) just by virtue of the meanings of the sentences

(A) The title 'Great Emancipator' refers to Abraham Lincoln.

(B) Abraham Lincoln is also known as the Great Emancipator.

If one used such a novel definition to try to show that one could derive "X is known as Y " from "X is greater than Y ," one would be arguing fallaciously.

Nor can the inference from (A) to (B) be drawn by virtue of the meanings of the sentences if one just defines 'refers to' in causal terms. That is, if one uses (A) to mean "Tokens of 'Great Emancipator' stand in causal relation R to Abraham Lincoln," one cannot infer from (A) that Abraham Lincoln is also known as the Great Emancipator. One might, however, be able to infer (B) from the conjunction of the two claims (A^* ): "Tokens of 'Great Emancipator' stand in causal relation R to Lincoln" and (C): "For every signifier token M and every object N , if M stands in causal relation R to N , then M refers (in the ordinary sense) to N ." But

(A^* ) and (C) jointly entail (B) only because (A^* ) and (C) jointly entail (A), and (A) entails (B). (A^* ) alone does not entail (A), however, even if there is a causal relation R that always in fact holds between signifiers and their referents.

4.11—
The Form of Ascriptions of Intentional and Semantic Properties

One of the motivations for undertaking this analysis of symbols was an objection to CTM that was suggested in chapter 3. This objection, called the Conceptual Dependence Objection, involved two important claims about ascriptions of semantic and intentional properties. The first claim was that terms used in ascriptions of semantic and intentional properties are ambiguous: ascriptions of semantic and intentional properties to symbols and ascriptions of semantic and intentional properties to mental states have different logical forms and indeed involve attributions of different properties. The second claim was that ascriptions of semantic and intentional properties to symbols are conceptually dependent upon attributions of cognitive states. In Aristotelian terms, the homonymy of semantic and intentional terms is an example of homonymy pros hen, and the focal meaning of the terms is that which applies to cognitive states. These claims were offered only provisionally in chapter 3, however, and a major reason for undertaking this analysis of the nature of symbols was to provide resources for investigating the claims.

I shall argue in the next chapter that the analysis that has been offered here bears out both claims. For present purposes, I shall confine myself to commenting on the logical form of ascriptions of semiotic properties to symbols. We have discovered that the surface form of ascriptions of semantic values and intentionality to symbols is misleading. When we say, for example, "(Inscription) I refers to X ," it looks as though the verb phrase 'refers to' expresses a two-place predicate with arguments I and X . This way of reading the sentence, however, is wrong in two respects. First, the locutional schema 'refers to' is ambiguous, and may be used to express four very different propositions. More perspicuous expressions of these propositions are supplied by our technical terminology:

(1) I is interpretable (under convention C of linguistic group L ) as referring to X .

(2) I was intended (by its author A ) to refer to X .

(3) I was interpreted (by some reader R ) as referring to X .

(4) I is interpretable-in-principle as referring to X .

Second, on none of these interpretations does 'refers to' turn out to be a two-place predicate linking a symbol and its referent. The first interpretation, an attribution of semantic interpretability, involves implicit reference to a linguistic community and the semantic conventions of that community. The second interpretation, an attribution of semantic authoring intention, involves implicit reference to the cognitive states (namely, the authoring intentions) of the author of the symbol. The third interpretation, an attribution of actual semantic interpretation, involves implicit reference to the cognitive states of an individual who apprehends I . Finally, if we look at the definition of interpretability-in-principle, we see that the fourth interpretation involves implicit reference as well, either to the availability of a mapping that takes I 's marker type onto an interpretation, or to possible conventions. What has been said of ascriptions of reference may be said of ascriptions of meaning and intentionality as well. In each case, there are four ways of interpreting such ascriptions, and these involve covert reference to intentions and conventions in just the same ways as ascriptions of reference to symbols involve it.

4.12—
Summary

This chapter has developed a set of terminology for dealing with attributions of syntactic and semantic properties to symbols. The terminology involves the disambiguation of the term 'symbol' into three sortal terms—'marker', 'signifier', and 'counter'—and a distinction between four ways in which an object may be said to be a symbol (a marker) and to have syntactic or semantic properties. The analysis has already produced a significant conclusion: once we have rendered ascriptions of semantic properties to markers more perspicuous by employing the terminology that has been developed here, it becomes apparent that the logical forms of these expressions involve complex relations with conventions and intentions.

This analysis provides the basis for an investigation of the claims of CTM. The next chapter will investigate the implications of this analysis for the nature of semantic attributions to minds and to symbols in computers. The one that follows it will examine an objection to the analysis

presented in this chapter and articulate an alternative reading of the semiotic vocabulary as employed by advocates of CTM. Afterwards, we shall examine the implications of this analysis for CTM's representational account of the nature of cognitive states and its attempt to vindicate intentional psychology by claiming that cognitive processes are computations over mental representations.

Chapter Five—
The Semantics of Thoughts and of Symbols in Computers

The preceding chapter presented an analysis of the nature of symbols, syntax, and symbolic meaning. The upshot of this analysis was that symbolhood, syntax, and symbolic meaning are all conventional to the core. There is no such thing as simply being a P , a count noun, or a referring term. Words used to attribute semiotic categories do not express simple one- or two-place predicates, but hide complex relationships involving conventions and intentions. I shall refer to the analysis presented in chapter 4 as the "Semiotic Analysis."

The ultimate reason for undertaking this Semiotic Analysis was to assess a particular kind of attack upon CTM: namely, the claim, urged on us by Sayre and Searle, that the notions of symbol and symbolic meaning were somehow unsuited to the tasks of explaining the intentionality of mental states and of "vindicating" intentional psychology. We shall begin to develop some definitive answers to this question in chapter 7. Before doing that, however, it is necessary to address two issues, which will be the task of this chapter and the one that follows. To take things in reverse order, the next chapter will address an important kind of objection to the Semiotic Analysis: namely, that it conflates a "purely semantic" element of languages that is nonconventional with conventional features that accrue to natural languages only because they are used for communication. On this opposing view, often identified (rightly or wrongly) with Tarski and Davidson, semantic analysis is applied to things called "abstract languages" that are nonconventional in nature,

while conventions come into play only in our use or adoption of such languages for communication.

The present chapter will draw out some consequences of the Semiotic Analysis in two very separate areas, both of which will prove important to the larger argument. First, the Conceptual Dependence Objection sketched in chapter 3 claims that the semantic vocabulary is paronymous, in that (1) the semantic vocabulary expresses different properties when applied (a ) to symbols and (b ) to mental states; and (2) the usage that is applied to symbols is conceptually dependent upon the usage that is applied to mental states, and not vice versa. In the first part of this chapter it will be argued that the Semotic Analysis gives us what we need to justify this claim of conceptual dependence.

Second, it will be useful and interesting to examine the application of the Semiotic Analysis to symbols in computers. On the one hand, applying this analysis makes it quite clear that, pace the Formal Symbols Objection described in chapter 3, computers can and do store and operate upon entities that are symbols with syntactic and semantic properties in all of the ordinary senses. That is, we can speak of syntax and semantics for symbols in computers in exactly the same ways we speak of them for utterances and inscriptions. On the other hand, it will become clear upon closer inspection that the functional analysis of computers is a completely separate matter from their semiotic analysis. Computers can be analyzed in functional terms and in semiotic terms, and computer designers take great pains to make these two descriptions line up with one another in practice. But it is not the functional properties of the computer that make things inside it count as markers, counters, and signifiers (or vice versa). Contrary to some writers, the study of computation adds nothing to our understanding of symbols per se.

5.1—
Semiotics and Mental Semantics

The Semiotic Analysis was an analysis of the properties of symbols. A part of this analysis considered what it is we are imputing to symbols when we impute to them meaning or reference or intentionality. This involved looking both (1) at the logical form of such utterances, and (2) at the conditions for their satisfaction. Semantic terms like 'means' and 'is about' turned out to be both ambiguous and surprisingly complex. If, for example, I say,

"Symbol X means P "

I could be asserting one or more of the following:

(1) X is interpretable under convention C of language L as meaning P .

(2) X was intended by its author S to mean P .

(3) X was interpreted by some observer H as meaning P .

(4) X is, in principle, interpretable as meaning P .

Each of these locutional schemas has a distinct logical form and a distinct set of argument slots that can be filled by different kinds of objects. Some of these arguments do not always appear in the surface grammar of attributions of semantic properties in ordinary language, though they are likely to be filled in when a speaker is called upon to clarify her utterance. In the first three cases—that is, conventional interpretability, authoring intention, and actual interpretation—some of these suppressed arguments refer either to conventions of a linguistic community or to intentions of those who produce or apprehend the symbol tokens. It also turned out that there was a plausible reading of interpretability-inprinciple which construed it as a modal variation upon interpretability in a language.

Here, I think, we have all we need to justify two claims sketched in the articulation of the Conceptual Dependence Objection in chapter 3:

(1) Terms in the semantic vocabulary express different properties when applied to mental states from those they express when applied to symbols.

(2) The applications of semantic terms to symbols are conceptually dependent upon their applications to mental states.

5.1.1—
The Homonymy of the Semantic Vocabulary

The case for homonymy is fairly straightforward. First, if a natural language verb V is used in two contexts, A and B , and the logical form of V -assertions in A differs from that in B , then V is used to express different predicates in the two contexts. Moreover, predicates with different logical forms express different properties . In particular, two predicates expressing relational properties can only express the same property if they relate the same number of relata. Predicates with different numbers of argument slots in their logical form relate different numbers of

relata, and hence express different properties.^[1] Likewise, two predicates with the same number of arguments do not express the same property if the things that can fill their argument slots come from different domains.

Second, the predicates used to express semantic properties of symbols have argument slots that must be filled by references to conventions and intentional agents . They thus express complex relational properties that essentially involve conventions and agents. This much is a straightforward consequence of the Semiotic Analysis. One may contest the analysis on other grounds; but if one accepts it, one has already bought into this consequence.

Third, the logical forms of attributions of semantic properties to minds and mental states do not contain argument slots to be filled by references to conventions or intentions, and hence they attribute properties distinct from the semiotic properties . I have always thought that this was pretty self-evident, but sometimes people have accused me of just asserting this point without arguing it. The only way I see to demonstrate this point is to test each of the schemas developed in chapter 4 as a possible interpretation of attributions of semantic properties to mental states and see whether any of them seem intuitively plausible. So suppose John is having a thought T at time t , and what he is thinking about is Mary . We say (in ordinary English)

"John is thinking about Mary,"

or (in awkward philosophical jargon)

"John's thought T is about Mary."^[2]

Now can this be analyzed in terms of conventional interpretability in a language? That is, could the logical form of this utterance possibly be the following?

(1) John's thought T is interpretable under convention C of language L as being about Mary.

The answer, I think, is clearly no . The more you think about "meanings" of utterances, the clearer it becomes that there is a notion of conventional meaning in a language that applies there, and that it is part of what we meant all along when we spoke of meaning for symbols. But it is hard to see how that notion could apply to thoughts . Except for special cases like the interpretation of dreams, there are no conventions for interpretating thoughts. Nor do thoughts require such conventions for interpretation: thoughts come with their meanings already attached. You can-

not separate the thought from its meaning the way you can separate the marker from its meaning. This is why some writers describe the semantics of mental states as intrinsic to them.

Likewise for the other semiotic modalities:

(2) John intended that this thought T be about Mary.

(3) H apprehended John's thought T and interpreted it as being about Mary.

We do sometimes have thoughts as a result of intentions to have thoughts, as suggested in (2). John might, for example, deliberately think about his wife Mary while he is away on a business trip on their anniversary. Or, dealing with transference on a therapist's couch, he may intend to think about Mary but end up thinking about someone else instead. These things happen, but they are surely not what we are talking about when we say John's thought T is about Mary. Usually the intentionality of our thoughts is unintentional.

As for (3), there is some question about whether we apprehend one another's thoughts at all. We surely guess at one another's thoughts, and may rightly or wrongly surmise that John's thought at a given time is about Mary. But this is very different from seeing a marker as a marker and then interpreting it. We never apprehend thoughts as markers. And more to the point, even if we do apprehend people's thoughts and interpret them, this is not what we mean when we attribute meaning to their thoughts. I might say of a symbol, "It means X to Jim ." But it surely makes no sense to say, "John's thought means 'Mary' to Jim " (or for that matter, "John's thought means 'Mary' to John"). Finally, when we say that John's thoughts are about Mary, we certainly do not mean merely to assert the existence of a mapping relationship (i.e., interpretability-in-principle) from John's thought to Mary. If we try to apply the logical form of the semiotic vocabulary to our attributions of meaning to mental states, the results are nonsensical.

So semantic terms like 'means' and 'is about' have a different logical form when applied to mental states. It does seem reasonable to construe the logical form of these attributions as involving a three-place predicate relating subject, thought-token, and meaning, as the surface grammar suggests. There are no hidden references to conventions and intentions. As a consequence, the semantic vocabulary also expresses distinct properties when applied to mental states. When applied to symbols, it expresses relational properties in which some of the relata are conventions

or producers and interpreters of symbols. But these relata are missing in the case of mental states. In short, differences in logical form point to differences in properties expressed.

It thus behooves us to differentiate between two classes of properties that are expressed using the same semantic vocabulary: there is one set of semiotic-semantic properties as described by the Semiotic Analysis in chapter 4, and a separate set of mental-semantic properties attributed to mental states.

5.1.2—
Conceptual Dependence

It is also quite straightforward to show that attributions of semiotic-semantic properties are conceptually dependent upon attributions of mental-semantic properties. In the case of authoring intentions and actual interpretation, the analysis of semantic attributions alludes to meaningful mental states on the part of the author or interpreter: their intentions and acts of interpretation. Claims about authoring intention and actual interpretation are built upon a more fundamental stratum of attributions (or presuppositions) of meaningful mental states to human individuals. In the case of conventional interpretability the case is only slightly less direct. For a large part of what linguistic conventions consist of is the shared beliefs and practices of members of a linguistic group. Thus any appeal to conventions assumes a prior stratum of meaningful mental states as well. It thus turns out that the semantic vocabulary is ambiguous and indeed paronymous as claimed by the Conceptual Dependence Objection. Words like 'means' and 'is about' are used differently for mental states and for symbols, and the usage that is applied to symbols is conceptually dependent upon the usage that is applied to mental states.

