If absence of proof is not proof of absence, but absence of evidence is evidence of absence, what makes proof different from evidence?
Example: we currently have no evidence supporting the existence of planets orbiting stars in other galaxies, because our telescopes are not powerful enough to observe them. Should we take this as evidence that no galaxy except ours has planets around its stars?
Another example: before the invention of the microscope, there was no evidence supporting the existence of bacteria because there were no means to observe them. Should’ve this fact alone been interpreted as evidence of absence of bacteria (even though bacteria did exist before microscopes were invented)?
Generally, the answer to your question is Bayes’ Theorem. This theorem is essentially the mathematical formulation of how evidence ought to be weighed when testing ideas. If the wikipedia article doesn’t help you much, Eliezer has written an in-depth explanation of what it is and why it works.
The specific answer to your question can be revealed by plugging into this equation, and defining “proof”. We say that nothing is ever “proven” to 100% certainty, because if it were (again, according to Bayes’ Theorem), no amount of new evidence against it could ever refute it. So “proof” should be interpreted as “really, really likely”. You can pick a number like “99.9% certain” if you like. But your best bet is to scrap the notion of absolute “proof” and start thinking in likelihoods.
You’ll notice that an integral part of Bayes’ Theorem is the idea of how strongly we would expect to see a certain piece of evidence. If the Hypothesis A is true, how likely is it that we’ll see Evidence B? And additionally, how likely would it be to see Evidence B regardless of Hypothesis A?
For a piece of evidence to be strong, it has to be something that we would expect to see with much greater probability if a hypothesis is true than if it is false. Otherwise there’s a good chance it’s a fluke. Furthermore, if that evidence is something that we wouldn’t expect to see much either way, than it’s not very informative when we don’t see it.
So you see how this bears on your examples. I’m not especially familiar with astronomy, so I don’t know whether it’s true that we haven’t seen other galaxies with planets, or how powerful our telescopes are. But let’s assume that what you’ve said is all true.
If we know our telescopes aren’t powerful enough to see other planets, then the fact that they don’t see any is virtually zero evidence. The probability of us seeing other planets is basically the same whether they’re out there or not (because we won’t see them either way), so our inability to see them doesn’t count as evidence at all. This test doesn’t actually tell us anything because we already know that it will tell us the same thing either way. It’s like counting how many fingers you have to determine if the stock market will go up or down. You’re gonna get “ten” no matter what, and this tells you nothing about the market.
The same reasoning applies to the bacteria example. If we’re not more likely to see them given that they’re real than we are given that they’re not real, then our inability to see them is not evidence in either direction. The test is a bad one because it fails to distinguish one possibility from the other.
But all this isn’t to say that it would be valid to reject these notions based on the absence of these evidences alone. There may be other tests we can run that would be more likely to come out one way or the other based on whether the hypothesis is true. So no, it wouldn’t make sense to reject the existence of planets or bacteria, because in both of your examples people are using tests that are known to be useless.
If we’re not more likely to see them given that they’re real than we are given that they’re not real, then our inability to see them is not evidence in either direction. The test is a bad one because it fails to distinguish one possibility from the other
For a sense of scale: the most distant extrasolar planet is 21,500 ± 3,300 light years away, and rather hypothetical—look at the size of the error bar on that distance.
we currently have no evidence supporting the existence of planets orbiting stars in other galaxies, because our telescopes are not powerful enough to observe them. Should we take this as evidence that no galaxy except ours has planets around its stars?
Yes we do. We have evidence about how physics (ie. gravity) works and about the formation phases of the universe. That earth and the other planets here exists is evidence. We just didn’t happen to have one particular kind of evidence (seeing them). And no, until we developed (recently) the ability to see evidence of them ourselves you would not have been entitled to that piece of evidence either. Because we should not have expected to see them. Seeing planets with tech that should not see them would have been evidence that something else was wrong.
If absence of proof is not proof of absence, but absence of evidence is evidence of absence, what makes proof different from evidence?
Proof is absolute, evidence is probabilistic.
Example: we currently have no evidence supporting the existence of planets orbiting stars in other galaxies, because our telescopes are not powerful enough to observe them. Should we take this as evidence that no galaxy except ours has planets around its stars?
No, absence of evidence is not evidence of absence if evidence is impossible, but it is evidence of absence if evidence is possible but absent.
The simple answer is that absence of proof towards a possibility is not proof that that the possibility cannot exist, merely that there is no actual proof either way. However, in this specific case, the absence of evidence pointing towards the existence of a fifth column that is engaging in sabotage is evidence that indicates that the fifth column does not exist. I agree that the specific terminology is a bit confusing, but that is the simple explanation as to your question.
Proof means “extremely strong evidence”. Absence of proof and absence of evidence are both evidence of absence. Their strength is determined by the probability with which we’d expect to see them, conditional on the thing existing and not existing.
