Scientific "proof"?

I've had many occasions to take issue with the notion of scientific "proof" and how that notion is understood by non-scientists. In particular, non-scientists have trouble accepting that scientific proof is, in fact, impossible!

Perhaps if one thinks back to one's happy days learning geometry in high school, the notion of mathematical "proof" will be recalled with fond memories! Or perhaps not. In any case, in mathematics, "proof" of a theorem is accomplished when one follows the laws of mathematical logic, beginning with some premise, say X, and then asserting that Y follows from X. If that theorem can be shown to be derivable from the axioms of the mathematical system in question (e.g., Euclidean geometric axioms) according to the laws of mathematical logic, proof is obtained. Once established, a proof cannot be contravened. No one disputes the Pythagorean Theorem of Euclidean geometry, for instance. Once proven, it remains proven for all time. There might be a different proof that's more "elegant" in some way, but the theorem has been established beyond doubt in any case. You can dispute the premises associated with a theorem (theorems typically involve an "if X, then Y" statement, so X might be disputed, but if you grant X, then a proof of the theorem makes Y inevitable), or you might see that in a different axiom system, that proof isn't valid, but within the constraints of the exercise, there can be no further dispute regarding that theorem. A proof in mathematics is forever, and has no qualifications whatsoever, other than the aforementioned possibilities: dispute the premise or consider a different set of axioms.

What about science? Many people believe that such a thing as "scientific proof" exists. For instance, one might argue that the Law of Gravity has been proven beyond any question. A large number of experiments (and common experience) suggests that it might be very difficult to come up with an example where the Law of Gravity has been shown to be invalid. However, "absolute proof" is tricky. No number of experiments can ever establish absolute proof, although they certainly can make a compelling case for those scientific hypotheses that survive a large number of rigorous experimental tests. Nevertheless, from a purely logical standpoint, it might be the case that we simply haven't done the right experiments to test the hypothesis in question adequately. In fact, it's impossible to "prove" that no experiment exists that would be capable of invalidating any scientific hypothesis. So we are entitled in certain cases to behave as if absolute proof has been obtained, since the hypotheses in question have survived some tough tests, but we must submit to the logical possibility that a counter-example might someday be found, even though we have yet to find any.

Scientific hypotheses are always provisional and can never be subjected to absolute proof! Einstein has, in fact, created a new version of the Law of Gravity that differs in very interesting and subtle ways from that first formulated by Isaac Newton. Thus, in this sense, Newton's Law of Gravity has been "disproven" and replaced by Einstein's Law of Gravity, even though for centuries no one ever dreamed of looking at the circumstances associated with what Einstein figured out regarding gravity. So far, Einstein's version has survived every test, as did Newton's version for centuries. There can be no logical guarantees for Einstein's version, however. Our understanding of gravity is limited and our hypotheses about it are always subject to re-examination, new tests, and possible revision. The putative Law of Gravity has nothing like the rock-solid standing of the Pythagorean Theorem, and never will.

It's the very nature of the scientific enterprise that we test our ideas against evidence. This is the fundamental basis of the so-called "scientific method." There is no simple formulaic way to describe the "scientific method," however. Hypothesis testing is dependent on the nature of the evidence available to use to test our ideas, and is a source for considerable creativity in science. It is by no means a simple algorithm to be applied to all scientific ideas. In some sciences (including meteorology, geology, and astronomy), it's impossible to run controlled experiments to test our ideas. Hence, such sciences depend on how to use and interpret whatever observational evidence is available, rather than running tightly controlled experiments (as in a laboratory). This doesn't diminish the scientific standing of those disciplines, however. They just have to be more creative in how to test their ideas and more cautious in their interpretations of the results of their tests.

To the extent that we can conduct experiments that can give our ideas a rigorous test, we can have some faith in accepting our current understanding as "not yet invalidated" hypotheses. But no scientific experiments can provide the sort of logical inevitability that mathematical logic offers. "Scientific proof" is not a valid understanding of how science actually works!

Hence, whenever you hear someone talk of "scientific proof," you can be assured that this person has an incorrect understanding of science!