Chapter 4
Compositional Semantics and Meaning

4.1 Introduction

A compositional-semantic theory (CST) may be defined as a finite set of axioms such that for each member of some set of expressions, there is a semantic property such that the set of axioms logically entails a theorem that says of the expression that it has the semantic property.

Here's a boring example of a CST: the set [C] of axioms (a) and (b):

This set meets the conditions I just stated for something to be a CST. But it is hard to see what could be interesting about [C], what it might be useful for.

Here's a more interesting example: a CST that entails for each Arabic-decimal numeral, a theorem that says which number is conventionally expressed by that numeral:

[D]

(1) ƒI(x) =df

0 if x = "0", 1 if x = "1", 2 if x = "2", 3 if x = "3", 4 if x = "4", 5 if x = "5", 6 if x = "6", 7 if x = "7", 8 if x = "8", 9 if x = "9", or if (x) > 1.

The -notation is a conventional way in algebra for abbreviating an expression for the sum of a number of similar terms. Let "A_i" stand for an algebraic expression of arbitrary complexity in which the symbol "i" occurs one or more times, and let "A_n" denote the expression obtained from "A_i" by substituting a numeral n for every occurrence of "i" in "A_i". Then the abbreviation that the -notation represents may be defined as follows:

A_i =_df A₁ + A₂ + . . . + A_n

Here are definitions for the two functions, (x) and g(x,i), used in the theory [D]:

(x) =_df the number of characters in the string x.

g(x,i) =_df the ith character from the right of string x.

For each of the infinitely many Arabic-decimal numerals, [D] entails a theorem that says which number is conventionally expressed by that numeral. Take the numeral "3652" for example. [D] tells us that the number conventionally expressed by "3652" is ƒ_I("3652"). Since ("3652")=4, and 4>1, the definition of ƒ_I tells us that ƒ_I("3652") is

Unpacking the -notation we get that ƒ_I("3652") is

Noting that g("3652",1)="2", g("3652",2)="5", g("3652",3)="6", and g("3652",4)="3", and doing the subtractions in the exponents, we get that ƒ_I("3652") is

And since according to the definition of ƒ_I given in [D], ƒ_I("2")=2, ƒ_I("5")=5, ƒ_I("6")=6, and ƒ_I("3")=3, we get that ƒ_I("3652") is

21 + 510 + 6100 + 31000

which is 3652. So, [D] logically entails, assuming arithmetic, that the number conventionally expressed by the Arabic-decimal numeral "3652" is 3652.

An interesting feature of [D], besides its being finite and yet entailing for any of infinitely many Arabic-decimal numerals a theorem that says which number that numeral conventionally expresses, is its apparent ability to shed light on just how the number that an Arabic-decimal numeral conventionally expresses is determined from the parts and syntactic structure of the numeral. That is, [D] seems to show how certain semantic features of members of a set of complex linguistic expressions are determined by facts about the parts and syntactic structures of those complex expressions. Looking at [D] we might conclude that the simple Arabic-decimal numerals each contribute, whenever they occur within an Arabic-decimal numeral, a unique number: "0" contributes the number zero, "1" contributes the number one, "2" contributes the number two, and so on through "9" which contributes the number nine. [D] also shows how the syntactic structure of an Arabic-decimal numeral can be seen to contribute to the determination of what number the numeral conventionally expresses. The position from the right within an Arabic-decimal numeral which a simple Arabic-decimal numeral occupies is, of course, a syntactic feature of the numeral, and this feature determines what we can call the position-weight of the simple Arabic-decimal numeral. If a simple Arabic-decimal numeral occurs in the nth position from the right of an Arabic-decimal numeral, the position-weight of the simple numeral will be . We can define the full-weight of a simple Arabic-decimal numeral k that occurs within an Arabic-decimal numeral as the product of the contribution of k itself and k's position-weight. Then, the number conventionally expressed by any Arabic-decimal numeral N is the sum of the full-weights of each of the simple Arabic-decimal numerals in N. [D] shows the substance of all of this quite elegantly. Thus, in examining [D], we might come to feel that we have learned something about how each of the simple symbols and certain syntactic features of an Arabic-decimal numeral contributes to the determination of the number expressed. And learning this sort of thing might be interesting to us for one reason or another.

More generally, a CST can be interesting when it is able to show how semantic features of complex expressions might be determined from features of the parts of those expressions and the syntactic arrangement of those parts. And CSTs that philosophers and linguists have been interested in have generally worked by saying something about each of the simple parts of the members of a class of complex expressions and about the basic syntactic structures of those complex expressions.

Notice that [D] does not tell us what the notion of an Arabic-decimal numeral conventionally expressing a number amounts to, that is, [D] doesn't provide an analysis of the relation that holds between an Arabic-decimal numeral and a number when the former conventionally expresses the latter. Of course, [D] does entail the following:

But since [E], even if it is true, is not metaphysically necessary - if things had been different, "3652" might have conventionally expressed the number 310 -, it cannot betaken as an analysis of the relation in question. And it seems clear that nothing else that [D] entails will be an analysis of that relation.

