I ran across this argument from Crispin Wright’s Truth and Objectivity (as paraphrased in Drew Khlentzos’ Naturalistic Realism and the Antirealist Challenge, pp. 25-29). It purports to show that truth and assertibility cannot be equivalent, by generating a problem in the case of undecidable propositions. I think it works but would be interested in hearing from others.
Suppose that we define deflationism regarding truth to mean the following:
(T1) The predicate “true” functions purely as a device for endorsing assertions, and refers to no other norm than justified or warranted assertibility. The extension of “is true” coincides with the extension of “is warrantedly assertible”.
and
(T2) The disquotational schema (DS), “p” is true iff p, constitutes a complete explanation of the meaning of “true.”
But for p we can insert a sentence we can neither verify nor refute (Wright uses Goldbach’s conjecture as his example). In so doing, we can generate an “absurdity,” to use Wright’s term – I’d just call it a problem or a mistake.
For DS implies that
(i) “It is not the case that p” is true iff it is not the case that p.
and
(ii) It is not the case that p iff it is not the case that “p” is true.
and, in combination,
(iii) “It is not the case that p” is true iff it is not the case that “p” is true.
So far, so good. But watch what happens when we substitute “assertible” for “true” in (iii), as would seem to be allowed by (T1):
(iv) “It is not the case that p” is assertible iff it is not the case that “p” is assertible.
This last sentence tells us we can assert that p is not the case if we find that p is not assertible. But that can’t be right. Using Goldbach’s conjecture as the example, it would mean that we can say that every even number above 4 is not the sum of two primes, since we can’t assert that every even number above 4 is the sum of two primes. But the conjecture is undecidable (as of now); we can’t assert anything about its truth value.
Let’s line up (iii) and (iv):
(iii) “It is not the case that p” is true iff it is not the case that “p” is true.
(iv) “It is not the case that p” is assertible iff it is not the case that “p” is assertible.
What has gone wrong? I suggest the following: (iii) simply says that, should we discover that p isn’t true, it will therefore be the case that “not-p” is true. But (iv) says that, if we discover that p isn’t assertible, it’s OK to assert that not-p. But this is a mistake. As Wright puts it, “While ‛is true’ and ‛is warrantedly assertible’ are normatively coincident, satisfaction of the one norm does not entail satisfaction of the other.” It’s a bivalence problem. So we have to abandon (T1).
The argument seems solid to me. Khlentzos thinks so too, though he believes (T1) is not essential to the deflationist’s case anyway. He believes the deflationist doesn’t need to claim that the extension of “is true” has to coincide with the extension of “is assertible”.
So: Does the argument go through? And are claims about what is assertible bound by bivalent logic in the same way as claims about what is true? Do they have to be?
). (T1) is Wright’s premise, not mine. I suppose you could recommend to him that he not see it this way, but since he does . . . the question is, is the argument, with (T1) as one of its premises, valid? What do you think?