Can Truth Conditional Semantics Explain Linguistic Competence?

[The issue of this post has been discussed by Jeff Speaks in a recent paper here. Hence, even though I am setting things up in a different manner and with a different target, I am not claiming originality on the main point. Speaks’ point deserves reiteration since it raises a challenge that has not been sufficiently addressed by proponents of truth conditional semantics. Another sidenote: a more precise title for this post would be: “Can TCS explain *the possibility of* linguistic competence?”. But it just looked too awful with such a long heading…]

Natural languages are infinite. Human beings are finite. Yet humans are competent with natural languages. A finite being cannot learn, one by one, what each of the infinitely many expressions of a language means. How is it possible that a finite being acquires competence with an infinite language? The task of answering this question is one of the central themes that drive the truth conditional project. Hence, if it turned out that truth conditional semantics (TCS) cannot provide a satisfying answer that should be worrisome to the Davidsonian. This post is about whether the Davidsonian should be worried. In the end, I believe, she should.

Let us start by considering, with respect to some infinite language L, the following question:

Q How can a finite being acquire competence with L?

Competence with a language L relies on (or arises from, or consists in) knowing what the expressions of L mean. If we could specify a finite set of knowable propositions P = {that p1, … that pn} such that knowing that (p1 & … that pn) was (in some sense) sufficient for knowing, of every expression of L, what it means, we would be in a position to answer Q: a finite being can acquire competence with L by coming to know P. This has explanatory value since P itself is finite.

Suppose, though, that P had the following feature: if someone X is competent with the infinite language L*, then knowing P is, for X, sufficient to understand L. If, however, X does not understand L*, then P will be of no help to her in coming to know L. Suppose someone suggested providing an answer to Q based on P. A rather natural response to such an attempt seems to be this: You have explained how a finite being X can come to know L given that X already has knowledge of some other infinite language L*. But the interesting question was precisely how it is possible that X has knowledge of an infinite language. So maybe you have answered Q, but this only shows that Q was a bad way of phrasing the question. We are really interested, not in Q, but in:

Q* How can there be an infinite language with which a finite being is competent?

To answer Q* we must not presuppose competence with any infinite language. If TCS can only answer questions of the Q-kind, but not Q*, it falls short of explaining a fact which is frequently alluded to in order to motivate the whole enterprise: the fact that finite beings understand infinite languages. Can current TCS-approaches provide an answer to Q*? I will try to show that the one developed by Ernie Lepore and Kirk Ludwig (L&L) in their recent book “Donald Davidson’s Truth Theoretic Semantics” cannot. (References are to this book.)

Terminology: A truth-theory for a language L given in a metalanguage L* is interpretive iff all of its axioms are interpretive. An axiom for an L-expression E is interpretive if it uses an L*-expression E* synonymous with E to state satisfaction / reference conditions (e.g., an interpretive axiom for the German “ist rot” given in English will use “is red” rather than “is red and self identical”). (See 85-89 for a more rigorous account). A T-sentence “S is true iff p” is interpretive iff S and “p” have the same meaning. A canonical proof procedure is a syntactical procedure that yields only interpretive T-sentences.

Suppose that for some language L we had both an interpretive truth theory T given in a language L* and a canonical proof procedure. According to L&L, we can now give a theory of meaning TM for L. TM contains the following axioms (60; I ignore context sensitivity):

[1] Every instance of the following schema is true:
S in L means that p iff it is canonically provable on the basis of the axioms of an interpretive truth theory TT for L that S is true in L iff p.

[2] T is an interpretive truth theory for L whose axioms are …

[3] Axiom … of T means that … (for each axiom).

[4] A canonical proof in T is …

(Replace dots appropriately.) Is TM of any help in answering Q*? That is, do the axioms of TM taken together express some finite set of propositions P such that knowing P would be sufficient to understand some infinite language without thereby presupposing competence with some infinite language?

If X knows everything that TM states, X will be in a position to infer, for every S of L meaning that p, that “S is true in L iff p” is a canonical theorem of an interpretive truth theory for L. ([2] provides the axioms and tells her that they form such a theory, while [4] provides a canonical proof procedure and states that it is such a procedure.) But X’s knowledge that “S is true in L iff p” is such-and-such is simply knowledge about a linguistic item. If you don’t understand German, then knowing that a theory T has “Schnee ist weiß” as a theorem will not be sufficient to know that it is provable on the basis of T that snow is white. Likewise, if X does not understand “S is true in L iff p”, then knowing that it is a canonical theorem of T will not be sufficient for X to know that it is canonically provable from T that S is true in L iff p. But then (even given that X understands the schema in [1]) she will be in no position to infer that S means in L that p. Hence, if X is not competent with L*, knowing that [1], [2] and [4] will be of no help in coming to understand L. This leaves [3].

But how could [3] help? It would help if the following was the case: if you have a set of sentences S (e.g. the axioms of T) and are able to apply certain syntactical transformation rules to them (e.g. the canonical proof procedure), then telling you what the sentences in S mean will ensure that you know the meaning of the derived sentences. Given this, TM would indeed provide an answer to Q*. But of course, this is simply false. (In fact, if it were the case, it would be quite incomprehensible what we needed the whole theory-of-meaning-thing for to begin with. If telling X what the axioms of a truth theory mean was sufficient to ensure that she understood all the theorems, then telling X what the axioms of a truth theory in L* for a language L mean would be sufficient to ensure that she is competent with an infinite language at least as strong in expressive power as L.)

Theories along the lines of TM cannot provide an answer to Q*. L&L seem to be content with this. They write:

This should not come as a surprise. For there is no question of a standpoint for understanding meaning that is outside of language altogether. (9)

I am not sure that they fully appreciate the point, and in any case, I am sure I do not fully understand their reply. But since this is already a somewhat lengthy post, discussion of their reaction will have to wait.

Posted by Miguel.


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