Right. Proving a negative in the rhetorical or philosophical sense is not the same as proving a negative in the mathematical sense when the mathematical stateme

Right. Proving a negative in the rhetorical or philosophical sense is not the same as proving a negative in the mathematical sense when the mathematical statement has an exact inverse. You can't prove God doesn't exist. You can only prove he does given the right evidence, but lack of evidence doesn't prove non-existence. This is why Bayesian reasoning has been in use for a long time in science. It moves past the proof obsession to discussing likelihood.