In reflection on the argument I presented earlier concerning whether the A-theorist who believes that God knows all truths about the future (and who is a libertarian) could accept the PSR, perhaps the A-theorist has another problem. [Edit: alternatively, if the Open Theist replies that God does know all truths about the future, namely by knowing nothing about the future because there are no such truths, then we can say ‘God knows all things which will come to pass, or become true, in the future’.]
According to a Correspondence theory of truth, some statement is true if and only if it agrees with reality. In other words, a proposition is true because it corresponds to the way the world actually is. However, on the A-theory, future-tensed propositions are not true according to this ‘correspondence’ definition of truth. They do not correspond to the way the world is, but are true either by some other reason, or else their truth is itself a brute fact. Perhaps the A-theorist will argue that it is a fact about the way the world is now that the future-tensed proposition F, is true (or false), but that seems unsatisfying precisely because there is no truth-maker in the ‘correspondence’ sense.
Moreover, it seems hard to imagine what theory of truth would license the claim that, on A-theory, propositions about the future can be true. The Pragmatist theory of truth stipulates that “a statement is true iff it is rationally acceptable under ideal epistemic conditions.” The Coherentist theory of truth stipulates that “a statement is true iff it is consistent with some preferred set of sentences.” Neither of these seem to provide the A-theorist with an account of truth according to which she can maintain that future-tensed propositions are ‘true’ and known infallibly/incorrigibly by God.
Perhaps the A-theorist will adopt a radical modal definition of truth, such as “A statement is true iff it is intelligible, and not false.” Here one would appeal to the Law of Excluded Middle and argue that any proposition is either true or false, and cannot be anything ‘in-between‘ or ‘in-the-middle-of‘ true and false. Moreover, if it is not false, then it follows that it must be true. One may only be able to find out whether or not the proposition uttered in the future-tense is true or false once the scenario it describes either comes into reality or else fails to, but that can be called an epistemic issue. Some scenario becoming real may involve an epistemic transaction, but not a transaction which affords the previously made statement in the future tense a truth value. Or so the A-theorist might argue (though it seems to me obvious that a statement made in the present, issued in the future-tense, at least if A-theory were true, would not have a truth value when uttered, but would come to have a truth value when the scenario described either becomes real or fails to become real – but perhaps that betrays how wedded I am to the correspondence theory of truth).
Thus, it seems that the A-theorist who believes in God, and believes that God knows all things about the future, cannot accept the correspondence theory of truth – or at least I don’t see any way for them to do so.