If absence of proof is not proof of absence, but absence of evidence is evidence of absence, what makes proof different from evidence?
Example: we currently have no evidence supporting the existence of planets orbiting stars in other galaxies, because our telescopes are not powerful enough to observe them. Should we take this as evidence that no galaxy except ours has planets around its stars?
Another example: before the invention of the microscope, there was no evidence supporting the existence of bacteria because there were no means to observe them. Should’ve this fact alone been interpreted as evidence of absence of bacteria (even though bacteria did exist before microscopes were invented)?
Hi DevilMaster, welcome to LessWrong!
Generally, the answer to your question is Bayes’ Theorem. This theorem is essentially the mathematical formulation of how evidence ought to be weighed when testing ideas. If the wikipedia article doesn’t help you much, Eliezer has written an in-depth explanation of what it is and why it works.
The specific answer to your question can be revealed by plugging into this equation, and defining “proof”. We say that nothing is ever “proven” to 100% certainty, because if it were (again, according to Bayes’ Theorem), no amount of new evidence against it could ever refute it. So “proof” should be interpreted as “really, really likely”. You can pick a number like “99.9% certain” if you like. But your best bet is to scrap the notion of absolute “proof” and start thinking in likelihoods.
You’ll notice that an integral part of Bayes’ Theorem is the idea of how strongly we would expect to see a certain piece of evidence. If the Hypothesis A is true, how likely is it that we’ll see Evidence B? And additionally, how likely would it be to see Evidence B regardless of Hypothesis A?
For a piece of evidence to be strong, it has to be something that we would expect to see with much greater probability if a hypothesis is true than if it is false. Otherwise there’s a good chance it’s a fluke. Furthermore, if that evidence is something that we wouldn’t expect to see much either way, than it’s not very informative when we don’t see it.
So you see how this bears on your examples. I’m not especially familiar with astronomy, so I don’t know whether it’s true that we haven’t seen other galaxies with planets, or how powerful our telescopes are. But let’s assume that what you’ve said is all true.
If we know our telescopes aren’t powerful enough to see other planets, then the fact that they don’t see any is virtually zero evidence. The probability of us seeing other planets is basically the same whether they’re out there or not (because we won’t see them either way), so our inability to see them doesn’t count as evidence at all. This test doesn’t actually tell us anything because we already know that it will tell us the same thing either way. It’s like counting how many fingers you have to determine if the stock market will go up or down. You’re gonna get “ten” no matter what, and this tells you nothing about the market.
The same reasoning applies to the bacteria example. If we’re not more likely to see them given that they’re real than we are given that they’re not real, then our inability to see them is not evidence in either direction. The test is a bad one because it fails to distinguish one possibility from the other.
But all this isn’t to say that it would be valid to reject these notions based on the absence of these evidences alone. There may be other tests we can run that would be more likely to come out one way or the other based on whether the hypothesis is true. So no, it wouldn’t make sense to reject the existence of planets or bacteria, because in both of your examples people are using tests that are known to be useless.
If we’re not more likely to see them given that they’re real than we are given that they’re not real, then our inability to see them is not evidence in either direction. The test is a bad one because it fails to distinguish one possibility from the other
Thank you. That’s what I did not understand.
For a sense of scale: the most distant extrasolar planet is 21,500 ± 3,300 light years away, and rather hypothetical—look at the size of the error bar on that distance.
The nearest dwarf satellite galaxy is 25,000 light years away, so I suppose we’ve got a chance of seeing planets there.
The nearest actual galaxy is Andromeda, at 2.5 million light years.
Yes we do. We have evidence about how physics (ie. gravity) works and about the formation phases of the universe. That earth and the other planets here exists is evidence. We just didn’t happen to have one particular kind of evidence (seeing them). And no, until we developed (recently) the ability to see evidence of them ourselves you would not have been entitled to that piece of evidence either. Because we should not have expected to see them. Seeing planets with tech that should not see them would have been evidence that something else was wrong.
Proof is absolute, evidence is probabilistic.
No, absence of evidence is not evidence of absence if evidence is impossible, but it is evidence of absence if evidence is possible but absent.
(try saying that quickly 3 times :)
Benelliot and others have explained this well, but note that we do have direct evidence for planets in other galaxies. We’ve had it for about two years.
The simple answer is that absence of proof towards a possibility is not proof that that the possibility cannot exist, merely that there is no actual proof either way. However, in this specific case, the absence of evidence pointing towards the existence of a fifth column that is engaging in sabotage is evidence that indicates that the fifth column does not exist. I agree that the specific terminology is a bit confusing, but that is the simple explanation as to your question.
Proof means “extremely strong evidence”. Absence of proof and absence of evidence are both evidence of absence. Their strength is determined by the probability with which we’d expect to see them, conditional on the thing existing and not existing.