Friday, February 17, 2006

Cantor's Set Theorem as a Proposed Disproof of God's Omniscience

Update 1/13/2013: Here's a post that's been vitiated at http://scientopia.org/blogs/goodmath/2012/12/31/a-bad-mathematical-refutation-of-atheism. The author is right; I had no idea what I was talking about. I was 16 and full of myself. Here's the post for your amusement. I won't have time to do a lot of necessary revisions on this blog until at least the summer of 2013, if not later:

MYTH
Cantor's Set Theorem disproves divine omniscience

God is omniscient in the sense that He knows all that is not impossible to know. God knows Himself, He knows and does, knows every creature ideally, knows evil, knows changing things, and knows all possibilites. His knowledge allows free will.

Cantor's set theorem is often used to argue against the possibility of divine omniscience and therefore against the existence of God. It can be stated:
1. If God exists, then God is omniscient.
2. If God is omniscient, then, by
definition, God knows the set of all truths.
3. If Cantor's theorem is true,
then there is no set of all truths.
4. But Cantor’s theorem is true.
5. Therefore, God does not exist.
However, this argument is false. The non-existence of a set of all truths does not entail that it is impossible for God to know all truths. The consistency of a plausible theistic position can be established relative to a widely accepted understanding of the standard model of Cantorian set theorem. The metaphysical Cantorian premises imply that Cantor’s theorem is inapplicable to the things that God knows. A set of all truths, if it exists, must be non-Cantorian.
The attempted disproof of God’s omniscience is, from a meta-mathematical standpoint, is inadequate to the extent that it doesn't explain well-known mathematical contexts in which Cantor’s theorem is invalid. The "disproof" doesn't acknowledge standard meta-mathematical conceptions that can analogically be used to establish the relative consistency of certain theistic positions. The metaphysical assertions concerning a set of all truths in the atheistic argument above imply that Cantor’s theorem is inapplicable to a set of all truths.