What is the relation between truth-theoretic semantics and speaker competence?
We distinguished between what I called the initial and extended projects in Davidson's work. The first question in this connection is which of these projects we have in mind here. The initial project aims to shed light on the compositional structure of natural language, but not to say what it is for the semantical primitives of a language to mean what they do. The extended project may be thought of as addressing the general question "What is it for words to mean what they do?" It subsumes the first but also addresses the question of what it is for the primitives of a language to mean what they do. The first only aims to illuminate the connection between the primitives and the complexes. I will consider only the initial project here, the project of giving a compositional semantics for a language.
This aims to do the following: (a) to "give the meaning" of every object language sentence (b) on the basis of axioms attaching to primitives which reveals how the primitives contribute to fixing what those sentences mean.
Truth-theoretic semantics is one way of trying to implement this aspiration. I've described it as employing an ingenious bit of indirection. The idea is to exploit the recursive machinery of a truth theory to link axioms attaching to semantical primitives, where we use metalanguage terms which interpret the object language terms for which truth/reference/satisfaction conditions are being given, via proofs that draw only on the content of the axioms, to T-sentences in which the sentence in the metalanguage used to give truth conditions for the object language sentence interprets the object language sentence. This is a way of satisfying the goal specified in (a) and (b) -- relative to appropriate knowledge about the truth theory, as we have been saying. A benefit is that it does it without appeal to assigning entities to every expression (a silly idea on the face of it). An additional and important benefit is that it shows something about the connection between meaning and truth in a systematic way. We see in each step in a proof the contribution of a particular object language expression to fixing the interpretive truth conditions of the sentence containing it. The axiom for each is employed, and so we see for each object language expression in the sentence how it contributes to fixing the interpretive truth conditions of the sentence.
What is the relation of all of this to semantic competence? One might disclaim any ambition to say anything about what competence in the language comes to, other than that it of course respect the output in the sense of requiring competent speakers to interpret sentence as the theory says. At times Davidson talks as if he has nothing more in mind. But whatever the case with Davidson, I think we learn more. But what?
First, what we don't learn: we don't learn anything about how a speaker's competence is realized (ipso facto, anyway), in the sense of what realizes the speaker's dispositions to use words as he or she does. It is no part of truth-theoretic semantics (as I understand it) to say anything about that. Someone might have that project and fold truth-theoretic semantics into it. This is what Larson and Segal do in their book Knowledge of Meaning. They suggest that semantic competence consists in a speaker's propositional knowledge of a truth theory. This clearly goes beyond what could be gleaned from just keeping track of how speaker's use words. It is an empirical hypothesis about how the competence speakers have is realized--an implausible one. (Anyway, how would we confirm or disconfirm it? We might find particular rules suggested don't match the speaker's dispositions. But suppose a perfect match. Then consider the hypothesis that the competence is physically realized and that there is NO level of description of the speaker at which there is any explicit representation of the axioms of the theory. The speaker is not supposed to have conscious access to any of his knowledge. So what favors, what could favor, accepting the L&S sort of account over the more minimalist view?)
But truth-theoretic semantics does have a clear relation to speaker competence, particularly if it is thought of in the way I have urged, for it aims to reveal the structure of what is known by a competent speaker of the language. So: in what way?
Think of it this way. For a competent speaker, each word in her language is one that she knows, i.e., is competent in the use of. This amounts to having an ability to use it in conjunction with other words in the language to say various things (to keep it simple, we ignore nondeclaratives). That ability is sensitive to what contribution the word makes to fixing the conditions under which any sentence containing it would be true . Each axiom of the theory gives a rule for the use of an expression in the object language. They specifies how the word contributes to fixing interpretive truth conditions for the sentence. In seeing what that rule is, we see also what having the ability to use the word comes to in a very detailed way. For each axiom for a primitive, there corresponds in the speaker a skill in using the word, and what the skill is a skill in doing is expressed precisely by the rule given by the axiom.
Take conjunction as an example. Ignore quantifiers for the moment. We then give the following recursive rule:
For any sentences X,Y, X+'et'+Y is true iff X is true and Y is true.
What does this show about the skill a speaker of the language in the use of the word? It shows that the speaker will be prepared to assert (if she wishes to be sincere) a sentence of the form 'X et Y' only if she accept both X and Y; that if she accepts 'X et Y' then she will assent to X and assent to Y, and that if she assents to X and assents to Y, then she will be prepared to assent (other things being equal) to 'X et Y'. (It is more complicated with quantifiers and noun and verb phrase conjunction, and additional complications are added with interrogatives and imperatives, so this just illustrates a small part of what the competence really comes to--but in the full theory all is captured.) This is not something of course that the axiom says. It is something we glean from the axiom, knowing what it says, and knowing that the axioms meet Convention A.
One might say the following: okay, but this is trivial. What is trivial? It is trivial that if you set up the truth theory as you suggest, and know what you say, then the axioms express rules that are realized in the skills the speaker attaches to them in the way you suggest, and we can articulate it in the fashion you indicate. Okay: but sometimes trivial things have to be explained before we grasp them.
In any case, it is an empirical project to develop for a natural language an adequate representation in this form of what it is to have the skills relevant to speaking the language. And that is very far from being trivial, for it involves articulating what is merely implicit in how we use words, and it is a delicate and difficult task to trace out what all is contained in that, and see through the "haze of usage" (Higginbotham) to the contribution specifically of semantic competence. We look at actual use, we use thought experiments, we ask ourselves straight out whether one thing entails another, whether this and that can be said truly at the same time, what in our reactions is due to what our words mean as opposed to reactions to pragmatic implicatures or an affective reaction to a case, and so on. Carrying out the project successfully will tell us a lot about what the skill we have in possessing a language comes to. It amounts to giving a reflective account of that skill, which is something we certainly don't start out with, and is not easy to attain. And this is what it comes to, as Dummett put it, to give a theoretical representation of a practical ability, by developing an interpretive truth theory for a natural language.
What about the relation of this project to what realizes the competences we possess in possessing a language? You would think you'd want to complete this one first, for if you don't have a detailed representation of the competence whose realization you are trying to give an account of, it's going to be hard to say how it is realized.
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