It remains to be seen, however, what impact this will have on CTM's claims to explain mental-semantics in terms of the semantics of mental representations. Indeed, in light of this distinction between different uses of the semantic vocabulary, it will turn out that we have to clarify what kinds of "semantic" properties are even being attributed to mental representations. Are they semiotic-semantic properties (the natural assumption)? Or are they some other kind of properties that add a new ambiguity to the semantic vocabulary? Chapter 7 will examine the prospects of semiotic-semantic properties for explaining mental-semantics, and chapters 8 and 9 will explore two different strategies for attributing a distinct kind of "semantics" to mental representations.

5.2—
Symbols in Computers

At this point, I wish to shift attention to a second application of the Semiotic Analysis. In the remainder of this chapter, I shall consider the applications of the Semiotic Analysis to symbols in computers . There are really two parts to this exercise. First, I shall argue (against the Formal Symbols Objection articulated in chapter 3) that it is quite unproblematic to say that computers do, in fact, both store and operate upon objects that may be said to be symbols, and do have syntactic and semantic properties in precisely the senses delineated by the Semiotic Analysis. To be sure, the story about how signifiers are tokened in microchips is a bit more complicated than the story about how they are tokened in speech or on paper, but it is in essence the same kind of story and employs the same resources (namely, the resources outlined in the Semiotic Analysis). Second, I shall address claims on the opposite front to the effect that there is something special about symbols in computers, and that computer science has in fact revealed either a new kind of symbol or revealed something new and fundamental about symbols in general. I shall argue that this sort of claim, as advanced by Newell and Simon (1975), is a result of an illegitimate conflation of the functional analysis of computers with their semiotic properties. Or, to put it another way, Newell and Simon are really using the word 'symbol' in two different ways: one that picks out semiotic properties and another that picks out functionally defined types. Neither of these usages explains the other, but both are important and useful in understanding computers.

5.2.1—
Computers Store Objects That Are Symbols

In light of the centrality of the claim that computers are symbol manipulators, it is curious that virtually nothing has been written about how computers may be said to store and manipulate symbols. It is not a trivial problem from the standpoint of semiotics. Unlike utterances and inscriptions (and the letters and numerals on the tape of Turing's computing machine), most symbols employed in real production-model computers are never directly encountered by anyone, and most users and even programmers are blissfully unaware of the conventions that underlie the possibility of representation in computers. Spelling out the whole story in an exact way turns out to be cumbersome, but the basic conceptual resources needed are simply those already familiar from the Semiotic Analysis. I have divided my discussion of symbols in computers

into two parts. I shall give a general sketch of the analysis here and provide the more cumbersome technical details in an appendix for those interested in the topic, since the details do not contribute to the main line of argumentation in the book.

The really crucial thing in getting the story right is to make a firm distinction between two questions. The first is a question about semiotics: In virtue of what do things in computers count as markers, signifiers, and counters? The second is a question about the design of the machine: What is it about computers that allows them to manipulate symbols in ways that "respect" or "track" their syntax and semantics? Once we have made this distinction, the basic form of the argument that computers do indeed operate upon meaningful symbols is quite straightforward:

(1) Computers can store and operate upon things such as numerals, binary strings representing numbers, and so on.

(2) Things like numbers and binary strings representing numbers are symbols.

\ (3) Computers can store and operate upon symbols.

Of course, while one could design computers that operate (as Turing's fictional device did) upon things that are already symbols by independent conventions (i.e., letters and numerals), most of the "symbols" in production-model computers are not of this type, and so we need to tell a story about how we get from circuit states to markers, signifiers, and counters. I shall draw upon two examples here:

Example 1: The Adder Circuit

In most computers there is a circuit called an adder . Its function is to take representations of two addends and produce a representation of their sum. In most computers today, each of these representations is stored in a series of circuits called a register . Think of a register as a storage medium for a single representation. The register is made up of a series of "bistable circuits"—circuits with two stable states, which we may conventionally label 0 and 1, being careful to remember that the numerals are simply being used as the labels of states, and are not the states themselves. (Nor do they represent the numbers zero and one.) The states themselves are generally voltage levels across output leads, but any physical implementation that has the same on-off properties would function equivalently. The adder circuit is so designed that the pattern that is formed in the output register is a func-

tion of the patterns found in the two input registers. More specifically, the circuit is designed so that, under the right interpretive conventions, the pattern formed in the output register has an interpretation that corresponds to the sum of the numbers you get by interpreting the patterns in the input registers.

Example 2: Text in Computers

Most of us are by now familiar with word processors, and are used to thinking of our articles and other text as being "in the computer," whether "in memory" or "on the disk." But of course if you open up the machine you won't see little letters in there. What you will have are large numbers of bistable circuits (in memory) or magnetic flux density patterns (on a disk). But there are conventions for encoding graphemic characters as patterns of activity in circuits or on a disk. The most widely used such convention is the ASCII convention. By way of the ASCII convention, a series of voltage patterns or flux density patterns gets mapped onto a corresponding series of characters. And if that series of characters also happens to count as words and sentences and larger blocks of text in some language, it turns out that that text is "stored" in an encoded form in the computer.

Now to flesh these stories out, it is necessary to say a little bit about the various levels of analysis we need to employ in looking at the problem of symbols in computers and also say a bit about the connections between levels. At a very basic level, computers can be described in terms of a mixed bag of physical properties such as voltage levels at the output leads of particular circuits. Not all of these properties are related to the description of the machine as a computer. For example, bistable circuits are built in such a way that small transient variations in voltage level do not affect performance, as the circuit will gravitate towards one of its stable states very rapidly and its relations to other circuits are not affected by small differences in voltage. So we can idealize away from the properties that don't matter for the behavior of the machine and treat its components as digital —namely, as having an integral and finite number of possible states.^[3] It so happens that most production-model computers have many components that are binary —they have two possible states—but digital circuits can, in principle, have any (finite, integral) number of possible states. Treating a machine that is in fact capable of some continuous variations as a digital machine involves some idealization, but then so do most descriptions relevant for science. The digital description of the machine picks out properties that are real (albeit idealized),

physical (in the strong sense of being properties of the sort studied in physics, like charge and flux density), and nonconventional .

Next, we may note that a series of digital circuits will display some pattern of digital states. For example, if we take a binary circuit for simplicity and call its states 0 and 1, a series of such circuits will display some pattern of 0-states and 1-states. Call this a digital pattern . The important thing about a digital pattern is that it occupies a level of abstraction sufficiently removed from purely physical properties that the same digital pattern can be present in any suitable series of digital circuits independent of their physical nature. (Here "suitable series" means any series that has the right length and members that have the right number of possible states.) For example, the same binary pattern (i.e., digital pattern with two possible values at each place) is present in each of the following sequences:

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It is also present in the music produced by playing either of the following:

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And it is present in the series of movements produced by following these instructions:

(1) Jump to the left, then

(2) jump to the left again, then

(3) pat your head, then

(4) pat your head again.

Or, in the case of storage media in computers, the same pattern can be present in any series of binary devices if the first two are in whatever counts as their 0-state and the second two are in whatever counts as their 1-state. (Indeed, there is no reason that the system instantiating a binary pattern need be physical in nature at all.)

Digital patterns are real . They are abstract as opposed to physical in

character, although they are literally present in physical objects. And, more importantly, they are nonconventional . It is, to some extent, our conventions that will determine which abstract patterns are important for our purposes of description; but the abstract patterns themselves are all really there independent of the existence of any convention and independently of whether anyone notices them.

It is digital patterns that form the (real, nonconventional) basis for the tokening of symbols in computers. Since individual binary circuits have too few possible states to encode many interesting things such as characters and numbers, it is series of such circuits that are generally employed as units (sometimes called "bytes") and used as symbols and representations. The ASCII convention, for example, maps a set of graphemic characters to the set of seven-digit binary patterns. Integer conventions map binary patterns onto a subset of the integers, usually in a fashion closely related to the representation of those integers in base-2 notation.

Here we clearly have conventions for both markers and signifiers. The marker conventions establish kinds whose physical criterion is a binary pattern. The signifier conventions are of two types (see fig. 7). In cases like that of integer representation, we find what I shall call a representation scheme, which directly associates the marker type (typified by its binary pattern) with an interpretation (say, a number or a boolean value). In the case of ASCII characters, however, marker types typified by binary patterns are not given semantic interpretations. Rather, they encode graphemic characters that are employed in a preexisting language game that has conventions for signification; they no more have meanings individually than do the graphemes they encode. A string of binary digits in a computer is said to "store a sentence" because (a ) it encodes a string of characters (by way of the ASCII convention), and (b ) that string of characters is used in a natural language to express or represent a sentence. I call this kind of convention a coding scheme . Because binary strings in the computer encode characters and characters are used in text, the representations in the computer inherit the (natural-language) semantic and syntactic properties of the text they encode.

It is thus clear that computers can and do store things that are intepretable as markers, signifiers, and counters. On at least some occasions, things in computers are intended and interpreted to be of such types, though this is more likely to happen on the engineer's bench than on the end-user's desktop. It is worth noting, however, that in none of this does the computer's nature as a computer play any role in the story.

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Figure 7

The architecture of the computer plays a role, of course, in determining what kinds of resources are available as storage locations (bistable circuits, disk locations, magnetic cores, etc.). But what makes something in a computer a symbol (i.e., a marker) and what makes it meaningful are precisely the same for symbols in computers as for symbols on paper: namely, the conventions and intentions of symbol users.

Now of course the difference between computers and paper is that computers can do things with the symbols they store and paper cannot. More precisely, computers can produce new symbol strings on the basis of existing ones, and they can do so in ways that are useful for enterprises like reasoning and mathematical calculation. The common story

about this is that computers do so by being sensitive to the syntactic properties of the symbols. But strictly speaking this is false. Syntax, as we have seen and will argue further in the next chapter, involves more than functional description. It involves convention as well. And computers are no more privy to syntactic conventions than to semantic ones. For that matter, computers are not even sensitive to marker conventions. That is, while computers operate upon entities that happen to be symbols, the computer does not relate to them as symbols (i.e., as markers, signifiers, and counters). To do so, it would need to be privy to conventions.

There are really two quite separate descriptions of the computer. On the one hand, there is a functional-causal story; on the other a semiotic story. The art of the programmer is to find a way to make the functionalcausal properties do what you want in transforming the symbols. The more interesting symbolic transformations you can get the functional properties of the computer to do for you, the more money you can make as a computer programmer. So for a computer to be useful, the symbolic features need to line up with the functional-causal properties. But they need not in fact line up, and when they do it is due to an excellence in design and not to any a priori relationship between functional description and semiotics.

5.2.2—
A Rival View Refuted

Now while I think this last point is true, I can hardly pretend that it is uncontroversial . There is a rival view to the one that I have just presented, and this rival view has enjoyed quite a bit of popularity over the years. On this view, there is something about the functional nature of the computer that contributes to, and even explains, the symbolic character of what it operates upon. Due to the prevalence of this alternative theory, I think it is worth presenting it with some care and venturing a diagnosis of what has gone wrong in it.

Some writers claim that computer science has revealed important truths about the nature of symbols. Newell and Simon (1975), for example, claim that computer science has discovered (discovered! ) that 'symbol' is an important natural kind, whose nature has been revealed through research in computer science and artificial intelligence. Their central concern is with what they call the "physical symbol system hypothesis." Newell and Simon describe a "physical symbol system" in the following way:

A physical symbol system consists of a set of entities, called symbols, which are physical patterns that can occur as components of another type of entity called an expression (or symbol structure). . . . Besides these structures, the system also contains a collection of processes that operate on expressions to produce other expressions. . . . A physical symbol system is a machine that produces through time an evolving collection of symbol structures. (Newell and Simon [1975] 1981: 40)

Their general thesis is that "a physical symbol system has the necessary and sufficient means for intelligent action" (ibid., 41). They define a physical symbol system as "an instance of a universal machine" (ibid., 42), but seem to regard this as a purely natural category defined in functional terms, not as a category involving the conventional component involved in markers, signifiers, and counters. Indeed, they claim that computer science has made an empirical discovery to the effect that symbol systems are an important natural kind, defined in physical, functional, and causal terms. It looks as though their "symbols" are supposed to be characterized precisely by "physical patterns" (ibid., 40), although perhaps the functional organization of the system plays some role in their individuation. Their characterizations of how symbols in such systems can "designate" objects and how the system can "interpret" the symbols are also quite peculiar:

Designation . An expression designates an object if, given the expression, the system can either affect the object itself or behave in ways depending on the object.

Interpretation . The system can interpret an expression if the expression designates a process and if, given the expression, the system can carry out the process. (ibid., 40)^[4]

Newell and Simon regard the physical symbol system hypothesis as a "law of qualitative structure," comparable to the cell doctrine in biology, plate tectonics in geology, the germ theory of disease, and the doctrine of atomism (ibid., 38-39).

It is this kind of claim that has aroused the ire of critics such as Sayre (1986), Searle (1990), and Horst (1990), for whom such claims seem to involve gross liberties with the usage of words such as 'symbol' and 'interpretation'. In the eyes of these critics, Newell and Simon have in fact coined a new usage of words such as 'symbol' and 'interpretation' to suit their own purposes—a usage that arguably has a different extension from the ordinary usage and undoubtedly expresses different properties.

In one sense, I think this criticism still holds good. Here, however, I should like to draw a more constructive conclusion. For Newell and Simon are also in a sense correct, even if they might have been more circumspect about their use of language: computer science does indeed deal with an important class of systems, describable in functional terms, that form an empirically interesting domain. Their usage of the expressions 'symbol system' and 'symbol' do pick out important kinds relevant to the description of such systems. And the historical pathway to understanding such systems does in fact turn upon Turing's discussion of machines that do, in a perfectly uncontroversial sense, manipulate symbols (i.e., letters and numerals). But while it has proven convenient within the theory of computation to speak of functionally describable transformations as "symbol manipulations," this involves a subtle shift in the usage of the word 'symbol', and the ordinary notion of symbol is not a natural kind, nor are systems that manipulate symbols per se an empirically interesting class.

