Thursday, June 16, 2005

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 :)


  1. The problem with using colloquial examples to illustrate the word "proof", though, is that isn't what we face. Maybe we're more sensitized to the distinction in biology because the damned creationists use the word in a very strict sense, demanding absolute, irrefutable, exhaustive "proof"--they want a complete video recorded from the first progenote to the latest baby born, and anything less is grounds for complaint.

    So why try to make it clear: we aren't doing mathematical proofs, we are compiling and interpreting evidence.

    Of course, "evidence" also seems to have a very different meaning to the Genesis crowd, who think personal testimony is the same thing.

  2. Yes, fair enough. I quite agree with you that it's important to emphasize that science is in the business of "compiling and interpreting evidence" rather than constructing absolute proofs.

    (I should clarify that my post is somewhat tangential to your one, despite using it as a starting point. I don't mean to be challenging your main point at all -- indeed, I largely agree with it.)

  3. If knowledge is justified true belief (or some variation to avoid the Gettier problem) then the justification has to come from somewhere. If you define justification in terms of evidence, and evidence in terms of knowledge, then you have a circularity. If you don't define justification in terms of evidence, then I have no idea how you do define it.

    General and particular statements are different. The problem is to get from particular observed facts, such as the shaved head, to general theories that are true everywhere all the time.

    You cannot prove that a general scientific theory is true, but you can prove that it is false by providing counterexamples. All we can do is to provisionally accept the best theories that have not been proven false. This reduces the problem to determining what 'best' means.

  4. Nigel, I don't want to define evidence in terms of knowledge. I want to define proof in terms of knowledge. There's no circularity involved in that.

    "You cannot prove that a general scientific theory is true"

    Well, that's going to depend on how we define "proof" :)

    We cannot know any general statement with certainty. But nor can we know any particular statement with absolute certainty, so I don't see how that distinction is relevant here.

    Assuming that general statements can be justified (despite falling short of certainty), it isn't clear to me why such justification couldn't be strong enough to yield knowledge, and thus (fallibilistic) proof.

  5. If knowledge is justified true belief (or some variation to avoid the Gettier problem) then the justification has to come from somewhere. If you define justification in terms of evidence, and evidence in terms of knowledge, then you have a circularity.

    Check out Williamson's Knowledge and Its Limits. There he adopts a thorough going externalism, largely equates knowledge and evidence and rejects the idea that knowledge is justified true belief. The arguments aren't as strong as I'd originally hoped. But it still is one of my favorite epistemology books of the last while.

  6. proof doesnt exist in mathmatics either in its strict context - it is just a joke to demand absolute "proof" of anything since there are no absolute grounds on which it could even theoreticaly be based.

    But since almost no one ever uses proof in that strict sense it is odd for anyone to use it as the "true definition".

  7. It seems you're wanting to define a particular threshold of consensus as constituting proof. This, in hindsight, was the mistake logical positivists made: they thought that because because of the tremendous success of scientific method, science must have put us on the path towards objective truth. But in the end, they couldn't agree on where the threshold between objective fact and subjective concept was.

    Does the observation of one million white swans or one trillion white swans mean the next observed swan will certainly be white? It's a futile discussion.

    I enjoyed your entry, going to poke around more. Thanks.

  8. Erik, don't forget that the sort of "proof" I have in mind is fallibilistic in nature. That is, it does not require certainty. (It requires that the conclusion be true, but not that we have to establish this with absolute certainty -- it's an 'external' rather than 'internal' requirement. The only internal requirement is strong enough justification.) So I don't see that the fallible nature of induction poses any problem for us here.

  9. I would have thought that proof, strictly speaking, was deductive and absolute. When you prove a theorum, you actually have something that you can point to which necessitates its truth. Science, however, seems inductive, as far as I can tell. For instance, any kind of "proof" you had would always be consistent with some divergent theory.

    Of course, I am begging the question. You are suggesting a different kind of "proof". It seems coherent to me! However, I'm not sure if I would want to adopt the concept, as "proof" has such absolute connotations. Then again, as your hat example suggests, many people do use proof in that sense. Perhaps there should still be a distinction among them though. Proof 1 = the very existence of the evidence guarantees the truth of the conclusion. Proof 2 = well evidenced (and true). I would still want to say that there is an important sense in which science cannot prove things.

  10. Yes, fair enough, I would agree with that.

  11. Note... I wrote that last comment about the same time as the 2 comments before it were being written. Pretty similar though! heh

  12. in your original post, you say, '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.) '

    The thing is that the scientific method does not offer proof of these things - it offers understandings of observations and reason to not rationally doubt those understandings. But if we claim 'proof', scientific inquiry halts. The strength of a theory is only as strong as the attacks it survives from competing theories - we always need to try - as hard as we can - to prove something is not true. Imagine if Einstein, Plank and Bohr's attitudes had been, 'Newton's laws proved the mechanical nature of all objects.'

    Is what you're looking for something like pragmatism, construcionism?


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