In my last post, I discussed Lucas's presentist account of what grounds truths about the past. The upshot was that Lucas and his ilk must find someway of specifying those mental states of God which are supposed to be doing the grounding in their theory but without already presupposing that these states are memories (since that in turn already presupposes the very truths about the past which are supposed to be explained). But this gets us into a further problem.
Many presentist accounts of the grounding of past truths are susceptible to conceivability arguments against their proposed truthmakers. Consider a verificationist account, for instance, on which past truths are grounded in present evidence. If this account were correct, given the current evidence it would necessarily follow that we have exactly the past truths we in fact have. But this doesn't seem right. It is certainly conceivable that our universe have the evidence it in fact has yet have a completely different past (say, because God decided to miraculously make it so at this particular point in time, with no taking into account anything that came before). Russell seems right about this sort of thing. So it seems false that evidence is what grounds past truths since they seem to be only contingently related.
So a version of Lucas's view, reformed to take into account my last post, is going to say that there is some mental state S of God's such that it has the content p and that this is what makes it true that p (or that WAS(p), depending on how this gets spelled out). Now, one virtue of cashing this out in terms of memories was that it guaranteed the truth of p - no conceivability argument was possible against it. But now that we cannot specify S in terms of memories, it looks like this view is going to be susceptible to conceivability arguments perhaps after all - it seems likely that it will indeed be conceivable that God bear S to p and yet p not be true of the past. Indeed, it will be conceivable that S is not a memory at all.
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