In order to illustrate this claim, it will prove convenient to tell a story about the history of the use of the semiotic vocabulary in connection with computers and computation. The story begins with Turing's article "On Computable Numbers" (1936)—the article in which he introduces the notion of a computing machine. The purpose of this article is to provide a general characterization of the class of computable functions, where 'computable' means "susceptible to evaluation by the application of a rote procedure or algorithm." Turing's strategy for doing this is first to describe the operations performed by a "human computer"—namely, a human mathematician implementing an algorithmic procedure (Turing always uses the word 'computer' to refer to a human in this article); second, to develop the notion of a machine that performs "computations" by executing steps described by Turing as being analogous to those performed by the human mathematician; and third, to characterize a general or "universal" machine that can perform any computations that can be performed by such a machine, or by anything that can perform the kinds of operations that are involved in computation.

It is worth looking at a few of the details of Turing's exposition. Turing likens

a man in the process of computing a real number to a machine which is only capable of a finite number of conditions, q₁ , q₂ , . . . , q_R , which will be called "m -configurations". The machine is supplied with a "tape" (the analogue of paper) running through it, and divided into sections (called "squares") each capable of bearing a "symbol". (Turing 1936: 231)

(Note the scare quotes around 'symbol' here. One plausible interpretation is that Turing is employing this word in a technical usage, not necessarily continuous with ordinary and existing usage.)

To continue the description: the machine has a head capable of scanning one square at a time, and is capable of performing operations that move the head one square to the right or left along the tape and that create or erase a symbol in a square. Among machines meeting this description, Turing is concerned only with those for which "at each stage the motion of the machine . . . is completely determined by the configuration" (Turing 1936: 232). The "complete configuration" of the machine, moreover, is described by "the number of the scanned square, the complete sequence of all symbols on the tape, and the m -configuration" (ibid.). Changes between complete configurations are called "moves" of the machine. What the machine will do in any complete configuration can be described by a table specifying each complete configuration (as a combination of m -configuration and symbol scanned) and the resulting "behaviour" of the machine: that is, the operations it performs (e.g., movement from square to square, printing or erasing a symbol) and the resulting m -configuration.

The symbols are of two types. Those of the first type are numerals: 0s and 1s. These are used in printing the binary decimal representations of numbers being computed.^[5] Those of the second type are used to represent m -configurations and operations; for these Turing employs Roman letters, with the semicolon used to indicate breaks between sequences. The symbols are typified by visible patterns,^[6] and are meant to be precisely the letters and numerals actually employed by humans. Indeed, the operations of the computing machine are intended to correspond to those of a human computer (i.e., a human doing computation), whose behavior "at any moment is determined by the symbols which he is observing, and his 'state of mind' at that moment" (Turing 1936: 250). Again, Turing first describes the behavior of a human computer (ibid., 249-251), and then proceeds to describe a machine equivalent of what the computer (i.e., the human) does:

We may now construct a machine to do the work of this [human/SH] computer. To each state of mind of the [human] computer corresponds an "m -configuration" of the machine. The machine scans B squares corresponding to the B squares observed by the [human] computer. (ibid., 251)^[7]

To summarize, Turing's description of a computing machine is offered as a model on which to understand the kind of computation done by

mathematicians, a model on which "a number is computable if its decimal can be written down by a machine" (ibid., 230).

Now there are two things worth noting here. First, if there is a similarity between what the machine does and what a human performing a computation does, this is entirely by design: the operations performed by the machine are envisioned quite explicitly as corresponding to the operations performed by the human computer (though Turing is not careful to say whether "correspondence" here is intended to mean "type identity" or "analogous role"). Second, while this machine is unproblematically susceptible to analysis both (a ) in terms of symbols and (b ) in the functional terms captured by the machine table, it is important to see that the factors that render it susceptible to these two forms of analysis are quite distinct .

On the one hand, it is perfectly correct to say that this machine is susceptible to a functional analysis in the sense of being characterizable in terms of a function (in the mathematical sense) from complete configurations to complete configurations. Indeed, that is what the machine table is all about. What renders the machine appropriate for such an analysis is simply that it behaves in a fashion whose regularities can be described by such a table, and any object whose regularities can be described by such a table is susceptible to the same sort of analysis, whether it deals with decimal numbers or not.

On the other hand, it is perfectly natural to say that Turing's machine operates upon symbols. By stipulation, it operates upon numerals and letters. Numerals and letters are symbols. Therefore it operates upon symbols. Plausibly, this may be construed as a fact quite distinct from the fact that it is functionally describable. Some functionally describable objects (e.g., calculators) operate on numbers and letters, while others (e.g., soda machines) do not. Likewise, some things that operate upon numbers and letters (e.g., calculators) are functionally describable, while others (e.g., erasers) are not (see fig. 8). Moreover, what makes something a numeral or a letter is not what the machine does with it, but the conventions and intentions of the symbol-using community. (Whatever one thinks about the typing of symbols generally, this is surely true for numerals and letters.)

Now how does one get from Turing's article to Newell and Simon's, forty years later? I suspect the process is something like the following. For the purposes of the theory of computation (as opposed to semiotics), the natural division to make is between the semantics of the symbols (say, the fact that one is evaluating a decimal series or an integral) and the formal

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Figure 8

techniques employed for manipulating the symbols in the particular algorithmic strategy.^[8] And from this standpoint, it does not matter a whit what we use as symbols—numerals, letters, beads on an abacus, or colored stones. And more to the point, it does not matter for the functional properties of the operations performed by the machine whether it operates on numerals and letters (as Turing's machine was supposed to) or upon equivalent sets of activation patterns across flip-flops or magnetic cores or flux densities on a disk. As far as the theory of computation goes, these can be treated as "notational variants," and from an engineering standpoint, the latter are far faster and easier to use than letters and numerals. And of course these circuit states (or whatever mode of representation one chooses) are at least sometimes "symbols" in the senses of being markers, signifiers, and counters: there are conventions like the ASCII convention and the decimal convention that group n -bit addresses as markers and map them onto a conventional interpretation, and there are straightforward mappings of text files in a computer onto ordinary text.

The occupants of computer memory thus live a kind of double life. On the one hand, they fall into one set of types by virtue of playing a certain kind of role in the operation of the machine—a role defined in functional-causal terms and described by the machine table. On the other hand, they fall into an independent set of types by dint of (possible) subsumption under conventionally based semiotic conventions. Both of these roles are necessary in order for the machine to plausibly be said to be "computing a function"—for example, evaluating a differential equation—but they are separate roles . If we have functional organization

without the semiotics, what the machine does cannot count as being, say, the solution of a differential equation. This is the difference between calculators and soda machines. More radically, however, addresses in computer memory only count as storing markers ("symbols" in the most basic sense) by virtue of how they are interpreted and used. (We could interpret inner states of soda machines as symbols—that is, invoke conventions analogous to the ASCII convention for thus construing them—but why bother?) On the other hand, we also do not get computation if we have semiotics without any functional-causal organization (writing on paper) or the wrong functional-causal organization (a broken calculator).

Now I think that what Newell and Simon have done is this: they have recognized that computer science has uncovered an important domain of objects, objects defined by a particular kind of functional organization that operates on things that correspond to symbols. And because they are interested more in the theory of computation than in semiotics (or the description of natural language), they have taken it that the important usage of the word 'symbol' is to designate things picked out by a certain kind of functional-causal role in systems that are describable by a machine table. What they have not realized is that this usage is critically different from an equally important, but distinct, usage necessary for talking about semiotics. Nor, as Searle and Sayre have noted, do writers who make this move seem adequately sensitive to the dangers of paralogistic argument that emerge from this oversight.

5.3—
A New Interpretation of 'Symbol' and 'Syntax'

It thus appears that there is good reason to think that some writers in computer science have at least implicitly employed the words 'symbol' and 'syntax' in a fashion that has proven quite fruitful in their investigations, and yet which bears marked discontinuities with the ordinary uses of those words. In rough terms, in the context of discussion of computers, the words 'symbol' and 'syntax' are sometimes used to designate entities and their properties that play particular roles in a functionally describable system. This is of interest for our purposes in evaluating CTM for the simple reason that it may be this usage of the words 'symbol' and 'syntax' that CTM's advocates have in mind, and not the ordinary usage explicated in the Semiotic Analysis in chapter 4. However, in order to

clarify how this would affect CTM, it is necessary to make this implicit usage of 'symbol' and 'syntax' more exact by supplying some technical terminology and an analysis. We may develop this category in the following way. The role that is played by the things Newell and Simon call "symbols," quite simply, is one of picking out items in functionally determined categories. The technical use of 'symbol' serves to pick out entities that fall into types based upon the role they play in a functionally described system. A corresponding technical use of 'program' or 'formal rule' picks out causal regularities between functionally described structures in such a system.

We may even state a formal definition for this use of 'symbol,' which may be replaced with the technical term 'machine-counter':

A tokening of a machine-counter of type T may be said to exist in C at time t iff

(1) C is a digital component of a functionally describable system F ,

(2) C has a finite number of determinable states S : {S₁ , . . . , s _n } such that C 's causal contribution to the functioning of F is determined by which member of S digital component C is in,

(3) the presence of a machine-counter of type T at C is constituted by C 's being in state s_i , where s_iÎ S , and

(4) C is in state s _i at t .

The notion of a machine-counter is defined wholly in nonconventional terms. It can also do an important part of the work that is to be done by the legitimately syntactic categories employed to describe computers: machine-counter types correspond to the counter types that could be used to describe a computer in syntactic terms. To put it differently, for every machine-counter type T of a system S , there is a syntactic description of S available in principle that contains a counter type T^* such that T and T^* provide functionally equivalent characterizations of S . Any X that is a machine-counter of type T is thus interpretable-in-principle as a counter of type T^* . Notice, however, that the notion of a machine-counter is not built out of a simpler notion corresponding to a marker . Since functional role is constitutive of machine-counter type, the typing of machinecounters is not dependent upon some prior categorization. In this respect, the functional description of computers differs from semiotic description, which depends on a fundamental level of marker typing.

5.4—
Implications of a Separate Usage of 'Symbol'

It may well be, then, that the usage of the words 'symbol' and 'syntax' in computer science poses a challenge to the Semiotic Analysis presented in chapter 4, but the challenge it seems to pose is not that that analysis is the wrong analysis of the ordinary usage of 'symbol', but that there is a new and technical usage of 'symbol' which needs to be considered as well. The implications of this for the assessment of CTM seem to be fairly straightforward. It looks as though there are at least two sorts of things the advocate of CTM might mean in talking about "symbols" in computers: (1) she might mean that they are markers and counters, or (2) she might mean that they are machine-counters. And hence when she speaks of "mental representations" being "symbols," she might mean that they are markers and counters, or she may mean that they are machine-counters. These are very different kinds of claims and need to be be assessed separately.

Arguably the case is similar with respect to semantics. It is not clear that there is any coherent nonconventional notion of "meaning" forthcoming from computer science that is analogous to the notion of a machine-counter. But it could be that CTM's advocates are using the semantic vocabulary in some fashion distinct from that used to express semiotic-semantic properties. Or, even if they do not yet see the problem and hence do not explicitly mean to use the semantic vocabulary in a new way, they might most charitably be viewed as doing so. That is, it is possible that the best way to read advocates of CTM when they speak of mental representations as having "semantic properties" is to read them as attributing not semiotic-semantic properties, but some distinct class of properties peculiar to mental representations. These properties, presumably nonconventional in character, we might designate MR-semantic properties, in contrast with the semiotic-semantic properties of symbols and the mental-semantic properties of mental states. It is unclear what such properties might be, but we may nonetheless signal with our terminology that some distinct, nonconventional set of properties is intended in this way.

It has turned out, then, that computers can be said to "manipulate symbols" both in the ordinary sense of doing things with objects that in fact have conventional interpretations and in a distinct technical sense having only historical connections to the ordinary usage explicated by the Semiotic Analysis. This, however, by no means undercuts the Semiotic

Analysis as an analysis of what it is to be a symbol in the ordinary sense. On the one hand, that analysis applies perfectly well to many things in computers. On the other hand, the technical usage—that is, the notion of a machine-counter—expresses distinct properties from those expressed by the ordinary usages of the word 'symbol'. It is necessary to see whether either family of usages of the semiotic vocabulary will provide a viable version of CTM, and it is necessary to explore both.

The analysis of these alternative interpretations of CTM will be undertaken in chapters 7 through 9. Chapter 7 will assess the merits of CTM if it is interpreted as attributing the semiotic properties to mental representations. Chapters 8 and 9 will look at two ways of interpreting CTM in a way other than that suggested by the semiotic categories.

Chapter Six—
Rejecting Nonconventional Syntax and Semantics for Symbols

Chapter 4 presented the Semiotic Analysis of the nature of symbols, syntax, and symbolic meaning. According to this analysis, linguistic symbolism is thoroughly dependent upon conventions and intentions of language users. Indeed, this is not merely some contingent fact about symbols in public languages that accrue to them because of their public character, but a feature that is built into the very logical form of predicates in the semiotic vocabulary: to attribute semantic or syntactic properties to a symbol—or indeed, even to call a thing a symbol—just is to relate it to certain conventions and intentions. We saw in the last chapter that this has the consequence that the semantic vocabulary is in fact ambiguous, expressing different properties when applied (a ) to symbols and (b ) to mental states. In particular, attributions of meaning to symbols are conceptually dependent upon attributions of meaningful mental states. We saw as well that symbols in computers are symbols in the ordinary semiotic sense, although the paths by which interpretive conventions apply to them may be more circuitous than in the case of discursive symbols such as utterances and inscriptions. But we also saw that recent discussions of symbols in computers by writers such as Newell and Simon seemed sometimes to imply a distinct and technical usage of the word 'symbol' that picked out not the semiotic properties of the symbols, but their functionally defined type. I argued there that functional typing and symbol typing in the ordinary sense are conceptually (and ontologically) distinct, and that bringing them together in computers is a highly contingent matter that in fact makes up much of the programmer's

art. The relationship between functional analysis and semiotics is one of craft and not of definition or dependence.

This will lay the basis for the analysis of CTM that will take place in the three chapters that follow this one. Chapter 7 will evaluate the prospects of CTM on the assumption that the "symbolic" and "semantic" properties imputed to mental representations are semiotic-semantic properties. Chapters 8 and 9 will address the possibility that CTM's "symbols" are not "symbols" in the ordinary semiotic sense, but simply functionally typed entities. These two chapters will explore two avenues for interpreting the "semantic" properties imputed to mental representations in a fashion that does not impute convention- and intention-based semiotic-semantic properties.

