Intuitionistically, truth is identified with provability: A is true means that it is possible to prove A. In his essay "Intuitionistic logic a philosophical challenge, Logic and Philoshophy" (1980) Prawitz affirms that Tarski's theory of truth is compatible with the intuitionistic position (p.3):
It may be thought that this theory should support classical logic. By combining the truth conditions for disjunctions and negations, we get that a sentence "A or not-A" is true if and only if the truth condition of A obtains or does not obtain. Since this truth condition just expresses the meaning of the sentence, its logical validity follows if we furthermore assume the principle that a truth condition either obtains or does not obtain, independently of our means of knowing which case is the actual one. But this principle, which we may call with Dummett the platonistic principle of truth, must of course not be taken for granted in a discussion of the validity of the law of excluded middle.
That is, Tarski's material condition is respected by intuitionism, since e.g.
- 'A or not A' is true if and only if the truth conditions of A obtains or not obtains.
is itself pretty neutral as long as haven't affirmed the validity of the excluded middle.
I have three questions:
- Is this claim correct?
- Also, is this argument enough to support it?
- What does this has to say about the BHK interpretation?