Irrealism and Tarski

According to Tarski, Schema (T), of which instances have the form:

1. "..." is true if and only if ...,

where the same text is put for the two instances of "...", is compatible with both realism and irrealism, with correspondence theory and coherentism.

Let's explore this claim. Suppose we are irrealists (nevermind that we might then prefer some other term, like "epistemicist") who have some epistemic notion of truth, e.g, a sophisticated version of the claim that S is true if and only if it would be arrived at in the ideal limit of inquiry. Abbreviate the epistemic definition of the truth of S as E(S). I will at times use the the ideal limit formulation for explicitness, but it should really be considered a stand-in for whatever more sophisticated story is to be given.

If we accept both Schema (T) and the epistemic definition of truth, then we have to accept every instance of:

2. E("...") if and only if ....

But (2) gets us into trouble. First of all, if we accept the Law of Excluded Middle (LEM)—that for all p, p or not p—then we have to accept the implausible claim that for all p, E(p) or E(~p). For many values of p, that is simply implausible for any of the epistemic versions of E. Thus, it is not plausible that in the ideal limit of inquiry we will conclude that Napoleon died with an even number of hairs on his head, and it is not plausible that in the ideal limit of inquiry we will conclude that it wasn't the case that Napoleon died with an even number of hairs on his head.

So, our irrealist who accepts (1) will, it appears, have to deny LEM. This shows that Schema (T) is not neutral between realists and irrealists. For while a realist can accept Schema (T) and either believe or not believe LEM, the irrealist is forced by the acceptance of Schema (T) to deny LEM. And if we see LEM as self-evidently true (though that remark begs the question against the intuitionists), then Schema (T) will in fact be unavailable to our irrealist.

Let us consider the irrealism further. Here is an instance of (2) (with the toy version of ideal-limit irrealism):

3. We would in the ideal limit find out that there are conscious beings in the Andromeda Galaxy if and only if there are conscious beings in the Andromeda Galaxy.

This is a startling claim. Moreover, it is a claim that is part of a large family of equally startling claims relating how things are far away and what we would find out. These claims, furthermore, are not merely accidentally true, since the characterization of truth had better not be an accident.

Let's push on further with instances of (2). For instance:

4. The ideal limit of inquiry is never reached if and only if in the ideal limit of inquiry we would conclude that the ideal limit of inquiry is never reached.

But the right hand side of the biconditional doesn't hold: in the ideal limit of inquiry we would not conclude that the ideal limit of inquiry is reached. So, the left hand side doesn't hold. Consequently, we have an a priori argument that the ideal limit of inquiry is reached. But unless one is a theist (who thinks that God has always already reached that ideal limit), it is absurd to suppose we'd have an a priori argument for that—that would yield give an atheist an a priori argument for the claim that we won't all perish tomorrow. The present example is one that cannot be leveled against irrealists who do not engage in any kind of idealization. But I suspect that non-idealizing irrealist views degenerate into relativism.

If this is all right, then in fact the irrealist cannot afford to accept Schema (T), and Tarski is wrong in thinking Schema (T) is neutral.

But non-acceptance of Schema (T) comes with a price, too. We either have to allow that truth of "There is conscious life in the Andromeda Galaxy" does not suffice to show that there is conscious life in the Andromeda Galaxy, or we have to allow that there could be conscious life in the Andromeda Galaxy, even though it is not true that there is conscious life in the Andromeda Galaxy. That is absurd. Of course, as an argument, this is question-begging.

Let's see if we can do better. If the irrealist's use of the word "truth" does not conform with Schema (T), the word "truth" does not match what seem pretty clearly to be central cases of our use of the word. Thus, when the irrealist says that "truth" depends on inquiry, the irrealist is not actually talking of what we mean by "truth", and is not disagreeing with the realist. And assuming that the irrealist doesn't say crazy things like (3) and (4), it is not clear wherein the irrealist is being an irrealist. (I would be quite happy if it were shown that irrealism is impossible.) But if the realist can give a correspondence theory of the concept of "truth" that conforms with Schema (T), then the conformity with Schema (T) would be evidence that the realist is not using "truth" in a Pickwickian sense.

To put the main points differently, epistemicism can be first and second order. First-order epistemicism affirms all the instances of (2). Second-order epistemicism affirms all the instances of

5. "..." is true if and only if E("...").

Now: (a) first-order epistemicism makes sense but is crazy, (b) second-order epistemicism together with Schema (T) leads to first-order epistemicism, and (c) second-order epistemicism without Schema (T) uses the word "truth" differently from how we use it, since our usage is governed, in part, by Schema T. The challenge for the epistemicist is either to deny that first-order epistemicism is crazy, or to show how second-order epistemicism without Schema (T) is talking about "truth".