Before proceeding to this analysis, however, it is perhaps prudent to address a possible objection to the Semiotic Analysis. Thus the present chapter will address the objection that we can separate "pure syntactic" and "pure semantic" components of our analysis of symbols from a conventional component that accrues to them solely because they are used for public languages. In particular, we shall examine the claim that Tarskian semantics provides us with such a "purely semantic analysis," as seems often to be assumed by philosophers of mind.

6.1—
A Criticism of the Semiotic Analysis

While the analysis of symbols and symbolic representation presented in chapter 4 is in certain ways novel and no doubt will be regarded as controversial in some respects, one general thrust of the analysis—the idea that the nature of utterances and inscriptions depends upon the conventions and intentions of speakers and writers—may plausibly be regarded as a "mainstream" view. It is a view widely held by writers both within cognitive science and outside it,^[1] and is indeed endorsed in some form by CTM's most important advocates (see Fodor 1981). There are some particular twists to my articulation of this view—notably, the distinction between the technical sortal terms 'marker', 'signifier', and 'counter', the claim that there are four separate "modalities" of conventional being, and the claim that not only semantics but also syntax and symbolhood are conventional in nature. But most objections to these features of my account as an account of utterances and inscriptions would probably take the form of an intramural debate between writers who embrace a semiotics based on convention and intention.

When this account is offered as a general account of symbols and sym-

bolic meaning, however, it sometimes meets with greater resistance. For it is often claimed that what this analysis really gives us is an account of the nature of specifically communicative or discursive symbols —or perhaps of symbols-as-used-communicatively —and not an account of symbols, syntax, and symbolic meaning generally, much less a general account of representation.

Now to this latter claim—that the account in chapter 4 is not a general account of representation —I gladly defer. It was not my intent there to supply a general account of representation or an analysis of the uses of the word 'representation', nor does doing so fall within the rhetorical scope of this book. What we are discussing here, after all, is not the general claim that thought involves representation, but the more specific claim that it involves symbolic representation.^[2] It is necessary, however, to address the claim that the Semiotic Analysis presented here is somehow specifically an analysis of discursive symbols—of symbols-used-communicatively, and not symbols per se .^[3] For this claim will be of direct relevance to the analysis of CTM, as the symbols postulated by CTM's advocates are not used communicatively. For purposes of brevity, I shall put this objection in the critic's voice:

CRITIC : Look here, Horst. The analysis you give may be very well and good as an analysis of discursive symbols such as utterances and inscriptions, but you have been far too hasty in drawing the conclusion that all symbols are conventional in nature on the basis of these examples. The decision to confine yourself to conventional examples seems to be a matter more of fiat than of principle; and as a consequence, the analysis is question begging if it is presented as a general account of symbols and symbolic meaning. What you really have here is a hybrid analysis: what it describes is not precisely what it is for symbols to have semantic properties, but also how they come by them in a fashion that is conducive to communicative use of the symbols. Other symbols (e.g., mental representations and some representations in computers) also have semantic properties, but are not used communicatively. Arguably, the only reason that discursive symbols are conventional in nature is that this is necessary for their communicative role in natural languages. And so there is no reason to suppose that the semantic properties of mental representations would share this feature.

Moreover, as to your contention that there is no such thing as a symbol simply "being" of a particular type or "meaning something" apart from how it is interpretable under conventions, intended, interpreted, or

interpretable-in-principle, you have really shown less than you think. You are right that there is no question of a discursive symbol "meaning something" apart from how it is interpretable, intended, and so forth—at least if you mean by this (a ) that you can't have discursive symbols that are meaningful without getting their meanings in these ways, and (b ) that telling the story about how symbols are conventionally interpretable and how they were intended, and so on, already says all there is to say about what they mean. That is, your conditions are both necessary and sufficient for the attribution of symbolic meaning in the case of discursive symbols. But this is quite compatible with the possibility that symbolic meaning is a distinct property from conventional interpretability, authoring intentions, and the like. Consider the following analogy: suppose that someone wanted an analysis of redness, and you were to give an analysis in terms of the reflectance properties that a solid object would have to have in order for it to be red. It would be true that solid objects could not be red without having these reflectances and, arguably, that once you had said that an object had these reflectances, there was nothing more to its being red to be told. But it does not follow that being red is in general simply a matter of reflectances or that nothing can be red without having these reflectance gradients. There is, for example, red light . The property of being red is accounted for in one way in solids and in another way in light. It is thus a mistake to identify the property of being red with the properties solids must have to be red solids, because things other than solids can be red. Similarly, you can have physical triangles and abstract triangles, and the latter do not have all of the properties one would expect of the former. Give an account of triangularity that builds physical properties into the picture and you leave out abstract triangles. Similarly, temperature is mean kinetic energy of molecules for gases, but not for plasma. Give an account of temperature simpliciter as mean kinetic energy of molecules and you've arbitrarily ruled out the possibility of plasma having a temperature.

Now look at your examples: you've restricted your domain to communicative signs. You may be right that, for this domain, an account of semantic properties (and symbolhood and syntax) has to advert to conventions and intentions. But all that means is that things in this domain cannot realize such properties except by way of conventions and intentions. In some sense, temperature is mean kinetic energy for gases, but not for plasma. Redness is a matter of reflectance curves for solids, but not for light. And similarly, meaning is a matter of conventional and actual interpretation for communicative signs (and likewise syntax and

symbolhood), but (as you point out) not for mental states, and arguably not for symbols that represent but are not used communicatively . You have confused the analysis of the property of meaningfulness simpliciter with an account of how it gets realized in particular kinds of objects—namely, objects whose function is to communicate meaning. If you want to analyze meaning, the analysis had better work for noncommunicative symbols like mental representations as well. And if you do that, arguably you will end up with an analysis that is applicable to mental states, too, thus circumventing the conclusion that the semantic vocabulary is paronymous.

I cease to speak in the critic's voice.

6.2—
Initial Response

Now I think that this is in some ways a very difficult criticism to properly come to grips with.

First, I am in some ways uneasy about the examples. (And let me hasten to point out that they are my examples—any problems with them are not the responsibility of other parties.) For it is not clear to me that we really ought to say that there is a single property called "temperature" or one called "redness," given that they require completely different accounts in different media. (I am more compelled by "triangle," though arguably there simply are not any concrete triangles.) That is, I am not fully persuaded that these terms have not been proven to be ambiguous, or at least ill defined. Or, insofar as there do seem to be properties of temperature and redness, they seem in some way to be observer-related: temperature in terms of kinds of measurements and redness in terms of the propensity to produce particular sensations.

Beyond this, however, there seem to be two things that one would need in order for the critic's objection to be made to carry much impact. First, the critic would have to justify the criticism of my choice of paradigms by pointing to things that were said to be "symbols" and to have "syntax" and "meaning" in the same sense in which these things are said about utterances and inscriptions, yet which were susceptible to nonconventional analysis. Second, she would need to show how to provide an alternative analysis of symbols and symbolic meaning that could "factor out" the alleged "purely syntactic" and "purely semantic" components from the "merely communicative" aspects. I shall attempt to show that these enterprises are not viable in the remainder of this chapter. In

some places I will try to argue directly against the critic's analysis; in others, I shall try to show where the critic's story seems to have gone wrong.

6.3—
The Choice of Paradigm Examples

First, let us consider whether I have been arbitrary in my choice of utterances and inscriptions as my paradigm examples of symbolhood and symbolic meaning. In particular, are there in fact other paradigm examples available such that (a ) the words 'symbol' and '(symbolic) meaning' are predicated of those examples in the same sense in which they are predicated of utterances and inscriptions, and (b ) there is no covert reference to conventionality or mental states when these words are used of the alternative paradigms?

Now in a certain way, I find this a very odd objection. It is not as though we were overrun with things we call "symbols" that jump out as alternative paradigms. It is true that the words 'symbol' and '(symbolic) meaning' are said of other sorts of objects. In what follows, however, I shall argue that all of these usages are either (a ) homonymous and express different properties from those expressed by the same words when they are applied to utterances and inscriptions, or (b ) contentious in ways that render illicit their use as alternative paradigms in the present context.

6.3.1—
Some Existing Uses of 'Symbol' and 'Meaning'

First, there are clearly some alternative uses of the words 'symbol' and 'meaning' in ordinary English and existing usage in the sciences. Jung, for example, wrote a book entitled Man and His Symbols, in which the word 'symbol' is applied to things other than utterances and inscriptions. There seems to be a similar and related usage in cultural anthropology, which is interested, among other things, in the "symbols" employed by a culture—meaning not their linguistic tokens, but the way they express themes and mythic forms. However, it seems very unlikely that the fact that linguistic tokens and Jungian archetypes might both be called "symbols" indicates that there is a property (being-a-symbol) that is common to both sets of objects. It seems more likely that the word is homonymous and expresses different properties in the two cases, the existence of a common word being a function of family resemblance or analogy rather than property sharing.

Similarly, the word 'meaning' and its variants has some different or-

dinary uses. We say, for example, that dark clouds "mean rain," and that what some human beings long for most is a "meaningful relationship" with another human being. But here again it seems wrongheaded to assume that the word 'meaning' expresses the same property when applied to utterances, clouds, and relationships. Even in the case of theorists who speak of "natural meaning" or "natural signs" (e.g., Grice 1957)—and it is almost never "natural symbols "—it seems clear that the words 'meaning' and 'sign' (or, at a stretch, 'symbol') are used here precisely to express the relation that is sometimes called "indication" (see Dretske 1981, 1988), and not to express the same property that is predicated of utterances and inscriptions. To be sure, some writers (notably Dretske 1981, 1988) have tried to make a case that the kind of "meaning" that accrues to language (i.e., the usage of the word 'meaning' that is applied to linguistic tokens) can ultimately be explained in a fashion that depends heavily upon indication. But their point is not to give an account of what property is expressed by the ordinary usage of 'meaning', but to give an account of how this property arises. Indeed, Dretske (1988: 55-56) explicitly embraces Grice's distinction between two uses ("natural" and "nonnatural") of the word 'meaning'. If an indicator theory should prove adequate as an explanation of linguistic meaning, the status of that theory would be that of an empirical account that explains the presence of the property P expressed by the "nonnatural" sense of 'meaning' in terms of a distinct property Q that is expressed by the "natural" sense, and not an analysis of what property that word is used to express.

Thus these examples are of no help to the critic. First, the Semiotic Analysis in no way claims that the words in the semiotic vocabulary may not be ambiguous in additional ways, or that they cannot be used to express properties other than those mentioned in the analysis. (Who on Earth would want to claim that? ) Second, if the usage of the semiotic vocabulary in CTM is related to the convention-bound usage explicated in the Semiotic Analysis only by way of analogy or family resemblance, this seriously undercuts much of the appeal of CTM. For one thing, if these words express different properties when applied to mental representations, we are entitled to some explanation of what these properties are. For another, what the computer paradigm shows us how to do is to link up causal powers with the semiotic-semantic properties of the symbols. If the salient properties expressed by the words 'symbol' and 'meaning' in CTM express not semiotic-semantic properties but a distinct set of properties, we will need a new assessment of how these properties can be linked up with causal role, and hence we will require a new assess-

ment of the status of the vindication of intentional psychology, which depended so heavily upon the computer paradigm.^[4]

6.3.2—
Mental Representations as a Paradigm

Perhaps, however, one might say that one has an alternative paradigm of nonconventional symbols in mental representation itself. After all, people in cognitive science have been talking about mental representations in their theories for years, and most of them seem pretty clear that they do not mean to be talking about convention-dependent symbols. Ergo we have an alternative paradigm.

This approach, however, is either a case of homonymous usage or else it is question begging. For talk of symbolic representations in the mind is either (a ) an attempt to apply existing usage, fixed by the older paradigms, in a new domain, or else (b ) its relationship to existing usage is merely one of analogy or family resemblance. Fodor at one point seems to recognize this issue, but is rather cavalier in dismissing it. He writes,

It remains an open question whether internal representation . . . is sufficiently like natural language representation so that both can be called representation 'in the same sense'. But I find it hard to care much how this question should be answered. There is an analogy between the two kinds of representation. Since public languages are conventional and the language of thought is not, there is unlikely to be more than an analogy. If you are impressed by the analogy, you will want to say that the inner code is a language. If you are unimpressed by the analogy, you will want to say that the inner code is in some sense a representational system but that it is not a language. (Fodor 1975: 78)

It seems to me that Fodor ought to worry a bit more about his options here. For the notions of "symbol" and "meaning" play an absolutely central role in CTM, and so one should wish to know just what properties these words are supposed to express when applied to Fodor's hypothesized mental representations. If these words express the same properties they express when applied to linguistic tokens, they would seem to require whatever analysis is given to linguistic tokens generally. These turn out to be convention- and thought-dependent, and Searle and Sayre have suggested that this kind of dependence renders these notions unfit for explaining the intentionality of mental states. (This view will be argued in detail in chapter 7.) But if the use of words like 'symbol' and 'meaning' signifies only an analogy with language, one needs to hear what properties these words do express when applied to mental representations, in order to see if these properties are even candidate explainers for

the intentionality of mental states. In the first case, the critic's use of mental representation is contentious and question begging, as the question at hand is one of whether the ordinary usage of 'symbol' and 'meaning' can be applied to some internal states in a fashion that will do what CTM's advocates claim. In the second case, what we have is not an objection to the Semiotic Analysis, but a claim that it is not an analysis of the usage of the semiotic vocabulary employed by CTM's advocates.

6.3.3—
Symbols in Computers

It also might be suggested by some that symbols in computers present a counterexample to the Semiotic Analysis. In light of the discussion in the previous chapter, however, this is clearly a confusion. On the one hand, things in computers that are normally thought of as symbols—for example, representations of numbers or text encoded in the ASCII format—are clearly convention-dependent in exactly the same senses as are utterances and inscriptions. On the other hand, the implicit usage of the words 'symbol' and 'syntax' in writers like Newell and Simon (1975) to denote functionally typed kinds is clearly a distinct (i.e., homonymous) usage of the words 'symbol' and 'syntax'. Things in the computer do not fall into semiotic kinds because they fall out of the functional description of the computer; nor do they fall under the functional description provided by the machine table because they are markers and counters. Rather, the great accomplishment of successful program design is to get the semiotic types to line up with the functional types so that the computer will perform operations that happen to be of interest when interpreted as symbol manipulations. So, far from providing a counterexample to the Semiotic Analysis, computers are only properly understood when that analysis is employed.