I would like to say that the definition I have provided of a CST precludes any CST from being able to entail an analysis of the semantic notions its theorems ascribe to expressions. But I can't say that for an annoying reason. Suppose, to take a single example, that there was a finite theory * which entailed an analysis of the conventionally-expresses relation employed in [D]. Then, the conjunction of [D] and * will be a CST by my definition and it also entails an analysis of the semantic notion with which it is chiefly concerned. Of course, all the "CST work", so to speak, of this CST is done by [D]. * is just tacked on to [D].

Besides this, I have no argument against the possibility of a CST that worked only if it also provided an analysis of the semantic notions with which it is chiefly concerned. But this much is true: it does not follow from the definition of a CST that a CST provides an analysis of the semantic notions with which it is chiefly concerned. A CST, at least in principle, may employ semantic notions that it does not define.

And that being true it cannot be said that providing a CST in itself is providing an explication of the semantic notions it talks about.

I will make this same point in another way.

Does it follow from a CST's entailing a theorem that says that a linguistic expression has a certain semantic property that the linguistic expression actually has that property? No. Consider the theory [D'] which is identical to [D] except that the clause in the definition of ƒ_I which applies to numerals of length greater than one is now:

The theory [D'] is a CST that logically entails, assuming standard arithmetic, that the Arabic-decimal numeral "3652" conventionally expresses the number 310. That's false. And when a theory entails falsehoods, we say that the theory is false. Accordingly, we say that [D'] is a false theory and that [D] is a true one. Plainly, there are infinitely many false CSTs each of which purports to say for each Arabic-decimal numeral the number it conventionally expresses.<1>

What makes a CST true or false, of course, is whether or not the expressions the CST is concerned with have the semantic properties that the CST's theorems say that they have. And notice that if we would like to evaluate a CST for truth or falsity, we will at the very least need to know something about the semantic notions the CST's theorems ascribe to the expressions with which the CST was concerned. Let me elaborate.

[D] was concerned with Arabic-decimal numerals and for each of these entailed a theorem that, for a specific number, said that it - the numeral - had the semantic property of conventionally expressing that number. So to correctly evaluate [D] for truth or falsity, it is necessary to know, for each relevant particular number, under what conditions an Arabic-decimal numeral has the property of conventionally expressing that number. And we know, I take it, that the idea that a thing conventionally expresses some other thing is the idea that among some group of people the first thing conventionally expresses the second. When we say that an Arabic-decimal numeral, say "3652", conventionally expresses the number 3652, what we have in mind is, I believe, thatamong a certain group of people, viz., more-or-less, us, that numeral conventionally expresses that number. It was understanding, at least somewhat, the convention that holds among us with respect to the Arabic-decimal numerals that allowed me to judge that [D] is true and that [D'] is false.

We need to have some sort of knowledge of the semantic properties that a CST assigns to an expression in order to be able to judge the CST to be either true or false. That knowledge could be either theoretical knowledge of the semantic properties in question, though it rarely, if ever, is, or, some sort of pre-theoretic - or, as is sometimes said, intuitive - knowledge of those properties. If we don't know what certain property terms in a theory are about, we cannot judge the theory for truth or falsity, and, a fortiori, if we don't have an understanding of the semantic notions employed in a CST independently of the CST itself, then it will be impossible to evaluate the CST with respect to its truth or falsity.

It follows from this last point that, as I am conceiving things, we can hardly take a CST by itself as defining, in the sense of providing an analysis of, the semantic notions its theorems employ. Either the semantic notions employed in a CST are taken as primitive notions with respect to the CST or it is impossible to judge the CST for truth or falsity.<2> But since I have defined a CST as something that entails theorems that ascribe substantial features to linguistic expressions, that is, as something that can be evaluated for truth or falsity, the semantic notions a CST employs must be primitive with respect to the CST. But if the semantic notions employed by a CST are primitive with respect to the CST, then the CST will hardly serve as a definition, that is, an analysis, of thosesemantic notions.

Of course, one can choose to shun making true/false judgements with respect to [D] and [D'] - why one might do this I'll leave open. I can pretend - or even stipulate - that I don't know what the expression "conventionally expresses" means in either [D] or [D'], that is, I can leave that phrase as an uninterpreted expression of each of them. Though I might still call [D] and [D'] compositional "semantic theories", this would be, according to the way I have set things up, at best merely a faon de parler, and at worst, a mistake. The definition I give for the notion of a CST in the first paragraph of this chapter will have it that neither [D] nor [D'] is a CST any more: neither of them entails theorems that say something about the semantics of members of some class of expressions, or about anything else for that matter, since there occurs in each of them an uninterpreted expression. More specifically, since neither [D] nor [D'] entails theorems that say anything about the semantics of expressions, neither of them is, I should think, a semantic theory, and, since neither of them entails anything that can be said to be true or false, neither of them is even a theory in the usual sense of that term.

