Wednesday, April 29, 2009

God and Stuff

A couple of God questions this week.

kzndr asks,

"Are any of the classical arguments for the existence of God actually any good?"

The interesting one, though, is Anselm's argument that a perfect being must exist because existence is a perfection and God by definition is all-perfect. In its standard form, as Kant pointed out, it confuses existence (a precondition for having properties) with a property. One doesn't have or not have the property of existence, if one exists, then one may have properties (especailly if playing Monopoly).

There are, however, some strengths of modal logical language in which one can derive as a logical truth that God must necessarily exist. It requires what logic geeks call a language of strength S5 in which the fact that some sentence p might be true means that it must be the case that it is necessarily the case that p is possible. Is this the case? It is an axiom that we can assume or not so it is possible that the possible necessity of God means that it is necessarily true that God necessarily exists.

The possibility of a modal logic discussion, necessarily brings out Hanno. He asks,
"Is Quantum Mechanics incompatible with an omniscient God?"
The correct answer, of course, is a superposition of yes and no.

The problem is with the so-called measurement problem. When a system is unobserved its natural state is one of a superposition of all possible states. Take spin which is easy because it has two values -- up and down -- making it like a quantum coin flip. When we do not measure the spin of a particle, it will be in a superposed state of up and down. The Schrodinger equation, the fundamental rule of quantum mechanics, talks about how this superposition evolves over time. And it does. This is completely deterministic; nothing random. It's just like Newton's laws.

But the weird thing is that we never ever see anything in its superposed state. The instant we observe, the system collapses into one of its possible property states and we see it there. In our example, it becomes either spin up or spin down. But here is the wierd part, we don't...indeed, can't...know which state it will fall into. THAT is where the randomness of quantum mechanics shows up. There are no hidden variables that we just haven't found yet that will tell us ahead of time and we know from experiments that it really is in this superposed state of multiple possible observable states because we can get it to do things like interfere with itself.

So, now we come to God. We have a particle whose spin we have not yet, but are about to measure. It will be spin up or down, but isn't either yet. Can God know which it will be? No. But the question is whether this is a challenge to omniscience. One the one hand, the genuine randomness does seem to challenge the idea that God knows all facts at any time, but one could also argue that there simply isn't a fact to be known until the measurement, so God's omniscience is saved.