6.4—
Further Objections

In spite of the lack of clear alternative paradigms for the usage of the semiotic vocabulary, it nevertheless might be argued that even the ordinary usage of words such as 'symbol' in fact involves two distinct elements: a non conventional element that defines the essence of symbolhood, syntax, or semantics, and a conventional element that is required in the case of utterances and inscriptions only because they are symbols-used-communicatively, and conventions are needed for communication. Indeed, one might suggest that the notion of a machine-counter provides

an analysis of a "pure" notion of symbolhood and syntax, while some other kind of analysis might do the same for semantics. The notions of "symbol" and "syntax" might thus be adequately and perspicuously developed along functional or functional-causal lines, while semantics might be given a nonconventional analysis in terms of the kind of semantic theory proposed by Tarski, which depends on an (arguably nonconventional) notion of satisfaction .

6.5—
The Essential Conventionality of Markers

First, let us consider the bare notion of "symbol" captured by the term 'marker'. Is it possible to factor out the conventionality of the analysis of markers by attributing that conventionality to the fact that letters and numerals are symbols-used-for-communication? Or, alternatively, is it simply part of the essence of markers that they be conventional?

I think that it is not possible to factor out the conventional aspect of markers. To begin with, it seems quite clear that categories like "rho" and "0" and their genera "letter" and "numeral" are legitimate categories that form an important domain for characterizing some aspects of human life. The issue, then, is not one of legitimating these categories but of providing a proper analysis of them. I wish to argue that these categories cannot be adequately cashed out either (a ) in terms of physical properties, including abstract physical properties such as patterns, or (b ) in functional terms like those defining the notion of a machine-counter.

First, consider physical pattern. The problem here is that physical pattern is not a rich enough condition to distinguish between marker types. For two distinct marker types (e.g., P and rho) may share criteria such that the same set of physical patterns is employed for both types—that is, anything that is rho-shaped is P -shaped, and vice versa. Thus physical pattern is not sufficient for the explanation of marker types themselves, even though its presence is a sufficient condition for a physical particular to count as being interpretable as a token of such a type given the existence of the conventions associating the type with particular physical patterns . This, however, presumes the conventional type and does not explain it. Intuitively, what seems to be required is the additional fact that rhos and P 's play distinct roles in the language games of distinct linguistic communities—and hence marker types are defined in part by the role they occupy in the linguistic lives of communities of language users.^[5]

Yet the critic might very well seize upon this very characterization to make her point in another way. She might reason: if markers are determined by the role they play in a system of interactions between persons, then they are functionally defined . And hence they would appear to be a subspecies of machine-counters. Now perhaps the "system" needed for defining markers as a species of machine-counters would have to be a very complex one, involving entire linguistic communities, rules for coining new symbols, revising practices, and so on, but it is nonetheless a functionally describable system. Hence markers are machine-counters. It is just that the "machine" here is something on the order of a human society. The reason that markers have to be conventional is that the makeup of this particular system requires it for communication and decoding between individuals. (I cease to speak for the critic.)

This is admittedly a very seductive characterization. However, I believe that it suffers from several weaknesses. First, for anyone even a little bit taken with the work of Ryle, the late Wittgenstein, or Lebenswelt-philosophie, it is contentious at best to claim that the notion of a role within a language game or a form of life can be cashed out as a functional relationship in the bare mathematical sense of function required for a machine-counter. I shall not belabor this point here, but it seems that really what the critic ought to say is not that the role of a marker in a language game is fully explicated by something appearing in a machine-table description of a language, but rather that we can abstract away from a language in such a way that what we end up with is a machine table, and that we can do so in such a way that some of the machine-counters appearing on the table correspond to markers in the ordinary practice being described. This, however, raises two questions: (1) Can one in fact do this for the practices involved in marker usage? And (2) even if we can, does this amount to factoring out the notion of marker-hood into the notion of a machine-counter plus conventions needed for communicative usage?

I think that the only really honest answer to the first question at the moment is we don't really know . There are notorious problems with characterizing and simulating linguistic practices in situ, such as those described in Dreyfus (1972, 1992), Weizenbaum (1976), and Winograd and Flores (1986). Arguably, some such problems could be developed to apply not only to semantic and pragmatic competence but to the ways that marker-related practices are embedded in a larger web of practices as well. In brief, we are not really entitled to assume that these problems can be overcome, given the fact that the remarkable amalgam of brain-

power, person-hours, and research dollars represented in the artificial intelligence community has not managed to overcome them in the space of several decades.

But even if one could produce a machine table for linguistic groups that isolated markers in the desired way, it is not so clear that this would accomplish all that the critic desires. For while functional describability—even of the special sort required for machine-counters—may pick out kinds that are of interest for the purposes of computer scientists or others, functional kinds (in this mathematical sense of "functional") are notoriously cheap. As Block (1978) and others have noted, any object or system of objects one likes has some functional description—or, better, a very large number of such descriptions. But surely even if one were to factor out a conventional component of markers, what one should wish to have left as a "pure notion of symbolhood" is something more robust than mere functional describability. What the critic wants is something that is plausibly a nonconventional characterization of symbols per se —something that should be common to things that one might plausibly think are or involve symbols (say, computer memory states, brain states, and inscriptions) but not predicable of things that are functionally describable, yet not plausibly construed as symbols (say, molecules of water in a bucket). But the functional properties distinctive of machine-counters are not robust enough to do this. At best, they do half of what is needed—namely, unite computer memory states, brain states, and (perhaps) inscriptions—but they fail to distinguish these as a kind from the rest of creation. Thus the kind of "definition by role" one finds for machine-counters does not appear to be rich enough to explain the kind of "definition by role" needed for markers.

6.6—
Syntax, Functional Role, and Compositionality

It is likewise tempting to see the notion of a machine-counter as a way of factoring out a "purely syntactic" element from the notion of a counter, thus allowing us to treat the conventional aspects of the syntax of natural languages as features that accrue to them only because natural languages are used for communication. Some writers might well assert that the notion of a machine-counter cashes out what we do mean in talking about symbols and syntax—namely, that syntax really is nonconventional in character, and is rightly understood purely in terms of combinatorial properties of the units manipulated—in short, that syn-

tactic properties are purely a matter of functional role in the mathematical sense of 'function'.

Again, I wish to be very careful here. It is certainly possible to use the word 'syntactic' for any nonsemantic properties, or for any such properties that have to do with ordering or combination. However, I think that this does not do justice either to the ordinary usage of the word 'syntax' or to the categories that linguists call "syntactic." It does seem right, of course, to say that linguists are interested, among other things, in the formal, combinatorial properties of syntactic categories, much as physicists are interested in the formal properties of bodies qua massive (e.g., in Newton's laws) or as chemists are interested in the combinatorial properties of classes of elements. But the formal and combinatorial nature of the objects in these other sciences does not exhaust what it is to be, say, a gravitational body or a halogen; and likewise the formal characterization of syntax does not exhaust what it is to be of a particular syntactic category.

There are, I think, several good reasons for rejecting a formal or functional-role view of the nature of syntactic categories.

(1) The word 'syntax' has a natural domain: namely, linguistic entities. But Turing tables are applicable to any object that has a functional description. It has been argued by numerous writers (e.g., Block and Putnam) that all sorts of strange entities might have functional descriptions and be truly describable in terms of a Turing table. Syntax cannot simply be ordering, because there are plenty of things that are concatenated (e.g., cars in a traffic jam) that are not ordered syntactically . And even when there is a whole functionally describable system, it is not eo ipso a syntactic system. Were this so, the whole world would turn out to be syntactically structured, as everything has at least some trivial functional description. Of course, one could use the word 'syntax' in this way, but to do so would be to abuse a word that already has perfectly good uses, and would certainly underdetermine the kinds of distinctions envisioned by the linguist.

(2) At least some of the linguist's primitive categories tend to have semantic and pragmatic overtones: notions like "noun," "plural formative," "connective," and "pragmatic formative" all seem to be typed not only according to combinatorial properties but in terms of what kinds of things they are used to express or to do. Perhaps, however, one might say that these categories are identified in part on semantic and pragmatic grounds, and the task of the student of syntax is to find purely syntactic (i.e., formal) characterizations of the categories.

(3) More problematically, we seem to need a semantically pregnant notion of syntax if we are to use it to explain compositionality . For here is a common story about compositionality: a complex symbol string means what it means because of (a ) the meanings of the primitives, and (b ) the function of its syntactic structure. But the "function" implied here cannot simply be "function" in the mathematical sense, and it cannot amount merely to a description of the formal properties of the string of symbols. For lexical semantics plus formal syntax only tells us how we can concatenate meaningful lexical items in legal strings; it does not tell us how to interpret them. That is, it may tell us that "Borin bit the bear" and "The bear bit Borin" are both grammatical sentences in English, but it does not tell us who bit whom in each case. For there is a consistent interpretation of English (or any language) that reverses assignments of agent and patient (with corresponding changes for transformations into the passive voice), and there is nothing about the formal properties of the language that tells us which is operative. Indeed, there is nothing about the formal properties of the language that distinguishes meaningful sentences from grammatically well-formed nonsense (this despite a tendency of writers such as Tarski and Davidson to use the word 'meaningful' to mean "well formed"). So if we want to tell a more or less familiar story about compositionality, we need syntactic categories that are partially defined in terms of their contribution to compositional semantics, and such categories are not purely formal. Likewise, we need rules for composition that are semantically pregnant.

Nor is this a feature only of natural languages. The same observations could be made with respect to, say, predicate calculus or Hilbert's geometry. It is quite possible for a person to understand (a ) the uses of the individual symbols, and (b ) formal rules for symbol manipulation, without understanding what is asserted by a given equation. (I expect, for example, that this is the case for many students in college differential equations classes.)

(4) Two languages can have the same syntactic categories while having different functional descriptions. Intuitively, one wishes to say that different languages (e.g., English and French) share some of the same syntactic categories (e.g., "count noun," "plural affix"). But these categories enter into different combinatorial relations with other categories in the different languages, and hence differ with respect to their formal properties. We might, of course, conclude that they are thus, contrary to appearances, distinct syntactic categories. But this seems quite arbitrary and does violence to the natural construal of what the linguist is

up to. A simpler solution is to conclude that syntactic categories are not typed precisely by their formal properties.

(5) Two speakers of the same language may have different dialects that, say, permit different collocations and allow different replacements, but employ the same syntactic categories. But if the functional-role interpretation of syntax were correct, this could not be the case: differences in what are taken to be legal sentences and legal transformations would require differences in syntactic category as well. But surely this consequence is intolerable.

(6) A given speaker may revise her way of speaking (a functional change) without thereby replacing her syntactic categories. It may be, of course, that children learning a language at some points entertain incorrect hypotheses about how their native language works, and so when they learn the correct rules they are in fact trading in old categories for new. But adult speakers can also change their grammatical competence in ways that do not seem to require this kind of interpretation. (They can learn, for example, that 'as' becomes 'so' after 'not'.) It is surely too radical an interpretation to say that they are learning new syntactic categories just on the basis of the fact that the functional description of their syntactic competence changes. Better to say that syntactic categories are not defined in functional terms, although they may receive a functional description, and to say that the proper functional description of a category may differ across languages, dialects, and even changes in a given speaker's competence.

Thus it seems wrong to say that the notion of a machine-counter is a good explication of the ordinary sense of 'syntax' or of the linguist's sense of that word (and this even if many linguists think that syntactic categories are precisely functional-role categories). And it seems that convention is needed to get from combinatorial "syntax" to full-blooded syntax. In particular, it is needed to explain compositionality: two languages could have the same interpretation scheme for the lexical primitives and combinatorially equivalent syntaxes and yet have different assignments of meanings to complex expressions. Why? Because full-blooded syntax provides, among other things, a mapping from the ordered pair [meanings of primitives, syntactic form] to the meaning potential of the complex expression, and combinatorial properties do not provide such a function.^[6] What does provide such a function? In natural languages, it is surely a matter of convention. It is, of course, worth considering whether the combinatorial properties to which machines can be sensitive can be combined with something nonconventional to provide the

same results as combinatorial syntax, but that is quite another question (one that will be addressed in a later chapter).

6.7—
What Functional Description Can't Do

Given this analysis of the relationship of the functional description of computers to symbols and syntax, we might do well to ask what might have made the opposing view seem attractive in the first place. I believe that answer is to be found in a certain misunderstanding of what is going on in functional description. It has been noted by writers like Cummins (1975) and Block (1980) that there are several different uses of the word 'functional' and its variants. Cummins distinguishes the mathematical notion of function, which is employed in machine-table functionalism, from what he calls "functional analysis," which describes an object in terms of its role in a larger system (e.g., the function of the heart is to pump blood). And Block distinguishes functionalism as a thesis about the nature of mental states from "psychofunctionalism," which is a thesis about the meanings of mental-state terms .

I believe that the dangers of conflating mathematical functionalism and functional analysis are very great. CTM is concerned with mathematical functionalism insofar as mental processes are said to be describable by something like a machine table. It is sometimes claimed additionally that asserting that the mind has a math-functional description is tantamount to asserting that the nature of mental states is given by the completed machine table, and hence given in nonintentional terms—namely, that a math-functional description of the mind yields a functional analysis of mental states as well, or that it is the functional description of things in computers that confers upon them the status of symbols with syntactic properties. I wish to argue that this is false, and rests upon a basic misunderstanding of what goes on in functional analysis.

What does go on in math-functional description is simply a special case of mathematical abstraction employed in the modeling of real-world phenomena. Functional description, whether in computer science, in psychology, or in linguistics is completely parallel with the formation of mathematical models in mechanics and thermodynamics. (I do not mean to imply, of course, that the machine-table paradigm in psychology is as mature or as well confirmed as are our models of mechanics or thermodynamics—merely that they are the same kind of enterprise.) And from the standpoint of scientific research in psychology, this is one of the cardinal virtues of the computer paradigm: it purports to provide the re-

sources for a mathematization of psychology, much as, say, analytic geometry and the calculus provided the resources for the mathematization of classical physics.

But what is involved in mathematical modeling? First, such models involve abstraction . Laws of gravitation abstract away from other forces that are almost always operative in vivo: mechanical force, electromagnetism, strong and weak force. And likewise for laws governing the other fundamental forces. Additionally, all macroscopic laws abstract away from the statistical possibility of freak quantum events, and so on. Mathematical models are not universally quantified propositions about individual objects or events. If they were, most of them would be false. Rather, they are propositions about how certain forces in nature contribute to events in abstraction from other processes. (An interesting corollary: Why is psychology so hard to make into a rigorous science? Hint: abstract characterization becomes exponentially more difficult as the number of mutually dependent variables increases. How many mutually dependent modules are there in the brain?)

