Yes they do. If the world is controlled by an intelligent entity, then statistical proofs tell you about the behaviour of that entity, rather than impersonal laws of physics, but they still tell you what’s likely to happen.
Yes, however, it is conceivable that the intelligent entity is sufficiently complicated that no amount of evidence gathered within the universe could allow us to uniquely identify its nature. This is of course implausible based on prior probability, solomonov induction, etc., though.
Statistical proofs of things don’t necessarily work if the world is controlled by an intelligent entity.
Yes they do. If the world is controlled by an intelligent entity, then statistical proofs tell you about the behaviour of that entity, rather than impersonal laws of physics, but they still tell you what’s likely to happen.
Yes, however, it is conceivable that the intelligent entity is sufficiently complicated that no amount of evidence gathered within the universe could allow us to uniquely identify its nature. This is of course implausible based on prior probability, solomonov induction, etc., though.