Divine Simplicity and Grim’s Cantorian argument against Omniscience

It has occurred to me recently that one might be able to level Grim’s Cantorian argument against Omniscience against the A theory of time. For an example of this argument one can look to a paper written by Ben Wallis. The basic thesis of the argument is supposed to be that Grim’s argument proves that there can be no set of all truths, but an omniscient being must know the set of all truths; therefore no omniscient being exists. This is painfully oversimplified perhaps. However, as Kenny Pearce has pointed out, this entire argument seems to be avoided by an appeal to a strong classically western view of Divine Simplicity, where God’s being X is ontologically identical with God’s being Y, which is ontologically identical with God. I highly recommend reading this blog post by Pearce. So, it seems that this view of God as Metaphysically simple, which is necessary for a faithful Catholic to maintain given Vatican I along with the Fourth Lateran Council, allows one to dodge the argument, as it were. Leaving aside an attempt to argue here for this doctrine in Catholic theology, I take it that it is at least not absurd, and has not been shown to be logically impossible. I would appeal to Alexander Pruss here for an excellent essay on the three problems of Divine Simplicity. The argument is, very basically, that there is a meaningful distinction between two things (say, God’s being X and God’s being Y) being ontologically identical, and being semantically identical. We want to preserve a real semantic difference, while being able to apply statements literally and analogously to God, recognizing that every attribute of God is identical with God (his goodness, for example, is not accidental, but is part of his essence such that “goodness” just is synonymous with God’s essence). Pruss provides a clever analogy in section two of his essay, where he imagines an alien for whom hearing and feeling are both true and identical, even while our language about the alien’s hearing or feeling are predicated analogously (rather than equivocally), and there remains a real semantic difference between hearing and feeling. I also found this very good essay by Timothy O’Connor, a philosopher of the first rank who I have grown to admire (in large part thanks to his book Theism and Ultimate Explanation: the Necessary Shape of Contingency), who deals at length with the problem that contingent creation poses to divine simplicity.

Now, William Lane Craig has argued that an A theory of time is true, and properly basic, along with, at least to his mind, very difficult for a Christian to not accept. Now, there are many reasons why Catholics might have to be skeptical about this assertion (for instance, what it would imply about the Eucharist at the Last Supper ‘before’ Christ had died on the cross, etc) the most significant problem it poses for a Catholic is that it directly challenges God’s metaphysical simplicity. On an A theory of time tensed propositions exist, and they are not reducible to tenseless propositions (indeed, this is in part an argument advanced for the A theory of time, though it is dealt with really powerfully by Pruss here). In any case, William Lane Craig has argued that God is not metaphysically simple, and moreover that if the A theory of time is true and God exists (or God exists such that he is omniscient) then God cannot be metaphysically simple. The reason is simple, (pun intended): God must learn new propositions. Consider the proposition “X will occur”; this proposition is true so long as X is an event in the future, but as soon as it ceases to be a future event, but is a present event, the proposition “X will occur” is no longer true, and instead the proposition “X is now” is true. A moment later, this proposition is no longer true, and instead the proposition “X occurred” becomes true. God, if he knows all true propositions, must ‘learn’ new propositions in the sense that he must assign different truth value assignments to propositions as time moves on. The situation is more complicated still, as it implies an infinite number of changes (though this only implies a potential infinite in the case of a finite world), since God could know that “at time t ‘X will occur'”, but then must come to know that ” at time tx ‘X is now occuring'” and finally must then become ” at time tx+1 ‘X occurred'”. A moment later God must know that ” at time tx+2 ‘X occurred'”… and that “at time tx+n ‘X occurred'” where n stands for the number of moments of time (or events) which separate the present tense from event X or the moment at which ‘X is occuring’. Therefore every moment God is learning some finite number of new propositions, though he knew those propositions ‘before’ to be false.

W.L. Craig has argued, and so well that I think it is beyond reasonable contest, that the A theory of time implies for the Theist that God is in time, at least if the theist is committed to God’s omniscience. God must know all ‘true’ propositions, which is technically satisfied on Dr. Craig’s account of God’s relationship to time, since at any time God knows all true propositions as true, and knows all false propositions as false. Craig has argued that the strong view of divine simplicity is a medieval accoutrement of theology which isn’t entailed by the Bible, and since he is not a Catholic but an Evangelical, he is at liberty to disagree with the ecumenical councils. Thus, for him, he would maintain that his view of God does not pose any serious problems for Biblical theism. God is just not identical with all his attributes in a strong sense implying that “God knows that X occurs at time t3” is ontologically identical to “God exists”, even while being semantically different.

If this is the case, then can’t one use Grim’s Cantorian argument against Omniscience against an A theory of time? I think one can.

  1. God exists, and is omniscient.
  2. the A theory of time implies that God is not metaphysically simple.
  3. If God is not Metaphysically simple, then Grim’s argument proves that God cannot be omniscient
  4. If the A theory of time is true, then God is not metaphysically simple, and cannot be omniscient given Grim’s argument (from 2&3)
  5. But 1. is true, therefore God must be metaphysically simple (from 1&3)
  6. If God is Metaphysically simple then the A theory of time isn’t true (from 2)
  7. God is metaphysically simple (from 5)
  8. The A theory of time isn’t true (from 7&6)

That looks about right. I suppose Craig would respond that that omniscience is not modally constrained – but I have yet to figure out what that is suppose to mean. I see no sense whatsoever in that statement.

In any case, there may be ways out of the argument, such as attacking premise 3, by attacking Grim’s Cantorian argument and demonstrating that there is a way out of it other than classical metaphysical simplicity. However, that doesn’t prevent this from being an interesting argument worth exploring in the future. Moreover, the argument is going to be as strong as the alternative response to Grim’s argument opted for is weak. In any case, this is all just thinking out loud on my part.


About tylerjourneaux

I am an aspiring Catholic theologian and philosopher, and I have a keen interest in apologetics. I am creating this blog both in order to practice and improve my writing and memory retention as I publish my thoughts, and in order to give evidence of my ability to understand and communicate thoughts on topics pertinent to Theology, Philosophy, philosophical theology, Catholic (Christian) Apologetics, philosophy of religion and textual criticism.
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