It is possible, of course, to take [D] and [D'] as two possible definitions by stipulation of the expression "conventionally expresses". In that case, neither [D] nor [D'] enlightens us as to what any prior, perhaps ordinary, notion of conventionally expresses amounts to. Quite the contrary. If we take either [D] or [D'] as a definition by stipulation of "conventionally expresses", we are choosing to ignore whatever might have been our previous understanding of that expression, and to use either [D] or [D'], as the case may be, as the sole supplier of content for it. But since, as was just noted, neither[D] nor [D'] can be considered a CST, strictly speaking, we have not found a method whereby a CST is used to define a semantic notion. We defined by stipulation the orthographic type "conventionally expresses", but we have not discovered a definition, in the sense of an analysis of some sort, of some notion of conventional expression.<3>

A CST by itself cannot be used as a definition, in the sense of an analysis, of the semantic properties its theorems ascribe to the linguistic expressions with which it is concerned.

So much for introductory comments concerning CSTs. Now I will talk about how CSTs might help with a theory of meaning.

4.2 Compositional Meaning Theories and Compositional Truth Theories

There are two kinds of CSTs that have been of particular interest to philosophers concerned with meaning. These are compositional meaning theories (CMTs) and compositional truth theories (CTTs).

A CMT for a language L is a finite set of axioms such that for every sentence of L and every proposition , means in L if and only if logically entails a theorem that says that means in L.

A CTT for a language L is a finite set of axioms such that for every sentence of L, logically entails a theorem of the form " is true in L if and only if s" where in place of "" there will be a structural description<4> in the metalanguage of the sentence , and in place of "s" there will be a metalanguage translation of .<5>

There seem to be lots of examples of CTTs. It is moderately easy to provide aCTT for an interpreted first-order language as well as many other formal languages, and for large fragments of natural languages. But providing a CTT for an entire natural language has proved a difficult matter. A central problem for this task has been the accommodation of propositional-attitude sentences within a CTT. No one knows how to do this in a way that is wholly satisfying. I will return to this matter in a moment. Let me say something about CMTs first.

There are no interesting examples of CMTs. Not even one. Not even for the simplest language.<6> The reason for this is pretty straightforward: no one knows what the logical form is of sentences like "'Snow is white' means in English that snow is white". Without knowing the logical form of such a sentence, it cannot be known how to derive the sentence via the laws of logic from some set of axioms. And another way to put this is that we don't know what are the referents of the "that"-clauses of meaning-report-sentences. Of course, as I have set things up above in chapter 3, we are entitled to say that these things are propositions. But that doesn't get us far. What we would need to know is how propositions are compositionally determinable, that is, we would need to know operations that can be performed on word meanings given their syntactic arrangements in sentences, and these operations would have to allow us to compute the propositions that are the meanings of sentences in which they occur. What we need is what we had in the case of [D] above which computed the numbers conventionally expressed by Arabic-decimal numerals: we knew operations on certain small numbers that allowed us to compute the bigger numbers that complex Arabic-decimal numerals express. But what we need for a CMT is exactly what we don't have. We don't knowwhat propositions are and we don't know what should be assigned to the basic vocabulary of a language, so a fortiori we don't know what operations should be performed on such things to allow us to compute the things that propositions are supposed to be. In short, it seems that we don't know any of the things that we ought to know to know that there are CMTs. But perhaps that is not right. There are arguments some philosophers have offered why, even if we don't know what propositions are and how they might be computed from word-sized meanings, we still need to believe there are CMTs. I will discuss these arguments a bit later in the chapter. But I should think that given the antecedent lack of knowledge of any of the essential materials for constructing a CMT, belief in CMTs should be eyed with a healthy amount of scepticism.

There is a connection that it is good to keep in mind between CMTs and CTTs. If propositional-attitude sentences turn out to be accommodated in CTTs as relational, but not as relations to sentences, then apparently the "that"-clauses complements of propositional-attitude verbs will be referential singular terms that refer to propositions. But if this is true, then presumably such propositions will be determinable on the basis of the assignments by CTTs of referents to the terms that occur in the "that"-clauses. So whatever gets assigned by a CTT as the referent of a term in a "that"-clause will be the sort of thing that can help determine the proposition that is the referent of the "that"-clause. But if the referents provided by CTTs of terms in "that"-clauses can be used to compute these propositions, then these same things can be used by CMTs to compute propositions as well. So it looks like the existence of a CTT will entail the existence of a CMT if propositional-attitudes are accommodated by CTTs as relations to propositions.Notice also that any CMT for a language will entail a CTT for a language. This is true since the following inference schema is valid:

"s" means in L that s

"s" is true in L if and only if s

Thus, if propositional attitudes are in fact construable as relations to propositions, then there will be a CMT for a language if there is a CTT for that language, and there will be a CTT for that language if there is a CMT for it. Or, in other words, if propositional attitudes are relations to propositions, then there will be a CMT for a language just in case there is a CTT for it.

