Logical sets comprising a theoretical ontology are implicity incapable of providing comprehensive evidence for atheism. Logical sets of trans-infinite concepts are trans-infinite only in relation to other infinite sets none of which can be shown to contain all others including itself. Atheism would need to provide exhaustive data representation accurately regarding all Universal, trans-temporal and pre-Universal, before the big inflation and before any possible inflation or virtual loop, before anything ever was until the end of anything that could ever be (because of Wheeler's retro-causaliity idea) ways wherein God might exist to offer even minimal credibility (and it hasn't). Atheists to attain even a shred of credibility-for-others would need to demonstrate that human logic is capable of grasping the idea of God for-himself and negate that idea.
In the Bible the prophet Moses was allowed a small glimspe of the glory of God passing before him before he died. It isn't evident that even human philosophers are able to comprehend the nature of God or even of one Universe, as if it were a dot in infinite non-space less significant than a period at the end of a sentence.
Without such a logical set of inferences of the absolute trans-infinite set that captures all sets and ideas that might be represented in sets, no reasoning about the non-existence of God could be anything more than conditional, contingent and wrong. Atheism cannot be logically proven except as an existential belief for itself held by an individual in error.
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