I guess I shouldn’t have said “demonstrate”. From another perspective, how about the fact the the very existence and beauty of logic leave imply an awesome God, just like a beautiful field of flowers or a starry night sky? Not persuasive, I know, to someone who doesn’t want to be persuaded, but it was another slightly related facet of our discussion that occurred to me.
Erps. I are a typerist.
It gets back to the theme I'm working on concerning Rand running into what appear to be more or less universal problems in philosophy. Rand is attempting something bold and ambitious (some would say arrogant as well) by literally rewriting philosophy from first principles. None of what she says or does is unprecedented but it does seem to be largely original. And the difficulty with the refusal to "stand on the shoulders of giants" is that you end up having to climb up all that way by yourself, avoiding false paths that have already been identified, wasting time and effort re-inventing the philosophical wheel.
I think that she finds the arguments for the existence of God unsatisfying because they do not seem to follow those laws of the universe - nothing palpable, falsifiable, no experimental situation one might set up that will break one way if God exists and the other if He does not. It's a perfectly legitimate objection. Aristotle's conclusion was that those laws are necessarily subordinate to their source; Rand's was that those laws cannot be incompatible with their source and that compatibility must be proven for the source to be considered legitimate. Philosophy has been here before, many times.
You can certainly work an agnostic position out of it. Not an atheistic one, however, for exactly the same reason you can't work out a theistic one. This is precisely the reason that an atheistic position is essentially a matter of faith. If you can't prove that God is compatible with the laws of the universe, neither can you prove that He isn't. It's a false path.
A thing I'll be thinking about on this beautiful Easter Sunday. My best to all here!