Second, you get an exact and rigorous model only when you can express it in some mathematical form. Many of the most famous such models are expressed in the form of equations. (Laws are models expressed by equations.) But there are other kinds of mathematical structure that need not involve equations—for example, alternative geometries can serve as models of space-time, and geometric models are not equations. A model can be mathematically exact without relying heavily on laws. And even when laws are central to a theory, they are only a part of a larger model. For example, classical mechanics involves a model of space and time whose structure is Euclidean, while relativistic mechanics involves a model whose structure is non-Euclidean. Thus grasping a theory such as general relativity involves more than being able to manipulate the equations as algebraic entities. One needs to understand what relationships they express against the background of the larger model.

This leads to a third point, which is intended to be the real emphasis of this section. There are really two different ways of looking at a mathematical model, which correspond to two different levels of abstraction away from real-world phenomena in vivo. The ultimate goal of modeling, of course, is to describe and explain real-world phenomena. But real-world phenomena are messy, and scientific description aims at capturing such order as is to be found in their behavior. This involves separating different factors that are at work in vivo (gravity from mechanical force in physics, rationality from emotion in psychology) by way of abstrac-

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Figure 9

tion. We know we have a sufficient degree of orderliness when we can provide a mathematical model. This is the first level of abstraction: the use of a mathematical model to describe real-world phenomena (for example, the use of Newton's equations to describe gravitational attraction). At this level of abstraction, which I shall call the "rich construal" of the model, the model is by definition a model of some particular real-world phenomenon. Newton's equations are not just equations (i.e., algebraic entities); they are equations that express relationships between the real-world phenomena of gravitational force, mass, and distance.

But we may also perform a second act of abstraction and look at Newton's model purely in mathematical terms. We can perform algebraic operations upon his equations, for example, or examine the Euclidean assumptions of classical physics purely as geometric assumptions. The physicist and the mathematician often operate upon the same models, but do so under different constraints. The mathematician is concerned with the model as a purely mathematical entity. The physicist is concerned with it as a description of real-world phenomena. If we say that the physicist is concerned with a rich construal of the model, let us say that the mathematician is concerned with a sparse construal (see fig. 9).

It is important to see that any scientific theory is always more than the mathematics that sums it up. The formula describes the relevant form of a process or relation, but it does not itself determine what it is whose form it describes. For example, there are always an indefinite number of purely abstract objects that are described by the same mathemat-

ics, and usually a multitude of uninteresting concrete objects (for example, those formed by meriological relations) that are described by it as well. Moreover, there are sometimes multiple non trivial natural systems described by the same mathematics. The most notable case is probably that of thermodynamics and mathematical theory of communication, which treat of distinct domains but happen to share a substantial portion of their mathematical descriptions. The equations employed in these domains, treated as equations (that is, sparsely construed), do not tell you that they are about heat or information. The mathematics of thermodynamics and information theory does not provide a complete analysis of the nature of heat or information. What it provides is an exact description of relationships between the kinds of entities that are relevant to the domain in question. If you want to know about heat or information in detail, you will need the mathematics. But if all you have is the mathematics, you will not be able to derive a full-blooded description of the real-world phenomena merely from their mathematical characterization.

And so, in general, mathematical modeling does not provide an analysis of the full nature of a phenomenon, though it tends to specify that nature in more exact detail. At a rich level of description, we know that we are talking about, say, gravitation simply because we embarked upon the enterprise with the intention of talking about gravitation. Newton's equations do not tell us what gravitation is, they merely specify its form. At a sparse level of description, we are no longer talking about gravitation at all; we are merely talking about equations as equations. They are no longer being treated as a model of anything, and there is nothing about them that has the conceptual riches needed to explain real-world phenomena like gravitation or heat.

6.7.1—
Functionalist Theories of the Mind

I believe that this is precisely the case with functional description of the mind and of language as well. Let us begin with math-functionalist theories of the mind. The founding hypothesis here is that math-functional description of the sort provided by machine tables or general-purpose programming languages provides mathematical tools adequate to the task of describing the form of mental states and processes. Mental states and processes are real-world phenomena, and describing them is bound to involve some abstraction. We treat as irrelevant things like mechanical force (though people do get banged on the head, often to the detri-

ment of their thinking) and gravitation (though it has been claimed that some individuals are affected by the full moon and NASA does psychological experiments on the effects of free-fall), and so on. Likewise we treat some physiological factors like blood sugar and hormone levels as constant much the way we treat voltage levels in a computer as constant, abstracting away from the fact that variations in these things affect real-world performance in ways that are of considerable concern to doctors and systems operators, respectively. Perhaps this strategy for mathematizing psychology will pan out in the long run. Perhaps it is fundamentally flawed, as claimed by Dreyfus (1972) and Winograd and Flores (1986). Perhaps it would work in principle, but the number of mutually dependent variables makes it impossible to carry out in practice. My concern is not with the prospects of this strategy but with what it would provide if carried out in detail. And what it would provide is precisely analogous to what, say, Newton's equations provided for classical mechanics: a mathematically exact model of mental states and processes.

Given the preceding discussion of mathematical models in general, it should be clear why a psychological machine table would not be an analysis of the nature of mental states and processes. At a rich level of description, the model is indeed a model of mental processes . But we know it is a model of those processes and not something else for the very pedestrian reason that we knew it all along: the model is a model of the mind because producing a model of the mind was our goal from the outset. Such models can be better or worse insofar as they involve better or worse approximations of the form that is really present in processes in vivo (that is, in the sense that Einstein's model is better than Newton's, and Newton's is better than Descartes's). So at the rich level of abstraction, the content of the model is not a consequence of its mathematical form alone. At this rich level we do indeed have a description in which we can identify mental states as such and characterize them in terms of their location in a network of other mental states, inputs, and outputs. However, we can do this only by assuming the individual mental states as mental states and assuming the network, and then characterizing the relations precisely in terms of the machine table. At best, we can analyze one mental state in terms of its relation to the others, holding their existence and relatedness as a kind of background assumption. But in doing this we never break out of the web of the intentional, unless it should prove possible to define all of the inner states in terms of a neutrally characterized set of inputs and outputs. But arguably this "best case" itself involves a misunderstanding. For in such a case what we are

doing is picking out a set of states by dint of an abstract description of their causal interrelations. But this by no means assures that those causal relations are the essential properties of the states involved, nor that there could not be a variety of distinct state types that could occupy isomorphic causal roles.

On the other hand, at the sparse level the "model" is now just a mathematical entity. This level of abstraction is indeed useful even for the scientist (as opposed to the mathematician) at times, such as when one is interested in seeing whether, say, classical mechanics is a special case of relativistic mechanics, and does so purely by mathematical manipulations. But it cannot tell us what the interpretations of the mathematical symbols used to express the theory might be. For example, the formulas used for information theory do not tell us whether they are being used to express a model of information or of heat—or indeed that they are being used to express any real-world properties at all. In the case of the mathematization of psychology, here all we have is the machine table, which is a representation of a function in the mathematical sense. There is nothing about the table that tells us what the domain of the table is. Indeed, it could serve equally well as a functional description of all kinds of things: some abstract objects, some interesting real-world phenomena, some monstrous meriological contrivances. If we do not start out knowing that we are talking about the mind, there is nothing about the math-functional description that will tell us that we are doing so.

In short, math-functional description cannot provide us with an analysis of the nature of mental states and processes any more than equations for entropy can teach us the difference between heat and information. What it would do is no more and no less than what other mathematical models do in the other sciences: namely, to specify exactly the mathematical form of real-world phenomena of whose existence and nature we have some kind of independent knowledge.

6.7.2—
Functionalist Theories of Language

The functional analysis of language runs a parallel course. It is, of course, true that linguists are interested in formal descriptions of things like rules for legal formation of expressions in a language, transformation rules, and so on. And some might say that even conventions can usefully be examined as a kind of rule-governed activity which is subject to a more precise description. If linguistic conventions are established by practices of language users, perhaps this very network of practices can be mathe-

matized into a machine table or something of the sort, in which case language will have been given a functional characterization in terms of a system as large as a human society.

I do not wish to debate the long-range prospects of such an analysis here. My point is simply this: if such a characterization were to be given, its status would be the same as that of any other mathematically precise model. On a rich construal, it is a description of a language, but only because that was the intent of the modelers from the outset. On a sparse construal, it is simply some abstract mathematical structure without an interpretation. The nature of the mathematical structure—that is, the math-functional properties—does not explain the nature of language as language, though of course differences in such properties are important for, say, differentiating two natural languages (which may have different morphemic categories and different grammars) or differentiating natural languages from other language games like first-order predicate logic. Looking at the formal properties of a language or comparing those of different language games is a very useful enterprise, and reveals a great deal about particular language games. What it does not do is reveal the nature of symbolhood and syntax in their own right. Either one knows what those are beforehand and asks about specific systems of symbols and syntax (rich construal of the model) or else one has an uninterpreted mathematical model that does not essentially describe languages (sparse construal).

6.7.3—
The "Fallacy of Reduction"

This error of mistaking the properties of the mathematically reduced model of a phenomenon for the essential properties of the phenomenon itself is sufficiently important to merit a name: I shall call it the "Fallacy of Reduction." The Fallacy of Reduction is committed when you abstract away from features of a real-world process to give a more rigorous characterization of some of its features, and then assume that it is only the properties that survive the abstraction, and not those that are abstracted away from, that are relevant to the nature of the real-world phenomenon. Thus it is an instance of the Fallacy of Reduction to conclude that heat and information are "the same thing" because they share a mathematics. Likewise it is an instance of this fallacy to conclude that the functional describability of the mind would license the conclusion that mental states are functionally defined .

6.8—
The Possibility of Pure Semantics

It remains to consider the question of whether the Semiotic Analysis does justice to semantic notions—in particular, whether the analysis is a hybrid of a nonconventional "purely semantic" element and a conventional element that accrues only to symbols-used-communicatively. What I propose to argue is as follows: (1) The Semiotic Analysis provides a proper analysis of the properties expressed by the semantic vocabulary as they are applied to the paradigm examples of symbols such as utterances and inscriptions. (2) This analysis cannot be factored into a nonconventional "purely semantic" component combined with a conventional component that is needed only for communicative symbols. This has the consequence (3) that people who wish to speak of "meaningful mental representations" must either be (a ) attributing to those representations the convention-dependent semiotic-semantic properties, or else (b ) attributing to those representations a set of properties distinct from those normally expressed by the semantic vocabulary—properties that we may for convenience dub "MR-semantic properties."

In order for the critic to succeed in his objection to my analysis of symbols and symbolic meaning, it must be possible to show that the semiotic analysis I have presented blurs the distinctions between two different kinds of properties that accrue to discursive symbols: (1) their nonconventional semantic properties, and (2) the conventional properties that accrue to them specifically because they are symbols used in communication . The critic need not show that symbols such as utterances and inscriptions can in fact possess the first sort of property without the second, but merely that there is in fact an element of such symbols that is indeed semantic but in no way conventional, and that this element is what is shared by discursive symbols, the mental representations posited by CTM, and perhaps mental states as well. In effect, he must show that the Semiotic Analysis really shows only a causal dependence of semantic properties upon convention, not a conceptual dependence. And to do this, it must be possible to present an analysis of semantics that can apply to the paradigm examples of "meaningful symbols" which "factors out" a nonconventional semantic component from a convention-laden communicative element.

The basic issue that faces us in any attempt to factor out a "purely semantic" component from the Semiotic Analysis is this: one thing that does seem clear about the Semiotic Analysis is that there are separate

claims to be made about conventional interpretability, authoring intention, actual interpretation, and interpretability-in-principle. How are we to isolate a "purely semantic" component that is common to these four modalities in such a fashion that we do justice to the distinction between the modalities? That is, it seems that we have important and coherent notions of "being interpretable under convention C as signifying Y " and "being intended by S as signifying Y " and so on. The critic's claim is that these notions are in fact amalgams of a "purely semantic" component plus factors that are not essential to semantics but necessary for communication. So one important constraint upon an analysis developed along these lines is that it ought to do justice to the notions it is intended to analyze.

We may schematize the approach in the following way. For each of the modalities, the critic needs to articulate an alternative analysis that separates two components: a "purely semantic" component and a convention-bound communicative component. We may indicate our predicates as follows:

CONV(X,T,C_i,L ,L,Y): X is of a type T that is interpretable under convention C _i,L of L as signifying Y

AUTH(S,X,Y): X was intended by S as signifying Y

INT(H,X,Y): X was interpreted by H as signifying Y

PPLE(X,Y): X is, in principle, interpretable as signifying Y

Let us further note the putative "purely semantic" meaning as a relation as follows:

M(X,Y): X means Y (in the "purely semantic" sense)

The critic's strategy has to be one of formulating certain biconditionals for each of these modalities that reduce each of them to a claim that M(X,Y) plus some residual claim about communicative use. The form of such claims might be indicated thus:

where CONV^* denotes the aspects of CONV that remain once M(X,Y) has been factored out. (The exact logical form of CONV^* would require such an analysis to be performed in detail.) And similarly for the other modalities:

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What the critic wants is a notion of "pure meaning" that is necessary for each of the semiotic modalities, but is not sufficient for any of them (except of course for interpretability-in-principle, which is trivially satisfied with or without a "pure" notion of meaning). For if "pure meaning" is a sufficient condition for one or more of the other modalities, then it somehow secures the conventional element of semiotic-semantics as well, which is precisely what the notion of "pure meaning" is an attempt to avoid.

Although I have never seen an explicit attempt to analyze the conventional semantics of natural and technical languages in terms of a purely semantic component plus something else, such an analysis seems implicit in the way many people regard the kind of analysis of language associated with Tarski and Davidson. On this view, a "language" is viewed not as a historical entity distributed over a community situated in time and space, but as an abstract object that associates expressions with interpretations and may be adopted by one or many individuals—or, for that matter, by none at all. A language thus conceived is an abstract object, and hence presumably its existence is not dependent upon conventions. Where convention enters the picture is when a community or an individual uses such an object as a public language or an idiolect.^[7] It is here, in the adoption of a preexisting abstract object, that convention and intention enter the picture. There just are these abstract entities L₁ , . . . , L _n called "languages," and each of them essentially involves a semantic interpretation that is a mapping from expressions to their interpretations. Convention enters the picture when a community or an individual decides to use some particular language L_i as its language of representation and communication.

