Tarski's Style

Thus far I have talked freely in ways that Davidson eschews, of such things as propositions and contents. But the claim I am criticizing was:

When it comes to interpreting [a Tarski-style theory of truth] as a whole, it is the notion of truth, as applied to closed sentences, which must be connected with human ends and activities.

One might suspect that if we cleave to the bracketed qualification, Davidson has a case to make. But the points I have been making come out rather clearly when we consider a Tarksi-style theory.

Two initial points. First, look closely at the assertion Davidson makes about interpreting Tarski-style theories. Divide it into two parts:

(a)

The notion of truth is what gets connected with human ends and activities;

(b)

The notion of truth that gets connected to human ends and activities is truth applied to closed sentences.

These are quite different claims; one can accept the first and reject the second. It seems to me that one who follows the argument in Davidson's ``Truth and Meaning'' should do exactly that.

The dimly remembered picture one might have of this essay is that the Tarski-style theory recommended for analysis of natural languages was full of things that looked like this:

(12)

s is true iff p

where ``s'' is a mention of a closed sentence in the object language and ``p'' is a use of a sentence in the theorist's language. The picture that Davidson's claim brings to mind is that these postulates connect the linguistic objects the theory is about to their truth-conditions via the theorist's language. This connection then spreads out via the rest of the theorists language to descriptions of the ends and activities of the humans whose linguistic objects are in question. Hence, (a) it is the notion of truth that gets connected and (b) it is a sentence, namely s, to which truth is applied.

However, this picture ignores one of the later results in ``Truth and Meaning,'' that to be applied to languages that contains demonstratives, a Tarski-style theory needs revision. This is to say that such revision is required to apply this style of theory to natural language, since demonstratives are a universal feature of natural languages.

Here is one example of what a postulate in a suitably revised Tarski-style theory might look like:

(13)

``That book was stolen'' is true as (potentially) spoken by p at t if and only if the book demonstrated by p at t is stolen prior to t.

Here, unlike (12), we need a lot more than a sentence to get the truth predicate applied. We need a person, a time and a demonstrated book. The person and the time become relata of the truth-relation for Davidson; what about the book?

The knowledge expressed by (13) appears to include an understanding of the conditions under which the sentence ``That book was stolen'' can be assigned truth-conditions. There must be a demonstrated book. That is, the linguistic knowledge expressed by (13) includes knowledge of the setting in which a certain kind of linguistic object--in this case a sentence containing a demonstrative--makes contact with truth. In a Tarski-style theory of truth, suitably revised to be serviceable for natural languages, linguistic objects, speakers, and times have truth applied to them, in such settings.

Let us grant point (a) here. Truth is the notion that is applied. What is it applied to? A person, time and sentence. But now--why a sentence? What is it in the structure of (13) that demands a sentence as the linguistic object to which (together with a person and time) the notion of truth gets applied?

The answer was clear enough with (12).

(12)

s is true iff p

Nothing but a sentence would make sense on the left; what other part of speech on the left could be, without any supplementation or augmentation, connected by ``is true iff'' with a sentence on the right? But that rationale for preferential treatment for sentences is gone with (13). Consider:

(14)

``sleeps'' is true as (potentially) spoken by p at t if and only if the object under discussion by p at t sleeps.

(15)

``Reagan'' is true as (potentially) spoken by p at t if and only if Reagan meets the condition under discussion by p at t.

Point (a) remains inviolate in a theory that includes such things as (14) and (15). But point (b) is lost. The linguistic objects that truth is applied to are not closed sentences, but sub sentential expressions.

Given such postulates, our linguist might introduce reference as the relation that holds between ``Reagan'' and things of its syntactic ilk and the objects truth depends on when these things are spoken by persons at times discussing conditions, and expression as the relation that holds between ``was stolen'' and things of its syntactic ilk and the conditions truth depends on when spoken by persons at times discussing things. The linguist might then explain the truth of sentences as deriving from reference and expression, in virtue of the fact that reference is a way of putting things into discussion, and expression is a way of putting conditions into discussion, and a sentence is a way of creating the sort of discussion required for truth when it's not already underway. The truth of ``Reagan sleeps'' is thus over determined, since both ``Reagan'' and ``sleeps'' will be true. A welcome result.

As far as I can see, the points made with the free and easy terminology and ontology of sections 1-5 are perfectly compatible with things done Tarksi-style--so long as one means the revised Tarksi style that could actually be applied to a natural language.