Sorry but you are deluding yourself. Proof by exhaustion in a non-mathematical sense is definitely invalid simply because you can’t test ALL cases. Besides, there are enough cases that prove agw is wrong so it places your total approach to proving agw is right into the delusional world. If you discount the cases against agw simply because you won’t believe them, then you are really using another invalid method of proof – proof by filtering and censorship.
Also, your water fluoridation is invalid since you are using a negative hypothesis, not a positive one. The amount of fluoride in the water is too small to be an issue. If the level is increased sufficiently, then the water would become unsafe to drink. But of course there are many case studies to show water fluoridation is a problem for some people, so your blanket statement is invalid in any case. This is why proof by exhaustion only applies in certain mathematical cases.