This view of languages points to a possible analysis of the semiotic modalities: The conventional interpretability of an expression E in community L amounts to (1) the fact that E means Y in language L_i (i.e., the interpretation mapping for L_i maps E onto Y ), and (2) the fact that community L has adopted L_i . Likewise, authoring intention and actual interpretation are to be analyzed in terms of the employment of an abstract language. If S intends E to mean Y , then S is adopting language L_i and E means Y in L_i . If H interprets E as meaning Y , then H is adopting the

interpretive conventions of L _i and E means Y in L_i . The basic notions here are (1) meaning-Y -in-L_i and (2) adopting a (preexisting) language as a language of communication and representation.

It is perhaps clear why this view should be popular among people who wish to provide a semantics for mental representation—or, more generally, to "naturalize" semantics. For this view separates the purely semantic element (a mapping from expressions to objects and states of affairs) from a particular way that that semantic component gets hooked onto communicative languages. And this leaves open the door to the possibility that the same semantic properties might get connected with other things (mental representations, thoughts) in other ways. If one takes this view, the question for the cognitive scientist is to find a different relationship that plays the same meaning-conferring role for mental representations that conventional and intentional adoption of languages plays for natural languages.

This "pure semanticist" view has gained a great deal of currency. It also enjoys a great deal of intuitive plausibility, and it is attractive to many in cognitive science precisely because it seems to relieve cognitive science of the problems of conventionality by treating conventionality as a feature of the adoption of language for communicative use . It is a worthy opponent for the Semiotic Analysis. I happen to think that this view is wrong in some very fundamental ways, but to see why this is so we shall need to examine a concrete example of a project in "pure semantics" of "abstract languages," and do so in some detail. Those who have brought up this kind of view as an objection to the Semiotic Analysis tend to refer to it as "Tarskian semantics" or "Tarski-Davidson semantics," due to the influence of Tarski's work in semantics for formalized languages. Given Tarski's insistence that his analysis did not apply to natural languages, the connection here is not completely solid. But the basic moves of postulating "abstract languages" and treating their semantic analysis extensionally are indeed to be found in Tarski, and both the strengths and weaknesses of the view are to be found clearly in his work. Thus it seems in order to take a careful look at Tarski's work to see whether it really provides a viable "pure semantics."

6.9—
Tarski's Semantics

Tarski's work on truth, and Davidson's claim that Tarski's technique can also yield an account of meaning, have garnered a great deal of attention, and have been met with sharply polarized reactions. A great deal

of the literature discussing Tarski's work has been devoted to the problem of deciding just what Tarski's theory does —what kind of theory it is, and what it is a theory of . It is thus probably wise to begin by presenting some of the essentials of Tarski's account. Tarski wrote three papers that are of central importance to his work on truth: "The Concept of Truth in Formalized Languages" (1956b), "The Establishment of Scientific Semantics" (1956c), and "The Semantic Conception of Truth and the Foundations of Semantics" (1944). The first of these papers begins with the following synopsis: "The present article is almost wholly devoted to a single problem—the definition of truth . The task is to construct—with reference to a given language—a materially adequate and formally correct definition of the term 'true sentence' " (Tarski 1956b: 152, italics in original).

Tarski's project is thus one of providing a "definition" of truth that is "materially adequate" and "formally correct." This terminology requires some comment. It is somewhat controversial what Tarski meant by 'definition' and what he achieved in this regard. For the term 'definition' has acquired a specialized usage in metamathematics that implies something at once weaker and stronger than some more ordinary uses of the word. If one constructs a set theoretic model M(D) of a mathematical domain D , then a concept C in D is said to be "defined by" the set-theoretic construction that corresponds to it in the model.^[8] Thus, for example, in the Principia Mathematica, numbers are said to be "defined" by sets; but it is quite controversial whether this result really has any consequences with respect to the nature of numbers. So a logician's expressed desire to provide a "definition" of truth may easily turn out to be merely a desire to provide a model-theoretic construction characterizing truth in a language. However, Tarski does say things that indicate that he may be interested in more than this. He says, for example, that it is his wish to provide a "definition" that corresponds as closely as possible to familiar uses of the word. And what he explicitly cites as the familiar use of the word is the "classical" conception of truth in which truth is understood informally to consist in correspondence to reality. This will have direct consequences for the conditions Tarski believes to be relevant to the "material adequacy" of a truth definition.

Before moving on to these conditions, however, it is important to note that Tarski does not aim to supply any general definition of truth-in-any-language-whatsoever. Rather, truth-definitions are relativized to languages. The stated reason for this is that the "same sentence" can appear in different languages, and may be true in one, false in another, and

meaningless in a third. Tarski is thus taking "sentences" or "expressions" to be defined in terms of concatenations of graphemes or phonemes, an assumption that arguably is not completely unproblematic. So the search for a "definition of truth" is really a search for the conditions that must be met by a definition of truth relative to any language L . One such condition is "material adequacy," by which Tarski means, informally, that the truth-theory for L, T(L) , should have the consequence that, for any sentence S in L, T(L) assigns S the value TRUE iff what is asserted by S is true. Tarski suggests that the constraint that truth theories have such biconditionals as consequences be formulated in terms of a schema, which he calls convention T :

(T) X is true, if and only if, p ,

where p is a schematic letter to be replaced by a sentence of L and X is a schematic letter to be replaced by a ("structure revealing") name of the sentence that replaces p . He writes that "we shall call a definition of truth 'adequate' if all these equivalences follow from it" (Tarski [1956b] 1985: 50). Tarski refers to this conception of truth as "the semantic conception of truth" (ibid., 51), the point being that truth is defined in terms of relationships between expressions and states of affairs in the world (hence a semantic relationship), rather than being defined syntactically in terms of derivability from formally specified axioms. (This point, often glossed over today, was perhaps the most significant feature of Tarski's approach in the climate in which it was first propounded.)

The issue of "formal correctness" is driven by several concerns Tarski raises with respect to classes of languages that are not subject to the kind of definition he desires. First, he believes that languages can be characterized in the desired fashion only if they are "exactly specified," in the sense that in "specifying the structure of a language we refer exclusively to the form of the expressions involved" (ibid., 52). This excludes languages that involve lexical ambiguity and elements that are dependent upon pragmatics or context, such as demonstratives and indexicals. Second, he points out that certain classes of languages—languages that he calls "semantically closed"—are inconsistent because they are prone to the generation of paradoxes such as the antinomy of the liar. Languages are said to be "semantically closed" if they contain the resources for naming expressions occurring within the language, for applying the term 'true' to sentences in the language, and for stating the truth conditions

of the language (ibid., 53). The concept of truth, Tarski claims, is not definable for semantically closed languages.

It is perhaps obvious that these observations lead to the conclusion that truth is not definable for natural languages, since these are lexically ambiguous, employ demonstratives and indexicals, and have resources for referring to their own elements and making truth-assertions about them. Tarski embraces this conclusion, though other writers have since attempted to treat these features in a way that avoids Tarski's negative result. More easily overlooked is the fact that the linguistic features that interest Tarski include things like axioms and theorems, which play a large role in logic and mathematics, and are strongly connected with the notion of truth in those domains, yet are notably absent (not to mention irrelevant to empirical truth) in natural languages. This would be highly problematic if Tarski's stated aim was to provide a general "definition" of truth, but is perhaps innocuous so long as one is carefully attentive to the fact that what he is about is providing a model-theoretic characterization of truth for those languages for which this might be done.^[9]

The definition of truth is constructed out of a more basic notion of satisfaction . Satisfaction is a relation that obtains between any objects and a special class of expressions called "sentential functions," which are expressions such as "X is white" or "X is greater than Y ." (Sentential functions are differentiated from sentences in that they may contain free variables.) Intuitively, an object O satisfies a sentential function F if replacing the variable in F with the name of O results in a true sentence. This, however, will not serve as a definition of "satisfaction" for Tarski's purposes, as his aim is to define "truth." And so he employs another strategy—that of "defining" satisfaction for a language L in an extensional fashion. In order to accurately represent Tarski here, I shall cite his own text:

To obtain a definition of satisfaction we have rather to apply again a recursive procedure. We indicate which objects satisfy the simplest sentential functions; and then we state the conditions under which given objects satisfy a compound function—assuming that we know which objects satisfy the simpler functions from which the compound one has been constructed. (Tarski [1956b] 1985: 56, emphasis added)

From this definition of satisfaction for sentential functions, one follows for sentences (functions in which there are no unbound variables). Sentences are either satisfied by all objects (in which case they are true) or

else they are satisfied by no objects (in which case they are false). This, indeed, provides a definition of truth: "Hence we arrive at a definition of truth and falsehood simply by saying that a sentence is true if it is satisfied by all objects, and false otherwise " (ibid.).

Here we have a general schema for talking about truth in a language L , given that L falls within the specified class of languages. It is a schema for truth-definitions rather than a general truth-definition because the two more basic semantic notions of naming (or, to employ Field's [1972] useful paraphrase "primitive denotation") and satisfaction, are defined for expressions only relative to a language.

Given Tarski's desire for the introduction of all semantic terms only by definition, it is important to be attentive to the way in which satisfaction and primitive denotation are treated in Tarski's articles. For the "definition" of 'satisfaction' for a language L consists merely in (a ) providing a mapping from simple functions to the sets of objects that satisfy them, and (b ) providing a recursive rule for producing such a mapping for complex functions, given the values of the simple functions. And similarly, one may assume that the "definition" that would be given for the relation of primitive denotation would simply be a mapping from a class of expressions to a set of objects. These are "definitions" in the mathematician's sense of exactly specifying the function performed in settheoretic terms. But they are surely not "definitions" in the sense of explaining what satisfaction or designation consist in . This has led to some criticisms of the scope of Tarski's accomplishment, some of which (Field 1972 and Blackburn 1984) I shall allude to in developing a more general analysis of the problems with the notion of pure semantics. These and other concerns cast some doubt upon whether Tarskian semantics in fact provides the "pure semantics" desired by the critic of the Semiotic Analysis.

6.9.1—
A Nonconventional Analysis?

First, it is by no means clear that the analysis presented by Tarski renders the semantics of languages essentially nonconventional. Tarski says that we "indicate which objects satisfy the simplest sentential functions" (Tarski [1956b] 1985: 56, emphasis added). But in the context in which he is speaking, this "indication" can be interpreted in either of two ways, both of which are plausibly interpreted in conventional terms . On the one hand, one might wish to supply a semantic analysis of an existing formal language (say, Hilbert's geometry). In this case, one is ap-

proaching an existing public language game that is conventionally established. The ability to "indicate" the objects that satisfy the sentential functions in such a language game by no means shows that the relationship of satisfaction is essentially nonconventional. Making the mapping from expressions to interpretations explicit in no way implies that the preexisting system is nonconventional. And indeed the way in which the mapping is indicated in the formal model is itself conventional.

Alternatively, one may be defining a new language game de novo, and hence stipulating its semantic assignments. Here there is no preexisting convention-laden public language game. But in doing this one is necessarily defining a convention for semantic interpretation. Doing so by no means shows there is an independent stratum of meaning or even satisfaction that obtains apart from the conventions established by the theorist. At best, if there is a preexisting set of markers, there are infinite numbers of mappings between that set and sets of objects. And mappings do, indeed, exist independent of mapping conventions. But a mapping, per se, is not a semantic relationship. Nor does the existence of mappings that are independent of conventions establish the existence of semantic relations that are independent of conventions. Semantic assignments are represented by mappings and involve mappings, but mappings are not themselves semantic.

6.9.2—
The Conventionality of the Markers

Tarski has also made an illicit move in assuming that "sentences" and "expressions" that constitute the domain of the mapping can be defined in terms of concatenations of graphemes or phonemes, and the pure semanticist would be wrong in concluding that this amounts to a nonconventional definition. There are at least three problems here. First, as argued above, markers and counters are conventional in character. Thus, while it may be right to say that the same physical patterns may get concatenated in more than one language, it does not follow that the same complex markers are employed, nor that identical strings of markers in two languages are the same sentence. Second, the marker kinds themselves are underdetermined by physical pattern and are essentially conventional. Third, if sentences are defined in terms specific to their mode of representation, it is not clear how one is to account for the fact that the same sentence can be both spoken and written, and can potentially be represented in other modalities (e.g., Morse code, ASCII coding, etc.) as well. As an idealization, Tarski's move is permissible within certain

bounds; as a real definition, it seems inadmissible. This seems to undercut the pure semanticist's claim that Tarski's semantics is free from conventional taint. Even if we agree that the mapping from expressions to objects is nonconventional, the overall language is still conventional because the domain of expressions is conventionally established.

6.9.3—
Field's Argument

In a justly famous article, Hartry Field (1972) undertakes an extensive examination of Tarski's theory of truth. Field argues that Tarski succeeded in reducing truth to what Field calls "primitive denotation," but failed to define primitive denotation in nonsemantic terms. And thus, in Field's view, the remaining project in semantics for naturalists such as himself is to provide a nonsemantic account of primitive denotation. The crux of Field's argument is that merely extensional characterization of semantic notions such as denotation or satisfaction, while adequate for model-theoretic purposes, does not constitute a genuine reduction of semantic terms, any more than we may produce a genuine reduction of the notion of valence that proceeded by saying

("E ) ("N ) (E has valence nºE is potassium and n is +1, or . . . or E is sulphur and n is -2). (Field 1972: 363)

There seem to be at least two problems with merely extensional characterizations, on Field's view. First, they do not reduce semantic properties to nonsemantic properties in the sense of "reduction" employed in the sciences and relevant to the incorporation of semantics within the project of physicalism. Second, they seem to license unfortunate would-be "reductions": "By similar standards of reduction, one might prove that witchcraft is compatible with physicalism, as long as witches cast only a finite number of spells: for then 'cast a spell' can be defined without use of any of the terms of witchcraft theory, merely by listing all the witch-and-victim pairs" (ibid., 369).

Field seems right in his claim that Tarski's extensionally based account of his primitive semantic properties fails to yield any robust account of their nature. What Field directly argues is that Tarski's characterizations do not yield a reduction of these properties in terms that demonstrate compatibility with physicalism, but we shall see below in Blackburn's criticisms that this point can be generalized beyond Field's physicalistic agenda as well.

