This is the third of 17 posts, which are collectively Eternity, etc.
......I shall, then (see previous post), be arguing that Open Theists can accept God’s necessary omniscience, in the sense of His being bound to know each truth whenever it exists (insofar as truths exist). Richard Swinburne—the Open Theist that Mawson focused upon—disagrees; or rather, Swinburne thinks that because of future contingents (see section III) we should “understand God being omniscient as God knowing at any time all that [it] is logically possible to know at that time”[i]. But let us follow Mawson, and “say that a being is omniscient just if it is the case that for all statements, if a statement is true, then that being knows that it is true”[ii].
......It would be natural for atemporalists to take truth to be timeless, however. (Indeed, even Swinburne seems to do so.) So Mawson may well have meant, by the phrase “if a statement is true” in his definition, if a statement is ever true. But there are many reasons, e.g. Cantor’s Paradox [iii], why truth is not timeless. And whatever the merits of such arguments, our question here is whether God—who may well be the ground of truth—must be timeless. We should therefore avoid begging the question, as we use Mawson’s definition, by not also assuming that statements cannot change their truth-values.
......Of course, Swinburne’s position is, to say the least, not obviously incoherent. So I would not say that the Open God’s omniscience (in our sense) is logically necessary. A logical possibility is primarily a coherent conceptual possibility, logic being the study of correct reasoning. What I will be defending is the logical possibility—indeed, the plausibility—of a variety of Open Theism under which God is bound, of metaphysical necessity, to be omniscient. Metaphysical necessity generalizes the natural (non-Humean) laws of physics so as to allow for such non-physical things as spirits and to allow for miracles and other possible creations (e.g. a new earth) [iv]. And if there is a God, then all metaphysical possibilities would be grounded in Him.
......[i] Swinburne, Is There a God? p. 8.
......[ii] Mawson, Belief in God, p. 35.
......[iii] If there was a set of all the other sets, then via Cantor’s Diagonal Argument (see section VII), there would be more subsets than there are sets; but each subset is a set, so there is no set of all the other sets. That would be paradoxical if “set” meant things referred to collectively. And since for each set there are such truths as what its members are, so there is no set of all truths; Patrick Grim, “There Is No Set of All Truths,” Analysis 44 (1984): 206–8. The result that truth is not timeless follows if “set” is given its informal meaning, of an immutably complete collection. For other arguments to that effect, see Nicholas Denyer, Time, Action and Necessity: A proof of free will (Duckworth, 1981), pp. 79–82; Richard Sorabji, Time, Creation and the Continuum: Theories in antiquity and the early Middle Ages (Duckworth, 1983), pp. 132–5.
......[iv] For more details, see Mawson, Belief in God, pp. 65–7.