It doesn't prove whether Christians, Muslims, Jews, or Jainists have the right idea about God. It doesn't prove whether God is good or evil. It doesn't prove whether God is a personal, loving entity or something as impersonal as some self-causing physics concept that propogates the galaxy.
But I think it does prove the existence of God if God is defined as an entity so infinitely powerful that it becomes self-causing by permeating all time and space. I just don't logically see how something could come out of nothing. In my opinion, that's an absolute, self-evident truth the way Descartes' "I think, therefore I am" is. However, I was curious if any of the cynics had anything to say.


