Evidence, Knowledge, and Proof

Pharyngula writes: "Scientists don't talk about 'proof', period. We leave that to the mathematicians." Before I started reading B&W, I had tended to take 'evidence' and 'proof' as almost synonymous. Somewhere along the way I picked up Ophelia's irritation with the conflation, and now I too get annoyed whenever I see the words "science" and "proof" too closely associated. But I wonder if I'm right to do so -- perhaps there is a perfectly acceptable notion of 'proof' which could allow for the uncertainties of science?

The problem with 'proof', of course, is that it connotes certainty and completion. But scientific inquiry is never completed, and nor are its verdicts infallible. Nothing is set in stone or held to be beyond question. So, we might think, nothing is ever "proved".

But this may be a needlessly strict sense of the word "proof", if we may never apply it to anything but mathematics. It certainly doesn't match common usage, where we ask for proof of empirical facts all the time. Consider the following exchange:

A: "You shaved your head? Prove it!"
B: *removes hat to expose shaved head*

There you go -- B proved it. It would be inappropriate for A to respond "But it's possible that I'm just hallucinating, right?" Absolute certainty is not necessary for proof, any more than it is for knowledge. What matters, in either case, is that our justification or evidence is good enough - it need not be absolutely perfect.

Should we say that proof is merely "evidence so strong that it would be unreasonable to deny the supported conclusion"? Well, that's not quite good enough, for that would allow us to prove things that are actually (if surprisingly) false. So, as for knowledge, we must supplement the justification requirement with a truth requirement. If the conclusion is not true, then it cannot be known or proved.

Given these connections between the two, I wonder if we might be able to define proof in terms of knowledge? We might say that 'proof' is simply "evidence that is sufficient to establish knowledge of a conclusion". Knowledge entails truth, so we avoid the previous problem. But knowledge need not require certainty, so we also avoid the first problem. This definition would allow us to say, for example, that scientists have proved that Earth orbits the Sun, and that all Terran species evolved from a common ancestor. (Assuming that we do in fact know these things.) On many other issues, scientific evidence may support a conclusion, but not strongly enough to establish knowledge, and so such evidence would fail to constitute proof.

Does that sound like a plausible analysis of 'proof'?

P.S. When I first thought up this topic, I had planned to tie it in with the possibility of Gettier cases in mathematics. But I've now forgotten how I was going to do that. If you have any ideas, feel free to leave a comment -- perhaps you'll jog my memory :)