What this means, in part anyway, is that if a theorist wants to shun CMTs with their propositions and other abstracta, that same theorist will have to shun the relational view of propositional attitudes unless she or he takes the view that propositional attitudes are relations to sentences or perhaps some other sort of thing. Davidson and Davidsonians take up a course like that. They deny CMTs but insist on CSTs and yet, since they take propositional attitudes to be relational, are forced to take them as relations to public-language sentences. That is the fast version of that story at any rate. I point all this out now because I think it is good to keep in mind that either CTTs and CMTs stand and fall together or you are not a relational theorist about propositional attitudes or you construe them as relations to sentences.

With all this said, I would now like to look at how CSTs are supposed to help in a theory of meaning.

4.3 Meaning and Naturalizing CSTs

It's a real popular idea that somehow it is because we stand in some sort of cognitive relation to a CST that our sentences mean what they do. The idea that is of interest to me is summed up by the question of whether [E] can be the correct form of a theory of the actual-language relation:

[E]P uses L just in case RM(P,L)

where "L" is a compositional-semantic theory of some sort and "RM" is a relation that holds between a population and a CST just when the population uses the language that the CST is a CST for.

There are two sorts of problems which philosophers generally confront when they hope for a theory of the actual-language relation with the form [E]. First, they need to show that the sort of CST they require is available for every usable language. And second, they have to say precisely what RM is. Nobody has ever done either one of these things. I will discuss the second sort of problem in a bit. Right now I will just mention a few famous attempts to do something like provide a theory of the actual-language relation with the form [E].

4.3.1 Davidson and Peacocke and Intentional Relations to CTTs

Davidson is probably the first to suggest that the notion of meaning is best understood in terms of some sort of a relation a person or population stands in to a CST.<7> More specifically, he thinks that there are not going to be CMTs even if every usable language has a CTT and that CTTs play crucial roles in all the relevant meaningphenomena. He has done quite a bit of work towards trying to show that CTTs exist for natural languages, including suggesting a widely influential theory of propositional attitudes which casts them as relations to public-language sentences.<8> I am doubtful of the success of Davidson's treatment of propositional attitudes, but I won't discuss this matter here.<9> Davidson has never directly discussed his program in terms of the provision of an actual-language relation, but Peacocke shows how to speak about Davidson's project in those terms.<10> I will not discuss the details of either Davidson's or Peacocke's suggestions about meaning and truth-theories. Rather I will just make some brief comments about why I believe that a Davidsonian-style theory will not be able to work as a theory of meaning as I have set things up at any rate.

For Davidson usable languages enjoy CTTs without enjoying CMTs. But this will mean that any relation a group might stand in to a language via a CTT for that language, it will stand in to indefinitely many languages.

Consider a CTT for English. It will entail both [a] and [b]:

[a] "Snow is white" is true in English just in case snow is white.

[b] "Snow is white" is true in English just in case snow is white and 2+2=4.

Both [a] and [b] are true about the English sentence. But imagine a language called English* which is just the same as English except that "snow is white" means in it that snow is white and 2+2=4. The very CTT which was adequate for English and entailed [a] and [b] above will be perfectly adequate for English* as well. And that means that any relation that we stood in to English via that CTT, we also stand in to English* via that CTT. And it should be obvious that there are indefinitely many languages such thatthe very same CTT alluded to above for English will also be a CTT for them. But the actual-language relation must be more discriminating than this. We don't speak English*. We speak English. Therefore, it seems that no relation to a CTT can be the actual-language relation. CTTs don't determine the meanings of sentences.

Well, that is not quite right really. For if it turned out that there were CMTs for natural languages and that the actual-language relation could be glossed in terms of bearing a certain relation to a CMT, then you could talk about a relation to a CTT as well since a CMT will entail a CTT. Of course, in that case, it be pointless to talk about the relation to the CTT since it was the relation to the CMT that was doing all the work. Anyway, the Davidsonian program eschews CMTs, so this wouldn't be an option for a Davidsonian.

Davidsonians are unruffled by this sort of talk, of course. On the one hand, Davidsonians seem to believe that there will be certain sorts of CTTs that will be able to be used in the interpreting of sentences by language users and that if this is the case, whatever the case is with the notion of meaning, everything that needed to be explained will have been explained by the provision of a CTT and a statement of how it is used in processing. And on the other hand, the Davidsonian eschews the project of giving necessary and sufficient conditions for meaning, that is, for analyzing the concept of meaning as a Gricean is interested in doing. But in any event, the Davidsonian program seems to be quite inadequate for helping out the Gricean.

