In response to two recent posts, here and here, Jacques comments:
I'm mostly persuaded by your recent posts about theism and knowledge, but I disagree about your claim that
"Presumably God can prove the existence of God, if he exists, not that he needs to."
Think of your condition 5 ["It is such that all its premises are known to be true."] if you can prove that p then you can derive p from an argument with premises all of which are known to be true. Suppose that God has some argument A for the conclusion that God exists. As you point out, A will either depend on premises taken to be self-evident, or an appeal to the seeming self-evidence of further premises in sub-arguments for the premises in A that are not taken to be self-evident. But now suppose that there's some premise P such that A is a proof of theism for God only if God takes P to be self-evident and P really is self-evident — in other words, only if P is 'objectively' self-evident and not just 'subjectively'. Of course, P might well appear to God to be self-evident; it might even appear to him that the objective self-evidence of P is itself objectively self-evident, and so on ad infinitum. But how could He really know, or be rationally entitled to believe, that P really is self-evident in the relevant sense rather than just seeming that way to Him? Sure, if He already knows that God exists, and that He Himself = God, then He can infer that the fact that P seems to him self-evident entails its real objective self-evidence. But how can He know that unless He can prove that He = God?
BV: The question seems to come down to whether or not the distinction between subjective and objective self-evidence applies to God as well as to us. It does apply to us. But I don't see that it applies to God. God's is an archetypal intellect, which implies that divine knowledge is creative of its object, whereas our knowledge is clearly not. If God knows that p by making it the case that p, then there is no logical gap between subjective and objective self-evidence for God.
On the other hand, it could be that God isn't even capable of proving anything. Maybe proofs are only possible for ignorant thinkers (who don't know directly, by acquaintance all the facts). But if He could prove or try to prove things I suspect His situation would be no better than ours with respect to His existence. Of course that conflicts with the (definitional?) fact of His omniscience, but maybe the conclusion should just be that the traditional concept of the Omni- God is incoherent.
BV: The divine intellect is intuitive, not discursive. God knows directly, not mediately via inferential processes. To know something in the latter way is an inferior way of knowing, and as such inappropriate to the divine intellect. Does it follow that God can't prove anything? I would hesitate to say that given the divine omnipotence: if he wanted to construct a proof he could. The point is that he doesn't need to. But we do need to employ inferential process to articulate and amplify our knowledge both deductively and inductively.
The main question, however, was whether WE can prove the existence of God. My answer to that is in the negative. The reason is due to the nature of proof as set forth in my definition. But perhaps you have a better definition.
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