The Sagan quote you keep using does, in the circumstances I described, contradict a mathematical law -- that of Bayes' Theorem. Or, if you prefer something simpler, there is a logical equivalence between the two statements "If A, then B", and "If not B, then not A". I think this applies to this case, as follows:
All dowsers seem to claim that when their abilities are tested, they will be successful. Hence, we can say that if dowsing works, then it will be seen to work. This is our statement that A implies B -- and confirmed not by the scientists but by the dowsers. However, in the experiments I have mentioned earlier, that took place in conditions that were agreed to by the dowsers being tested, dowsing was not seen to work. Therefore, using the rule above, dowsing does not work.
This is of course far too dogmatic a statement, but then you can fall back on Bayes' Theorem to turn it into its equivalent in probability, which is that:
-- If you have searched for evidence of some proposition, and;
-- failed to find it, and;
-- if there is reason to believe that you would have found that evidence if the proposition were true, then;
-- The probability that the proposition is true decreases.
Therefore, we have that "absence of evidence can be evidence of absence". Not proof, of course, but evidence nonetheless.
"//An experiment that doesn't explore how isn't worth conducting.//
I disagree. An experiment that explores ‘If’ is worth conducting. Once it is established that the subject in question is not a delusion or a trick, the time then comes to explore ‘how?"
I think this is a fair point, actually, but for the fact that the experiments that explore "if" have already been conducted, and keep finding the answer "no". So I suppose I properly meant that such an experiment is not worth me conducting -- because it already has been, numerous times, with the same results. Apologies for that mistake.