4.3.2 Field, Fodor, and Naturalizing Truth

Hartry Field in his famous paper on Tarski's theory of truth<11> suggested a method for giving a naturalistic gloss of the truth predicate in which the notions of primitive denotation employed by Tarski-style truth theory are explicated in naturalistic terms. Field's project was not to provide a theory of meaning in that paper, but Jerry Fodor has recently suggested that the sort of thing that Field wanted to do with the truth-predicate would help us understand meaning:

Given a truth definition, the content of mental representations is determined by the interpretation of their primitive nonlogical vocabulary. So it's the interpretation of the primitive nonlogical vocabulary of Mentalese that's at the bottom of the pile according to the present view. Correspondingly, we would have largely solved the naturalization problem for a propositional-attitude psychology if we were able to say, in nonintentional and nonsemantic idiom, what it is for a primitive symbol of Mentalese to have a certain interpretation in a certain context.<12>

Note that if there is a finitely-statable translation theory for each public language which takes public-language sentences and provides Mentalese translations of them, then it follows that if Mentalese enjoys a CMT, then so do all public languages. For, for each public language L, if TL is a finitely-statable translation theory for L that takes L-sentences and provides M-translations, and if MM is a CMT for Mentalese, then the conjunction of TL and MM will be a CMT for L.

Fodor in the passage quoted above talks about what determines the content of mental representations. A mental representation for Fodor, of course, is a Mentalese sentence. The contents of Mentalese sentences for Fodor are propositions. So, when Fodor talks about determining the content of mental representation, he is just talking about determining the meanings of Mentalese sentences. So, Fodor seems to think thatsomehow a truth definition, that is, a CTT can determine the meanings of Mentalese sentences.

Fodor appears to be suggesting that if we give a gloss of the primitive non-logical vocabulary of Mentalese, we will have provided a theory of meaning for Mentalese. So, Fodor's claim in the above quoted passage is apparently equivalent to the claim that if we could do with the truth predicate for Mentalese what Field wanted to do with the truth predicates for natural languages, then we will have produced a CMT for Mentalese.

Scott Soames and others have pointed out with respect to Field's suggestion mentioned above, that merely giving a naturalistic gloss of the notions of primitive denotation will not be sufficient for naturalizing a truth predicate: one also has to supply a naturalistic basis for the semantic contributions made by each primitive syntactic structure.<13> The same thing will have to apply to Fodor's suggestion, of course. So, we should suppose, then, that the idea is that if notions of primitive denotation for Mentalese are explained in naturalistic terms, and a naturalistic explication is provided for the semantic contributions of the basic syntactic structures of Mentalese, the result will be a CMT for Mentalese.

This is all fine. And it will help with the notion of meaning if it is true provided there are compositional-translation theories taking public-language sentences into their M-translations, as was indicated above. With all that the actual-language relation, presumably, would be statable in terms of these glosses of the primitive notions of a CTT for Mentalese.

But, in essence, this just is another way of stating the Davidsonian projectdiscussed above. And it won't work for the same reasons. CTTs can't really determine meanings.

On the other hand, we can suppose that Fodor's suggestion is not that a naturalistic understanding the notions of primitive denotation and of the stock of simple syntactic structures mentioned in CTTs will help with meaning, but that a naturalistic understanding of the notions of primitive meaning and of the stock of simple syntactic structures mentioned in CMTs is what will help with our understanding of meaning. So the idea would be that if we could give a gloss of the notions of primitive meaning employed in a CMT and state the naturalistic conditions for the contributions to meanings made by each simple syntactic structure, then we would have enough stuff to explain meaning generally.

Well, this is fine too. If all that could be given, then it would seem that we would be able to explain the actual-language relation in terms of the translation of public-languages into Mentalese and a CMT for Mentalese appropriately naturalized as just discussed. I will discuss below the question of whether there are good reasons for supposing that Mentalese will enjoy a CMT.

I would like to point out here, that I know of no good theory of primitive meaning that would help at all with what a CMT needs. Surely Fodor's attempts to provide such a theory are not sufficient for this purpose.<14> For on the sort of theory that Fodor argues for, a predicate like "dog" (pretend that's Mentalese) will have as its meaning the property of being a dog. But, for well known reasons that property will not suffice as the thing assigned to "dog" by a CMT. A story by Schiffer is helpful here:Ralph came upon a race of creatures which he thought comprised a previously unencountered biological species, and he introduced the word 'shmog' to designate members of that species. "A thing shall be called a 'shmog'," Ralph said, "just in case it belongs to the species of those creatures." Unbeknown to him, however, shmoghood is doghood; Ralph had stumbled not upon a new species but a new race of dogs, and thus the property that 'shmog' has been introduced as standing for is none other than doghood.<15>

But 'shmog' and 'dog' will have to be synonymous for Fodor's theory since they will both stand in the relation that Fodor offers to the same property, the property of being a dog.

