"Proof by exhaustion in a non-mathematical sense is invalid."
Untrue, starbust. Determining the safety of a substance is a case in point. Water fluoridation is a good example: There is no evidence of its harm, yet it cannot be said that the safety of water fluoridation is proven absolutely. This fact is abused by anti-fluoridationists, though after several decades of safe useage, they are fortunately regarded by most as crackpots. Proof by exhaustion is a fact of life in the real world.
For the AGW hypothesis, all you can do is look for other causes. It is a fact that the observed changes have not as yet been explained by natural phenomena. Will it be disproven? That remains unknown, but after failing to be disproved for so long, I would think it unlikely.