6.9.4—
Blackburn's Argument

Simon Blackburn (1984) argues that Tarski in fact gives no definition of any semantic notions, but merely describes a "neutral core" that "connects together truth, reference, and satisfaction" but "gives us no theory of how to break into this circle; that is, of how to describe what it is about a population which makes it true that any of their words or sentences deserve such semantic descriptions" (Blackburn 1984: 270). Blackburn's chapter on Tarski and truth presents a number of insights that are not easily separated. But one important observation he makes is that the specific character of Tarski's characterizations of the semantic notions renders them ill suited to serve as definitions. In particular, there are two problematic features of these characterizations: their extensional character and their relativization to a language. First, in giving a list-description of, say, names in language L and their denotations, one does nothing to explain what the property is that is being characterized. A list-description tells you what objects are named by what terms, given that you know that the property characterized by the mapping is supposed to be naming in a particular language, but it tells you nothing about naming per se. One can make use of these lists only if one also knows that they are descriptions of how L -speakers use this set of expressions as names, and hence we have no real definition here (see ibid., 268-269). Second, the definition of, say, 'satisfies' for L1 is completely different from the definition of that same word (or a corresponding word) relative to L2 . The satisfaction relation is provided merely in terms of extensional characterization for particular languages . It is defined differently for each language individually, because there is a different mapping of expressions onto objects in each language, and there is no overarching notion of satisfaction apart from those relativized to particular languages. If satisfaction were really defined extensionally (indeed, even if it were fully accounted for in extensional terms), it would seem to be the case that there is no property or function called "satisfaction" common to L1 and L2 , but rather it would be more accurate to speak of separate notions of satisfaction-for-L1 and satisfaction-for-L2 . This, Blackburn observes, is a problem for Tarski's account. For although Tarski is surely right in relativizing truth to a language,

it does not follow that there is nothing in common to . . . truth as expressed in English sentences, and as expressed in those of any other language whatsoever. Reflection upon the application of an abstract semantic system to any actual population shows that there must be. (ibid., 270)

In other words, there is clearly something in common to notions such as truth or satisfaction across languages. But list-accounts for individual languages do not provide any indication of this common feature. Hence Tarski's analysis does not do an adequate job of "defining" the semantic properties.

I believe that this part of Blackburn's analysis is quite right. For our purposes, however, there is a certain aspect of Blackburn's approach that cannot be simply accepted without some justification. For when Blackburn says that Tarski does not tell us how to "break into the circle" of truth, reference, and satisfaction, he glosses this by saying that it gives us no theory "of how to describe what it is about a population which makes it true that any of their words or sentences deserve such semantic descriptions" (ibid., 270). Blackburn explicitly rejects the idea that one can separate a purely semantic account from a pragmatic account that ties a purely abstract language to the actual practices of a community (ibid., 269). This is, of course, very much in accord with what I wish to argue in this chapter. But by the same token, it is the very point which the fictional critic of this chapter wishes to contest. So the most we are really permitted to take from Blackburn here is the conclusion that Tarski's analysis does not provide a definition of the semantic terminology in nonsemantic terms (except perhaps in the model-theoretic sense of "definition"). What we are not licensed to conclude from Blackburn's arguments is the more robust thesis that the notions of satisfaction and primitive denotation presented by Tarski do not constitute notions that are legitimately semantical, yet do not have conventional elements.

At best, we might be able to make the following argument towards that conclusion on the basis of Blackburn's considerations. We might regard Tarski's "definitions" in one of the following two ways: (1) as attempts to give accounts of familiar semantical notions in nonsemantic terms, or (2) as stipulative definitions of how he is going to use those terms. If we interpret the definitions as stipulative in character, Blackburn's observations are enough to show that "denotation" and "satisfaction" thus defined are not really semantical notions at all, but merely model-theoretic counterparts of semantical notions. If we interpret Tarski in the first way, Blackburn's arguments show that Tarski has not successfully reduced the familiar semantical notions, but Blackburn has not shown that these notions are not "pure" in the sense of containing no conventional (or "pragmatic") element. This will require a further original consideration of the import of Tarski's work.

6.10—
"Pure Semantics" and "Abstract Languages"

The suggestion at hand, then, is that Tarski has employed notions of denotation and satisfaction and has characterized them for model-theoretic purposes in purely extensional (and nonconventional) terms—and, while his list-accounts do not provide any account of the nature of denotation or satisfaction (conventional or otherwise), the relations of denotation and satisfaction may yet be nonconventional in nature. And, moreover, the critic claims that the extensional characterization provided by Tarski is sufficient to show that we have notions here that can be applied indifferently to discursive symbols, thoughts, and mental representations.

I believe that this is the wrong moral to draw from Tarski's work. I further believe that the plausibility this thesis may enjoy derives from a common misunderstanding of what is going on in the formal (modeltheoretic) characterization of a language. Tarski himself differentiates between what he calls "descriptive semantics," which is concerned with describing how an actual group of people employs words, and what he calls "pure semantics," in which a language is considered in the abstract. Blackburn calls the domain of pure semantics "abstract languages," and this kind of locution, I submit, is the crux of the difficulty . For speaking of "abstract languages," as opposed to "languages considered in the abstract" suggests that there are these purely abstract entities called "languages," and it is to these that semantics applies, and the only job left for the descriptive theorist is to link a concrete community of speakers with the right abstract language. Thus many writers seem to see the problem of meaning as being identical to the problem of figuring out which abstract language a given community or individual speaks. Partitioning the problems in this way leads one to think that issues of semantics are all handled on the side of abstract languages which are, from the theorist's standpoint, stipulative in their semantic assignments. (I suppose from the metaphysician's viewpoint they are necessary and eternal.) Issues of conventionality, on the other hand, lie on the side of descriptive semantics. And if you view descriptive semantics as a matter of hooking up an abstract language, complete with semantics already intact, to a community of speakers, then it is natural to view the semantics of language per se as something outside of the web of convention and in the pristine world of abstract objects.

This story is alluring, but it is wrong. To see why it is wrong, it is necessary to tell a better story. The general moral is this: it is every bit as

misleading to confuse languages-considered-in-the-abstract with "abstract languages" as it is to confuse material bodies-considered-in-the-abstract (e.g., in terms of mechanical laws) with "abstract bodies" (e.g., point-masses). Strictly speaking, there are neither abstract bodies nor abstract languages, and features that are bracketed for purposes of abstract analysis are not thereby proven to be inessential. In short, the belief that the domain of semantics is a kind of abstract object called an "abstract language" is to fall prey to another instance of the Fallacy of Reduction discussed earlier in this chapter.

The Fallacy of Reduction, you will recall, consists in giving an abstract description of a phenomenon as a model and then treating the properties that are clarified by the "reduced" model (e.g., the mathematical description) as precisely those properties that are constitutive of the original phenomenon. There are some cases, no doubt, in which the properties retained in the model are precisely those constitutive of the original domain, but such is not generally the case. The mathematics of thermodynamics, for example, does not tell you that the subject matter is heat . (Indeed, the same mathematics applies to information.) And in the case of abstractions such as point-masses, one is indeed faced with fictional entities that do not exist in nature. So long as one bears in mind that one is involved in a theoretical activity that involves abstraction, speaking of point-masses is completely benign. But if we forget the act of abstraction and treat point-masses as the real domain of mechanics—or even as a real part of the objects of mechanics—we have been deceived by our own use of language.

So what is one doing in giving a formal model of semantics for a language? What one is doing here is really just a special case of what one does in giving a model generally—for example, in mechanics or thermodynamics. (Tarski himself is really quite explicit about this, likening the relationship between metamathematics and particular mathematical domains to that between one of the natural sciences and the objects it studies.) In any of these cases, one begins with an intuitively characterized domain consisting of a set of objects one wishes to characterize (say, bodies or sentences) and a set of properties or relationships to rigorously specify (say, gravitational attraction or truth-functionality). One then abstracts or idealizes the objects in one's domain in a fashion that brackets those properties the objects have in vivo that are irrelevant to the problem at hand. One brackets features of bodies such as color, magnetism, and even size when one is doing a theory of gravitation, treating

bodies as point-masses. And one brackets features of languages such as pronunciation, dialectical variation, nonassertoric sentences, linguistic change, and the conventionality of the symbols people really use when one is doing a theory of deduction. This kind of idealization is perfectly legitimate so long as the properties that are bracketed are truly irrelevant to the features one wishes to rigorously characterize. But of course the question of what may safely be bracketed depends entirely upon what aspects of the intuitively characterized domains one wishes to specify: a formal model of particle collisions should be sensitive to size and shape even if a model of gravitation is not, and a formal model of phonetics or pragmatics should be sensitive to features that are irrelevant to truth-functionality.

A formal model of a language (or of anything else) is thus a characterization of a language, viewed under a certain aspect and screening out other aspects of the language in vivo. It is, indeed, possible in some cases to construct artificial languages that actually lack some of the features that one idealizes away from in natural languages—for example, languages that lack lexical ambiguity, ambiguity in surface structure, notational variation, nonassertoric aspects, and change in usage. And indeed one usually constructs one's languages for mathematics and other deductive systems (Tarski's main interest) in a fashion that avoids these features. However, in the description of natural languages, one merely idealizes away from these features. Moreover, even with specialized languages, formal modeling idealizes away from other features—notably, those tied to the way the language is employed by its users. For example, what is called "denotation" in the model is bound up in what the language user does in referring in vivo, "satisfaction" is bound up with what the language user does in predicating in vivo, and so on.

As argued earlier in this chapter, there are two importantly distinct ways of looking at a model, corresponding to two different levels of abstraction one may adopt with respect to the intuitively characterized domain. At the first and milder level of abstraction, one views the model precisely as a model of the specified domain. One views Newton's equations as a model of gravitational interaction between bodies, or a Tarskian truth-definition as a model of truth in a language L . Here one is in fact looking at the initial domain, but viewing it abstractly through the lens of the model. One is making assertions about bodies, albeit bodies-considered-as-point-masses, or assertions about truth in a language L , but truth-characterized-extensionally. This is the "rich" characteri-

zation of the model. Yet one may also perform a second act of abstraction and look at the model itself in abstraction from what it is a model of . One may, for example, look at Newton's laws simply as equations that can be satisfied under particular constraints and can be evaluated using particular techniques, or one may look at a Tarskian model simply in terms of the set-theoretic relations it employs and the valid deductions one may make on the basis of those. Here one has ceased to look at the mathematical construction that started out as a model as a model (for a model is a model of something), and treats it as an independent entity. This is the "sparse" interpretation of the model.

Now this does indeed have the consequence that formal modeling distills a purely abstract object—the construction that is the model sparsely characterized. However, it is incorrect to view this as an "abstract language," for it is not a language at all, but merely an object consisting of a set of expressions, a set of objects, and some mapping relationships between them. One applies the names 'denotation' and 'satisfaction' to some of these relationships, but that is simply an artifact of the process through which we got to the model sparsely characterized. There is nothing about the model sparsely characterized qua set-theoretic construction that makes particular mappings count as denotation or satisfaction. Indeed, there is nothing about the model sparsely characterized that makes them count as anything but arbitrary mappings. (This, I think, is the essence of Blackburn's point.)

Now indeed in the model richly characterized, we are entitled to speak of these functions as "denotation" or "satisfaction"—or, perhaps more correctly, as the extensional characterization of the denotations and satisfaction conditions of particular languages. But the reason for this is that we started out talking about such relations as the features of the intuitively characterized domain that we wished to speak about, and have merely constructed a model that gives a rigorous specification of these properties in a fashion that is "materially adequate and formally correct."

Compare the analogy with a theory of gravitation. If we look at Newton's laws just as equations—as a model sparsely characterized—they tell us nothing about what relationships they are supposed to describe. We may call the variables by names like 'mass' and 'distance', but they are no longer variables signifying mass and distance. Of course they do signify those properties in the model richly characterized, but again that is only because the model richly characterized is obtained by starting from an intuitively characterized domain, performing certain idealizations, and applying a rigorous description to what is left. A mathematization tells

us only the relationships between the features we wish to describe—be they mass or denotation. It specifies only the form of the relations and not the nature of the relata.

As a consequence of this, it is important to see that a formal model of a language no more implies the existence of something called an "abstract language" than a formal model of gravitation implies the existence of things called "point-masses." The model richly characterized is precisely a description of a familiar intuitively characterized domain that uses an abstract object to describe certain properties of that domain. The "language" here is the full-blooded language we set out to describe, not some formal subset of it, and it is fraught with conventionality. The model sparsely characterized is not a language at all, even if we misleadingly use words like "denotation" for a mapping function it employs. All it is is a construction consisting of sets of expressions and objects and a set of mappings between them. Mappings in themselves no more add up to denotation than equations employed in mechanics or thermodynamics or the Mathematical Theory of Communication add up to mass or heat or information.

In short, there is no level at which we find what the critic needs: an "abstract language" that has genuinely semantic relationships but no conventionality. The model richly characterized has semantic relationships, but they are the conventional ones of full-blooded languages. The model sparsely characterized does not suffer from semantic conventionality (though it still presupposes the conventionally sanctioned symbol types that constitute its domain); but it does not involve genuine semantic relationships either, but merely the mathematical-logical form that those relationships in real languages share with many other nonlinguistic systems with which they are isomorphic. Tarskian semantics deals with (real, full-blooded) languages in abstraction from many features found in vivo, including their conventionality. But it does not succeed in uncovering "abstract languages" that can provide the domain for a "pure semantics."

6.11—
Conclusion

It would seem, then, that it is not true that semantics is properly concerned with a set of abstract entities called "abstract languages." It is true that we can begin with full-blooded languages and abstract away from their real-world features in order to be left with an object that is more suitable to rigorous study, much as we may do so in, say, physics. Indeed,

in both cases there are two levels of abstraction: a richly construed model that treats the real-world processes in terms of their mathematical relations, and a sparsely construed model that is a purely abstract mathematical entity. Neither of these, however, has the features needed to count as an "abstract language." The rich model indeed has the features needed to count as a language, but is not truly abstract: the linguistic categories it works with are the convention-laden ones of the full-blooded language . The sparse model is indeed abstract, but there is nothing about the model, as such, that would make it count as a language. This is equally true for the semantic and the syntactic aspects of language. And hence the criticism that the Semiotic Analysis is really a hybrid of a nonconventional pure semantics (and pure syntax) plus a conventional element required only for symbols used in communication fails.