A Cantorian Argument for Open Theism?

I'v just read an interesting paper on Enigman's website entitled "Omniscience and the Odyssey Theodicy". At one point in the paper, he employs Patrick Grim's well-known Cantorian argument against omniscience to argue for open theism over against an essentially epistemically static (EES) deity (my term, not his). The argument is intriguing.

According to set theory, anything can be a member of a set, including other sets. Hence, there can be no such thing as the set of all sets, for reasons pointed out by Cantor. Take any non-empty set (e.g., {1,2}) and form the set of all subsets (the power set) of the original (e.g., {{∅}, {1}, {2}, {1,2}}). That set will always have more members than the original set. And since this operation can be carried out for any set, there can be no such thing as the set of all sets.

This creates a problem for omniscience if that notion is defined set-theoretically, e.g., believing every member of the set of all truths. One can argue along Cantorian lines that there can be no such thing as the set of all truths. That is, for every set of truths, one can construct new truths that are not already members of the set.

As Enigman points out, if this is right, then it follows that an essentially epistemically static (EES) God - i.e., a God who cannot either acquire or lose beliefs - cannot be omniscient (in a set-theoretical sense). Such a God cannot know all truths. Moreover, there would have to exist truths that are forever outside the ken of an EES God. In contrast, according to open theism God is not epistemically static. He can acquire new beliefs. Indeed, his knowledge is, as Enigman puts it, "indefinitely extensible". As a result, there are no higher-order set-theoretical truths that God cannot eventually come to know. And this constitutes an advantage for open theism. On neither account can God know all truths, but, unlike EES theism, open theism is compatible with the idea that there are no truths that God cannot come to know.

Now, I think this is a very interesting argument for open theism, one that I have not heard of or considered before. I'm not sure that it's sound in its present formulation, though, because I'm not sure that omniscience is best understood in a set-theoretical fashion.

I would suggest that omniscience, in its primary sense, is best construed as a kind of knowledge by acquaintance. On this view, "omniscient" means being fully acquainted with all that is, where "all that is" need not be conceived as a set of discrete constituents, but rather as a continuous field. Here's an analogy. Consider a continuous plane surface. On that surface one may analytically isolate or pick out individual points and lines. In so doing, one brings those points or lines to the foreground, so to speak, but only over against a background, the continuous surface. Since the surface is continuous, no analysis of it can bring all of it into the foreground. There are always more points one could identify, more lines one could draw, etc. If this is right, then an omniscient God's knowledge doesn't come in presliced propositional packets; rather, it exists as a plenum of intelligibility. (I take the term "plenum" from Richard Creel's book Divine Impassibility.) Any part of that plenum can be analyzed out of it as a proposition, but no set of propositions can exhaust the plenum.

Now, even if that way of thinking about omniscience is on the right track, it may still be possible for an Enigman-style argument in favor of open theism to get off the ground. For if the plenum cannot be exhaustively analyzed in propositional terms, then no deity can have exhaustive propositional knowledge. However, an EES deity, on the one hand, is permanently stuck with whatever propositional knowledge he starts out with, whereas an open theist deity's propositional knowledge is indefinitely extensible. There is no point at which he can bring the entirety of the plenum into the foreground, but at the same time there is no part of the plenum that cannot be brought into the foreground. Hence, even on this analysis of omniscience an open theist God turns out to have a higher-quality sort of omniscience than an EES God.

By the way, while I don't endorse Enigman's "Odyssey theodicy" I think that's a really cool name. Kudos to Enigman for a stimulating paper.