The end of the semester is fast approaching, which means an even more hectic academic schedule, followed by a vacation. This post will be a brief remark on Sobel's treatment of omniscience, which completes his interlude on divine attributes. Following this, I will leave off until after the holidays, at which point I will deal with the remainder of the book, which treats arguments against the existence of God, and also 'Pascalian' practical arguments for belief in God.
The main puzzle Sobel finds with omniscience is one pushed by Patrick Grim. The thrust of the argument is this: (1) a Cantorian diagonalization argument shows that there can be no set of all truths. But, (2) for any being, there is a set containing all and only the propositions known by that being. Therefore, (3) no being knows all truths. (This is my simplified reconstruction; Sobel spells out some of the set-theoretic details related to (1).)
As Sobel rightly points out, there is no reason for the theist to accept (2) and, as a result, the argument fails. (Sobel also considers a similar argument from Grim to the effect that the sentence 'there is a being who knows every proposition' fails to express a proposition, because there are no propositions about all propositions. Sobel is, I think, correct in saying that Grim's premises involve details of a theory of propositions, rather than just an intuitive definition of propositions and 'aboutness', and any theory of propositions that has this consequence is clearly unacceptable.) All I want to note here is that Sobel doesn't point out what I take to be one of the more interesting reasons theists might reject the premise. Consider the following argument in support of (2):
(a) For every distinct proposition p known by a being S, S is in a distinct mental state which (partly) constitutes S's knowledge that p.
(b) No being can be in a proper class of distinct mental states.
Therefore, (c) No being can know a proper class of propositions, i.e. (2) is true.
(a) is plausible insofar as knowledge either is itself a mental state (as Williamson says), or else is partly constituted by belief, which is a mental state. (b) seems plausible probably because we typically think of mental states as concrete entities, and we balk at the idea of a proper class of concrete entities. (Having countably or continually many concrete entities is mind-boggling enough.)
I think Sobel probably has an argument like this in the back of his mind, and this is why he offers the suggestion (pp. 384-388) that if we aren't too wedded to pure actuality and atemporality as divine attributes, we might hold that only some set of propositions is before God's mind at any given time, but these propositions are such that God can easily (instantaneously) deduce any of the other propositions from them whenever he likes. Sobel calls this 'virtual' knowledge.
But, as Sobel realizes, the theist is at liberty to reject (b), and so to continue rejecting (2). What Sobel doesn't seem to realize, is that certain theists, those who accept the strong (Western) form of divine simplicity, are under independent pressure to reject (a). According to this view, God is identical to each of his attributes. Therefore, if God knows that p, and God knows that q, then God's knowledge that p = God's knowledge that q = God, and similarly for God's belief in each of these propositions. If this idea makes any sense (and I suppose we shouldn't just take for granted that it does), then God can know a proper class of propositions without being in a proper class of mental states.
[Cross-posted at blog.kennypearce.net]