Besides this, Fodor doesn't try to explain the naturalistic basis of other sorts of terms at all, like "justice", "sofa", etc. Nor does he try to explain the naturalistic basis for the semantic contributions of the simple syntactic structures of Mentalese. And as far as I know, nobody else has offered a serious attempt at such things either.<16>

So, even if the general story I came to attribute to Fodor would explain meaning if true, there are many crucial missing details that don't seem forthcoming. And on top of all of that, there is the question of whether it is plausible that Mentalese has a CMT. I will get to this below.

4.3.3 Chomsky and Intentional Relations to CMTs

Chomsky has made a suggestion concerning what a theory of the actual-language relation will be like:

We can perhaps make sense of Lewis's notion, "the language L is used by a population P," .... This notion unpacks into something like: each person in P has a grammar determining L in his mind/brain.<17>

A grammar for Chomsky is a "finite characterization" of a language: "the grammar is a system of rules and principles that determines a pairing of sound and meaning".<18> In otherwords, a grammar for Chomsky is a CMT.

But what is it for a grammar to be in a mind/brain? Chomsky introduces a special term, "cognizes", to express the relation that he takes language users to stand in to grammars:

...we cognize the grammar that constitutes the current state of our language faculty and the rules of this system as well as the principles that govern their operation.<19>

And he tells us that "...'cognizing' is tacit or implicit knowledge...".<20> So, Chomsky's theory of the actual-language relation goes something like this: a population P uses a language L just in case each member of P tacitly knows a CMT for L.

Chomsky's motivation for making the relation that we stand in to a grammar one of tacit knowledge is, evidently, concern for the empirical consideration that we surely don't know anything like a CMT for a natural language consciously. Linguistics would be a lot easier than it is if we did. But I am not wholly satisfied with merely suggesting that knowledge of grammars is tacit. For, I don't really know what sorts of things go on with tacit knowledge. I could tacitly know a grammar for Swedish for all I know and just never use it. I am, unfortunately, not a Swedish speaker, however. So, I don't feel clear enough with my intuitive grasp of what tacit knowledge amounts to to feel satisfied with the sort of proposal that Chomsky suggests. Of course, if the notion of tacit knowledge used by Chomsky were clarified, things might be different. But as things stand, Chomsky has not provided a clear statement of what relation we must stand in to a CMT of a language in order to speak the language.

But besides this, there is a compelling counter-example due to Schiffer to the sortof theory that Chomsky suggests which I will discuss presently.

4.4 What Reasons There are for Supposing Natural Languages Have CSTs

The theory of meaning should explain all cases of expression-meaning, not just natural-language meaning. But natural language is a central case, and with respect to the issues this chapter is concerned with all the more so. For philosophers who expect that CSTs will be a central feature of an explanation of meaning seem motivated at least in part by the impressive way that CSTs could help in explaining how finite beings like ourselves could have competence in infinite languages, as natural languages are presumed to be. For CSTs are finite statements that entail an infinite number of semantic truths. Presumably, our natural languages are infinite, and yet, any native speaker seems limited in comprehending and producing novel natural-language sentences only by irrelevant constraints like those of memory and interest. To explain this impressive fact about us, it is thought that there is must be some finite means of stating the facts about the languages that we speak, such that knowing such a statement will allow us to know all the facts about our languages that we seem to know.

But, though a CST surely might be able to help in understanding our competence in the use of really large languages, it is not the only way to so explain our competence.<21> For, suppose that we think in a LOT.<22> And suppose that each natural-language user has lodged in their head a finite device that translates sentences of their natural language into M and that this device works entirely on the basis of the syntactic forms of the natural language- and M-sentences it deals with. The idea is that this sort of device can be usedin the processing of natural-language sentences and can thereby explain the competence of natural-language users as well as a CST could, and yet, this sort of device would not presuppose the existence of a CST since it works wholly syntactically, without consideration of the semantic features of the sentences it deals with. Let's see how such a translation device might work and so explain competence in natural-languages.

Speech production can work in the following way given a translation device. Suppose that Eleanor tells Simon that Wittgenstein is clever. First, it is imagined that Eleanor desires to tell Simon that Wittgenstein is clever and that this desire is realized by the M-sentence "I tell Simon that Wittgenstein is clever" (pretend that that is an M-sentence) being tokened in Eleanor's desire-box. A subroutine of the translation device which constantly scans Eleanor's desire-box looking for sentences that begin with the string "I tell" locates this sentence. It detaches the part of the sentence that follows the "that", that is, it detaches "Wittgenstein is clever", and it sends this to the translator section of the translation device which finds the English language equivalent using wholly syntactic procedures. Eventually, other things being okay, Eleanor utters in Simon's presence this English-language sentence that was produced by the translator. No CST was required in this process.

