This post floats the suggestion that deflationism about truth is inconsistent with relativism about truth. Not that one should be a deflationist. But it would be interesting if deflationism entailed the nonrelativity of truth.
There is a sense in which deflationary theories of truth deny the very existence of truth. For what these theories deny is that anything of a unitary and substantial nature corresponds to the predicate 'true' or 'is true.' To get a feel for the issue, start with the platitude that some of the things people say are true and some of the things people say are not true. People who say that Hitler died by his own hand in the Spring of 1945 say something true, while those who say that no Jews were gassed at Auschwitz say something that is not true. Given the platitude that there are truths and untruths, classically-inclined philosophers will inquire: What is it that all and only the truths have in common in virtue of which they are truths? What is truth? What is the property of being-true?
The deflationist, then, is denying that truth has a unitary and substantial nature into which it would make sense to inquire. There is no Truth with a capital 'T.' Does it follow that the deflationist is committed to relativism about truth? Must he say that there is no such thing as objective correctness?
It seems not. For although the deflationist denies Truth, he need not deny truths. There are truths galore on the views of prominent deflationists; it is just that they have nothing nonlinguistic in common in virtue of which they are true. The deflationist tendency is to say that there is no more to Truth than is captured in such equivalences as:
Sentence 'S' (in language L) is true iff S
and
The proposition that p is true iff p.
One version of deflationism is Quine's disquotationalism according to which the function of the truth-predicate is to remove the quotation marks from a quoted sentence. Thus "'Snow is white' is true" says exactly what 'Snow is white' says, namely, that snow is white. And "'Grass is green' is true" says exactly what 'Grass is green' says, namely, that grass is green. And so on. There is nothing common to these sentences in virtue of which they are true. 'True' is just a device of disquotation; it does not pick out a genuine property.
It is easy to see that there is nothing here that is inconsistent with the absolutness of snow's being white or of grass's being green, etc. What's more interesting is that deflationary theories of truth would seem to rule out alethic relativism. Suppose a Nietzschean maintains that truth is the property of being power-enhancing, a property of those beliefs that enhance the power of the one who holds them. Deflationism rules out this substantive theory of truth along with every other substantive theory of truth. For if deflationism is true, then Truth has no nature; it is in a sense nothing at all. As such, it cannot be identified with the property of being power-enhancing.
This looks to be a general result. For truth to be relative, it would have to be identified with some relative property such as acceptability or rational acceptability, or rational acceptability by some ideally situated cognizers, or whatever. But such an identification could be made only if truth has a nature. On deflationism, however, truth lacks a nature. So truth on deflationism is nonrelative. Indeed, this seems to be a consequence of the above equivalence schemata. For the schemata imply that every proposition or its negation is true simpliciter, which rules out any proposition or its negation's being true-for-X, for some relativizing factor X.