This is the sixteenth of 17 posts, which are collectively Eternity, etc.
......You may be wondering how, if the Open God is forever acquiring arithmetical knowledge (see previous post), He could ever be omniscient (or how His understanding of His options could ever be perfect). It would not even help us here to think of omniscience in Swinburne’s terms, because however much arithmetic God knows it is logically—indeed, metaphysically—possible for Him to know more (according to section VII); and nor could He know all the interesting Beths (that could ever exist) [i], because the smallest Beth that He did not know would be of some objective interest.
......Nevertheless, such Perfect Being Theists as Augustine and Duns Scotus took the Platonic Forms to be divinely created (in view of God’s omnipotence) [ii], and similarly, Open Theists might take arithmetic to be divinely constructed [iii]. Suppose that arithmetical statements are true or false only when divinely proved or refuted (respectively). That process could not always be instantaneous, according to section VII, and of course, not yet knowing something that is not yet true would not obstruct omniscience. And while most of us think of arithmetic as timeless, by “arithmetic” we ordinarily mean finite arithmetic, and on the modern view such a God could have always known all of that (instantaneously constructed in His primal state). Indeed, He could have always known all the Beths that are not, for us, unimaginably large.
......My suggestion is therefore that God, being epistemically omnipotent, constructs each and every modal consequence of the concept of a thing (which He understands perfectly), and in particular the cardinalities of possible creations (doing so endlessly because such is the nature of that concept). He knows all the Beths that exist. Before He constructs a Beth, it has only a potential existence. And eventually (and arbitrarily quickly) He knows any Beth that could ever exist. And His understanding of such possible Beths is perfect (cf. how we could understand the essence of an arbitrary natural number, even on the older view of arithmetic).
......[i] For a similar suggestion, see Menzel, “God and Mathematical Objects,” pp. 93–4 n. 42.
......[ii] For Augustine, see Sorabji, Time, Creation and the Continuum, p. 252. For Duns Scotus, see Gunton, The Triune Creator, pp. 118–9. For more details, see Copan & Craig, Creation out of Nothing, pp. 173–80.
......[iii] Menzel, “God and Mathematical Objects,” defends such a view, called “theistic constructivism” by Copan & Craig, Creation out of Nothing, p. 191.