Something analogous, but in reverse, sort of, happens in speech comprehension. Simon hears Eleanor's sentence. A subroutine takes Simon's internal representation of Eleanor's sentence and sends it to the translator which this time produces the M-sentence "Wittgenstein is clever" (again, pretend this is an M-sentence). This M-sentence is concatenated to a string which was produced by some other subroutine "Eleanor said that"to produce the M-sentence "Eleanor said that Wittgenstein is clever". This string is then placed in Simon's belief-box. Simon believes that Eleanor said that Wittgenstein is clever.

This sketch of how a purely syntactic translation device might be employed in language processing leaves much vague, but the general scheme is as plausible as general schemes that explain language processing by way of CSTs. Thus, CST stories are not the only stories in town and so, it seems, our natural-language competence by itself doesn't require the acceptance of CSTs. All the interesting processing abilities that would be explained by a good CST story can also be explained by a good syntactic-translation device story as well, and this latter sort of story doesn't require CSTs.

Fodor has argued against the above sort of line, that even if language processing can be explained by syntactic-translation devices, that is, without CSTs, still, natural languages must enjoy CSTs because Mentalese must.<23> As already discussed above,<24> if Mentalese enjoys a CST, and if there is a finitely-statable translation function from a natural language to Mentalese, then the natural language will also enjoy a CST. The explanation of language processing by syntactic translation devices does seem committed to finitely-statable translation devices. So, the question of whether natural languages have translation devices comes down to whether Mentalese does.<25>

Fodor believes that their are two properties that Mentalese has that require a CMT for their explanation. First, Mentalese is productive, meaning that it has infinitely many sentences each with its own meaning, and second, Mentalese is systematic, meaning that the simple lexical items and syntactic structures of Mentalese contribute to the meaningsof the larger expressions in which they occur in a systematic way: roughly put, the fact that "Mary loves Bill" means that Mary loves Bill is intimately - systematically - tied to the fact that "Bill loves Mary" means that Bill loves Mary. The productivity and systematicity of Mentalese requires explaining, according to Fodor. Fodor's view is that only a CMT can explain these features of Mentalese.

Schiffer has argued that Fodor is mistaken in believing that only by positing a CMT for Mentalese can we make sense of its productivity and systematicity. Schiffer's argument is that (a) what needs to be explained about the productivity and systematicity of Mentalese is how these features can be founded in some finite basis, "some nonendless way the world is"<26> , (b) this can be explained by what he has called a compositional-supervenience theory for Mentalese, and (c) a compositional-supervenience theory for Mentalese will not require a CMT for Mentalese. I'll briefly discuss the notion of a compositional-supervenience theory and how such a theory can explain the productivity and systematicity of Mentalese.

Pretend that "dogs bark" is an M-sentence. On the LOT hypothesis, then, "dogs bark" will have to have a physical property - we can call it its belief-making property - such that having that property and being tokened in the belief-box is metaphysically sufficient for believing that dogs bark. A compositional-supervenience theory will entail a theorem that says that the belief-making property of "dogs bark" is a specific physical property, and it will also entail a similar theorem for every other sentence of M as well, and it will do all this with finite means. A true or correct compositional-supervenience theory for M gets everything right, that is, it will entail for each M-sentence a theoremthat says correctly what that sentence's belief-making property is. To be more precise, a compositional-supervenience theory for Mentalese will be equivalent to a conjunction of a finite specification of a function, call it fM,, from sentences to physical properties, and an axiom that states that for each sentence of M, fM() is 's belief-making property. Presumably, such a function fM will have to meet the following conditions:

(c1)for each of the finitely many simple lexical items w of M there is a particular physical property such that fM(w)=;

(c2)for each of the finitely many basic syntactic structures t of M which structures n subexpressions of M (for some finite n, n1), there is a function gt from n-tuples of physical properties to physical properties such that, for any expression e of M with structure t and containing the n subexpressions e1, e2, ..., en (in that order), there is a particular physical property such that =gt() and fM(e)=.

And for a compositional-supervenience theory to be true of M, the function fM that it specifies will also have to meet the following condition:

(c3)for each sentence of M and for each proposition , if means in M, then has the property fM() and having fM() and being tokened in the belief-box is metaphysically sufficient for believing .

It should be moderately clear that, if what is needed by way of an explanation of the productivity and systematicity of Mentalese is that it be shown how these features of Mentalese are based in some "nonendless way the world is", then given a true compositional-supervenience theory, the productivity and the systematicity of Mentalese is explained. For clearly, given a true compositional-supervenience theory for M, it will follow that M is productive since each M-sentence will be associated with its unique belief-making property, that is, with the physical property which is the supervenience basefor that sentence meaning what it does. In other words, each M-sentence will have its unique meaning given a compositional-supervenience theory, and, therefore, M will be productive. Likewise, given a correct compositional-supervenience theory, each M-word will contribute to the belief-making properties of M-sentences the physical property assigned to that word by the theory. This contribution will be the same no matter where the word occurs, and so it seems that the contributions of M-words is systematic, and that therefore Mentalese is systematic.

