Alan: 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.

Tom: But he never comes to know all truths (on Enigman’s scheme). So I don’t see the advantage. How does positing a God who acquires/loses beliefs (i.e., a God whose epistemic state changes to reflect reality) help with Grim’s Cantorian argument against omniscience? Grim’s argument holds for both epistemically static and changing states so long as both views define divine knowledge in propositional terms.

Alan: And this constitutes an advantage for open theism [in Enigman’s view]. 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.

Tom: Well, slightly better. But not really an advantage for somebody who believes God is omniscient.

Alan: 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.

Tom: I like this too. Propositional knowledge is a step away from what I think is a more genuine form of knowledge. By definition, propositional knowledge is a linguistic entity that describes reality. But there are non-propositional ways of apprehending reality, and some apprehensions (forms of knowledge) that can’t be expressed in propositional terms at all. That’s not to say that when a proposition is employed (by us), or needs to be employed by God that God doesn’t know the proposition in question. It’s just to say that God may apprehend or apperceive all reality on a direct, aesthetic, experiential level.

The bit I’m uncomfortable with about your example is that it represents how a finite knower approaches a continuously extending plane and “knows” it. The knower in this case—God—is the ‘ground’ of the infinity in question. Even in the case of mathematical truths or infinite sets, like the set of all even numbers, we may have to admit that at no time can God consciously contemplate all numbers (that would constitute an actual infinite, right?), but on the other hand we don’t want to say God is like us in approaching such set. That is, we can retrieve any even number because we know the ‘definition’ of an even number, or we know how to add and subtract, etc., so we can “figure out” and propositionally denote any particular member of the set. To say God does this suggests God arrives at his knowledge of some discrete slice of the plane (should he need to at some point in time) discursively. And I remember you also wanted to deny that God comes by his knowledge of truth discursively. In the case of God’s apprehension of the plane, God is its truth-grounds. God is the truth grounds for all infinities in fact. I’m just wondering if God’s being the grounds of infinite sets means his knowledge of any discrete part is acquired in ways (i.e., non-discursively) different than us. God’s knowledge of all even numbers, in other words, is essentially self-knowledge. And how do we say ‘how’ it is the infinitely creative and intelligent God apprehends himself as the source of all mathematical knowledge?

I don’t know how to avoid positing potentiality in God essentially. I know this is controversial, but in my view potentiality just is definitive of the fullness that God is. I talked to Greg about it and he agrees with me. He said this was the heart of his thesis. Creativity is an essential property of God. God is necessarily creative. But this doesn’t entail the Process idea of a necessary God-world relationship. In my view it just entails a necessarily creative loving expression between the divine persons. The analogy of a ‘dance’ is common. If we were to say God is a triune dance of love, then what I’m saying is that the steps to the dance, that creative movement the God is, never repeats itself. God is infinitely creative love in the sense that some aspect of the form of expressive love that defines the posturing of the persons with respect to each other need never be repeated. If there’s a better word than ‘potentiality’ for this, fine. Or maybe we can pull a Hegelian ‘good potentiality’ (instead of ‘infinity’) vs ‘bad potentiality’ out of our hats!

This may be the deep magic behind the infinity of mathematically truths and sets.

If we say, however, that creativity is a contingent property of God, then how do we posit God as the grounds of the necessity of mathematical infinitiees, like sets?

Tom

Post Edited (Tom) : 12/12/2008 10:03:25 AM (GMT-6)

Post Edited (One Love) : 12/12/2008 8:50:01 PM (GMT-6)

Let me add, D, that I'm saying there are brute facts that are not counter-categorical insomuch as they are implied by or correlative with categorically prehendible warranted beliefs. But that doesn't mean that the "how" of some of these brute facts is not SUPRA-categorical. E.g., I have no way of conceiving how God could know that there is not another "god" out there existing in a mode or in relations inconceivable to us that could trump Him. For I ground the competence of my apprehension in God's competent design. God's prehension, however, can not be grounded in competent design, for He was not designed.

Thus, the "how" of some of these brute facts is truly mysterious. We only know the brute facts, themselves, because of the logical relations they hold to other beliefs we have that are warranted, per our categorical modes of apprehension. To believe less than these warranted beliefs that imply these brute facts would cause us to be paralyzed volitionally and, hence, intellectually, or else it would cause us to be irrational and, hence, hypocritical. Those are our two options as I see it. We can not seem to volitionally choose to be systematically irrational. Even gross hypocrites don't realize the extent of their irrationality and hypocrisy, which is why they can seem so shameless.

One day, God will stop every hypocriticial mouth. Then, all will think as clear as a bell--then they will bow the knee and confess with the mouth that Jesus, son of Joseph and Mary, is and was he for whom and through whom all created things exist.