Man’s spontaneous tendency is to give credence to assertions and reproduce them, without even distinguishing them clearly from his own observations. In everyday life, do we not accept indiscriminately, without any sort of verification, rumors, anonymous and unverified reports, all sorts of “documents” of little or no worth? We need a special reason to take the trouble to examine the provenance and value of a document about what happened yesterday; otherwise, if it is not unlikely to the point of scandal, and as long as no one contradicts it, we take it in and hold on to it, we peddle it ourselves, embellishing it if need be. Every honest man will admit that a violent effort is necessary to shake off ignavia critica [critical laziness], that so widespread form of intellectual cowardice; that this effort must be constantly repeated, and that it is often accompanied by real suffering.
If I hadn’t read “Conservation of Expected Evidence” , it would never have occurred to me to think of truth-seeking as a zero-sum game and ask, if we have something extraordinary over here, then what is forced to be ordinary to compensate?
This may sound clever but it simply isn’t true. It is perfectly possible to find extraordinary evidence for a merely ordinary claim.
I’m sure I could find huge amounts of evidence for the claim the high speed car crashes are frequently fatal, but this doesn’t mean the claim “slamming into a large metal object at 70mph may kill you” ever deserved a low prior.
The intended meaning of “extraordinary evidence” in the original quote is simply “very strong evidence” or for a more Bayesian way of putting it “evidence which would be phenomenally unlikely if the claim in question was incorrect”.
The intended meaning of “extraordinary evidence” in the original quote is simply “very strong evidence”
Not at all! For many ordinary claims like “the Sun will rise tomorrow” we have quite strong evidences, while we lack that strong evidences about some more extraordinary claims.
The whole point of the quote is that if we lack extraordinary (which means extraordinarily strong) evidence about an extraordinary claim we shouldn’t believe it. I stand by that idea. Therefore I suspect all of your counterexamples are bogus.
“You can’t travel faster than light” is quite an extraordinary claim, which has not as strong evidences, as the ordinary “an apple falls down if you drop it” has.
“You can’t travel faster than light” has lots of strong evidence for it, or at any rate it is a very high-probability consequence of a theory which has lots of strong evidence for it. Its not even that extraordinary, it doesn’t contradict anything else we know to be true and it refers to a domain which we have no experience of (travelling at a speed measured in millions of meters per second) so the fact that its non-intuitive shouldn’t be so significant. Compare that with a genuinely extraordinary claim like “homoeopathy works” which is made extraordinary by dint of the fact that if its true we have to throw out the whole of physics, which has plenty of evidence for it.
It doesn’t have as much evidence as “an apple falls down if you drop it” but this fact is irrelevant. Bayesian probability is not a competition, just because we have more evidence for B than for A doesn’t mean we can’t have enough evidence for both of them. The situation would be different if A and B were mutually contradictory, but since they clearly aren’t in this case the fact that one has stronger evidence does not contradict the fact that the other still has strong evidence.
Its simple Bayesian logic, if a claim is extraordinary (meaning implausible/very low prior) then to confirm it you need extraordinary evidence (meaning extraordinarily strong). Any such evidence is unlikely by definition, but it does not have to be weird in the sense of being non-intuitive.
This is the last post I’ll make in this discussion because frankly this argument has become stupid. I seem to recall other discussions with you that went the same way so we obviously bring out the worst in each other.
For the purposes of the original quote extraordinary evidence did not mean weird, it meant very strong, as I just explained. Extraordinary claims certainly don’t require weird evidence to confirm them.
Charles-Victor Langlois and Charles Seignobos, “Introduction aux études historiques” (1898), via LanguageHat (http://www.languagehat.com/archives/001685.php).
And is that laziness so bad? If extraordinary claims require extraordinary evidence, presumably ordinary claims require merely ordinary evidence...
“Ordinary claims require merely ordinary evidence” is an overlooked and tremendously important corollary.
I have you to thank for that insight, actually.
If I hadn’t read “Conservation of Expected Evidence” , it would never have occurred to me to think of truth-seeking as a zero-sum game and ask, if we have something extraordinary over here, then what is forced to be ordinary to compensate?
I’m going to quote you on this in the rationality book. Email me with who you want credited if it’s not “gwern on LessWrong.com″.
Email sent. (Gosh, I think this will be the second book I’ll be mentioned in. How thrilling.)
As extraordinary evidences require some extraordinary claims as well.
This may sound clever but it simply isn’t true. It is perfectly possible to find extraordinary evidence for a merely ordinary claim.
I’m sure I could find huge amounts of evidence for the claim the high speed car crashes are frequently fatal, but this doesn’t mean the claim “slamming into a large metal object at 70mph may kill you” ever deserved a low prior.
It is not en extraordinary evidence for me, if it can be explained by some ordinary claims.
Nitwit games.
The intended meaning of “extraordinary evidence” in the original quote is simply “very strong evidence” or for a more Bayesian way of putting it “evidence which would be phenomenally unlikely if the claim in question was incorrect”.
Not at all! For many ordinary claims like “the Sun will rise tomorrow” we have quite strong evidences, while we lack that strong evidences about some more extraordinary claims.
The whole point of the quote is that if we lack extraordinary (which means extraordinarily strong) evidence about an extraordinary claim we shouldn’t believe it. I stand by that idea. Therefore I suspect all of your counterexamples are bogus.
“You can’t travel faster than light” is quite an extraordinary claim, which has not as strong evidences, as the ordinary “an apple falls down if you drop it” has.
You misunderstood.
“You can’t travel faster than light” has lots of strong evidence for it, or at any rate it is a very high-probability consequence of a theory which has lots of strong evidence for it. Its not even that extraordinary, it doesn’t contradict anything else we know to be true and it refers to a domain which we have no experience of (travelling at a speed measured in millions of meters per second) so the fact that its non-intuitive shouldn’t be so significant. Compare that with a genuinely extraordinary claim like “homoeopathy works” which is made extraordinary by dint of the fact that if its true we have to throw out the whole of physics, which has plenty of evidence for it.
It doesn’t have as much evidence as “an apple falls down if you drop it” but this fact is irrelevant. Bayesian probability is not a competition, just because we have more evidence for B than for A doesn’t mean we can’t have enough evidence for both of them. The situation would be different if A and B were mutually contradictory, but since they clearly aren’t in this case the fact that one has stronger evidence does not contradict the fact that the other still has strong evidence.
Its simple Bayesian logic, if a claim is extraordinary (meaning implausible/very low prior) then to confirm it you need extraordinary evidence (meaning extraordinarily strong). Any such evidence is unlikely by definition, but it does not have to be weird in the sense of being non-intuitive.
This is the last post I’ll make in this discussion because frankly this argument has become stupid. I seem to recall other discussions with you that went the same way so we obviously bring out the worst in each other.
If I understand you correctly, extraordinary claims have better evidence on average than more ordinary claims, since they need such.
It is not the case.
Michelson Morley experiment produced some extraordinary evidence. We needed some Einstein’s extraordinary claims to deal with that evidence.
Just one example from hundreds and more.
For the purposes of the original quote extraordinary evidence did not mean weird, it meant very strong, as I just explained. Extraordinary claims certainly don’t require weird evidence to confirm them.