Given that the productivity and systematicity of Mentalese are explained by a compositional-supervenience theory, and I believe that they are, the question comes down to whether or not having a correct compositional-supervenience theory somehow entails having a CMT as well.

Suppose that D is a physical property such that having D and being in the belief-box is metaphysically sufficient for believing that dogs bark. And pretend that "dogs bark" is an M-sentence that has this property. A correct compositional-supervenience theory will have to assign D to "dogs bark". So, it will follow from a correct compositional-supervenience theory for M that "dogs bark" has D. Will it also follow from a correct compositional-supervenience theory for M that "dogs bark" means in M that dogs bark? Recall that to mean in M proposition p, for any p, is simply to have a physical property such that having that property and being tokened in the belief-box is metaphysically sufficient for believing p. So, the question is, will it follow from a correct compositional-supervenience theory for M that "dogs bark" has a physical property such that having that property and being tokened in the belief-box is metaphysically sufficientfor believing that dogs bark? Well, of course, a correct compositional supervenience theory for M will metaphysically entail this, since in every world where a sentence has D it also has a property such that having that property and being tokened in the belief-box is metaphysically sufficient for believing that dogs bark: that is exactly what D must be if it is assigned by a correct compositional-supervenience theory to the sentence that realizes the belief that dogs bark when tokened in the belief-box. But, then, the question really is, not just will it follow, but will it logically follow from a correct compositional-supervenience theory for M that "dogs bark" has a physical property such that having that property and being tokened in the belief-box is metaphysically sufficient for believing that dogs bark? Or, to be really heavy about matters, does [F] follow logically from [D]?

[D] "Dogs bark" has D.

[F] "Dogs bark" has a property such that having that property and being tokened in the belief-box is metaphysically sufficient for believing that dogs bark.

Clearly [F] follows from [D] only if we have a premise like [E]:

[E]D is a property such that having that property and being tokened in the belief-box is metaphysically sufficient for believing that dogs bark.

So, whether a correct compositional-supervenience theory for M logically entails a CMT for M comes down to whether it will entail premises like [E] for M-sentences. Generally, if prolixly, the existence of a correct compositional-supervenience theory for M will logically entail the existence of a correct CMT for M if but only if for each M sentence , for each physical property , and for each proposition , if both and having andbeing tokened in the belief-box is metaphysically sufficient for believing , then a premise like [G] is logically entailed by a correct compositional-supervenience theory for M:

[G] is a property such that having that property and being tokened in the belief-box is metaphysically sufficient for believing .

To put it in a nutshell, a correct compositional-supervenience theory for M will entail a correct CMT for M just in case the former specifies a function from the belief-making properties to the appropriate propositions. But there is no reason to suppose that this will have to be the case. There is nothing that requires a compositional-supervenience theory to entail theorems with the form of [G]. If there were, then a correct compositional-supervenience theory for M would entail the existence of a correct CMT for M. But there is not, so it seems that the productivity and systematicity of M can be explained without commitment to a CMT for M.

Fodor has responded to this argument.<27> Essentially his response is that "supervenience without identity is mysterious"<28> and that if we do identify the belief-making properties assigned to sentences by a compositional-supervenience theory with the appropriate meaning properties, then we will have a CMT for M. But I think there are problems with both of these points. I will briefly say what I take these problems to be.

Of course supervenience is a very murky notion as far as metaphysical explanations go. But its acceptance as a notion that can do at least some metaphysical work has largely been due to a deep dissatisfaction with identity theses. So, unless Fodor provides some sort of calming arguments with respect to the woes of identity, it is difficult to see how to easily follow his suggestion here.<29> Fodor does seem to be tryingto allay worries about an identity thesis when he denies that there are issues of multiple realizability with identifying the belief-making properties with meaning properties.<30> But his merely denying this doesn't make it so, and I believe that the possibility that beliefs can be multiply realized simply does tell against identifying belief-making supervenience properties with meaning properties.

But, besides this, I don't understand, with regard to Fodor's second point, how exactly the identification of the belief-making properties with meaning properties will help.<31> The identity in [E] is not in question, nor are any of the identities reported by sentences with the form of [G]. But it has already been shown that this identity by itself doesn't make a CMT logically follow from a compositional-supervenience theory.

So I find both aspects of Fodor's responses to Schiffer's arguments unsatisfying. It seems that Fodor has not supplied a telling reason why one should accept that there will be CMTs for Mentalese. And, therefore, it seems that there are no reasons for accepting that there are CSTs for natural languages generally.

4.5 Summary

Of course, nothing in the above is an argument that there are no CSTs for natural languages. But, I do believe that the arguments that have been adduced for CSTs are shown by the above considerations to be lacking. And, in fact, nobody has yet provided a CST for a natural language. So, I think it is safest to stay clear of CSTs in trying to construct a theory of meaning. In the remaining chapters of this dissertation I will discuss a number of theories that avoid, or seem to, commitment to CSTs.