Davidson: Truth & Meaning

• We agree that a theory of meaning must talk about how the meaning of a sentence is constructed from the meanings of words.

• But what form should such a theory take?

• First, what is the meaning of part of a sentence? Can’t have everything refer to an entity—what does “the father of” refer to? [Model theory says: a set.]

• OK, but more generally we don’t need to think of complex sets relations or relations like $\lambda x. father(x, Annette) \land brother(x, Pierre)$ as “referring” to anything—the functional form is enough. (And no additional explanatory value in trying to compute its extension.)

• “It behooves us then to rephrase our demand on a satisfactory theory of meaning so as not to suggest that individual words must have meanings at all.” [They don’t need to have referents, but they still need some kind of local information content that allows them to have a “systematic effect on the meanings of the sentences in which they occur”. Is this not itself meaning?]

• In Frege-land, all our theory needs to be able to do is generate all statements of the form: t refers to x, where t is a composed expression and x is a referent. [By “all statements” I think we mean $\forall t: t\text{ is well-formed}$, not $\forall x$.] And now only for sentences, and nothing smaller.

• Problem: if the referent of a sentence is its truth value, all true sentences are the same. So we still need to rely on the structure of sentences to make equality judgments. [???]

• In particular, if I just say that the meaning of “Theaetetus” is [[Theaetatus]] and the meaning of “flies” is $\lambda x. f(x)$ for whatever $f$ is necessary to assign the right truth value to “Theaetetus flies”, I haven’t explained anything about meaning.

• Worrying about meanings in the lexicon doesn’t necessarily tell us anything about sentence meaning.

• Syntax comes with a clear decision problem: distinguish between well-formed and malformed sentences. Is there a corresponding test for semantics? [What’s wrong with “correctly predicting human judgments of truth or falsehood?]

• If we say that the meaning of each part is defined by whatever behavior it needs to take on to generate meanings for all sentences—that is, if sentence meanings are primitive and word meanings derived from these—we’re holists.

• One solution this suggests is simply to say that our theory should generate sentences of the form “s means that p”. But this is no good: p is itself a sentence, not a meaning. And understanding what “means that” does is the same as the original problem we set out to solve.

• So let’s instead make the theory generate sentences of the form “s is T iff p”. Here s is drawn from the object language and p from a metalanguage, but there’s nothing preventing us from assuming that the metalanguage contains the object language. [More radically, vice-versa!]

• (*) [What problem have we solved here? We originally said we wanted a theory of the form “s means m”, where m is a singular object containing the “meaning” of s. L must have stronger conditions in mind; so far this would let us take any arbitrary correspondence between the object language and the space of meanings to be a “theory of meaning”. We do not need (or necessarily want) a theory of meaning for entities smaller than sentences. We can make the proposal s means m less trivial if m lives in a space with more structure. If we take it to be the same space as s we’re begging the question. So instead we let our theory be generated by some predicate T. To be precise about what is being predicated, T is a function of s (and implicitly the model); its conditions are indexed by p (itself implicitly a function of the model). Now we have nontrivial structure (provided by the structure of the metalanguage), but also nontrivial interpretation (since everything lives in space of truth conditions).]

• Now we can talk about compositionality: compositionality explains how truth conditions are built up from parts.

• And we can evaluate a concrete implementation of a theory by actually looking at truth conditions.

• “in cases where we are unsure of the truth of a sentence, we can have confidence in a characterization of the truth predicate only if it pairs that sentence with one we have good reason to believe equivalent”—a sneaky way of making this about listener belief (though it doesn’t solve the property with tautologies).

• “Omniscience can obviously afford more bizarre theories of meaning than ignorance; but then, omniscience has less need of communication.” (312) [YES!]

• It will be difficult to come up with a unique theory of meaning for a language that we don’t speak by interacting with the speaker (q.v. Quine on translation).

• Also, we’re prevented from actually doing formal verification of a truth-conditional theory of meaning because (1) language admits Russell’s paradoxes and (2) language is complicated and ambiguous in a way that resists formalization.

• No satisfactory answer to (1), but for (2) we’ll be comfortable starting with a formalizable fragment of English and gradually work our way outward.

• And ambiguity is not actually a problem as long as it is representable in the metalanguage.

• But we still haven’t solved the problem with “believes that”.

• And we don’t even have a compositional analysis of “Bardot is a good actress”—what is good?

• [The first problem comes from our insistence that we should be able to replace any fragment of a sentence with another sentence that means the same thing. But the second is a real problem.]

• Also deixis—we can treat demonstratives as constants, but now we have to put the speaker’s circumstances into th edefinition of our truth function. [How could we possibly hope to do otherwise?]

• Formally, take truth to be a relation between a sentence, a person, and a time. [So close: “a sentence and a belief about the state of the world”]

I think the bullet labeled (*) above contains the substance of my understanding of this paper, and for motivating truth conditions as the kind of structured representation that deserves to be called the meaning of a sentence. It’s an important observation that many apparent paradoxes in truth-conditional accounts of meaning are sensitive to the information available to the implementer of the truth predicate—but he doesn’t seem to quite get to linking this claim to his claim that T needs to be indexed by speaker states. And we still haven’t said anything about compositionality….