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RichardKennaway comments on What Bayesianism taught me - LessWrong
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After accounting for the filtering, which way does it point? If you're left with a delta log-odds of zero, it's "evidence" only in the sense that if you have no apples you have "some" apples.
Yes, "Daaad, Zeus the Greek god ate my homework!" isn't strong evidence, certainly.
But the way it points (in relation to P(Zeus exists)) is clear. I agree with your second sentence, but I'm not sure I understand your first one.
I don't think it is. If Zeus really had eaten the homework, I wouldn't expect it to be reported in those terms. Some stories are evidence against their own truth -- if the truth were as the story says, that story would not have been told, or not in that way. (Fictionally, there's a Father Brown story hinging on that.)
And even if it theoretically pointed in the right direction, it is so weak as to be worthless. To say, "ah, but P(A|B)>P(A)!" is not to any practical point. It is like saying that a white wall is evidence for all crows being black. A white wall is also evidence, in that sense, for all crows being magenta, for the moon being made of green cheese, for every sparrow falling being observed by God, and for no sparrow falling being observed by God. Calling this "evidence" is like picking up from the sidewalk, not even pennies, but bottle tops.
What I was just about to say. See also Yvain on self-defeating arguments.
Okay, but...
How so?
Every white wall is a non-sparrow not observed by God, hence evidence for God observing every sparrow's fall. It is also a, um, no, you're right, the second one doesn't work.
How do we know that the wall is not observed by God?
Ah, quite so. God sees all, sparrows and walls alike. Both of those examples are broken.
An omnipotence-omniscience paradox: "God, look away!" - "I can't!"
“There's something a human could do that God couldn't do, namely committing suicide.”
-- someone long ago, IIRC (Google is turning up lots of irrelevant stuff)
And since we usually desire the one thing we cannot have ...
That one's easily solvable, isn't it? God could look away if he wanted to, but chose not to.
If sparrows do not exist, then "every sparrow falling is observed by God" and "no sparrow falling is observed by God" are both true. (And of course, every white wall is a tiny bit of evidence for "sparrows do not exist", although not very good evidence since there are so many other things in the universe that also need to be checked for sparrow-ness.)
Well, we could use the word "evidence" in different ways (you requiring some magnitude-of-prior-shift).
But then you'd still need a word for "that-which-[increases|decreases]-the-probability-you-assign-to-a-belief". Just because that shift is tiny doesn't render it undefined or its impact arbitrary. You can say with confidence that 1/x remains positive for any positive x however large, and be it a googolplex (btw, TIL in which case 1/x would be called a googolminex).
Think of what you're advocating here: whatever would we do if we disallowed strictly-speaking-correct-nitpicks on LW?
There's a handy table, two of them in fact, of terminology for strength of evidence here. Up to 5 decibans is "barely worth mentioning". How many microbans does "Zeus ate my homework" amount to?
You may be joking, but I do think LW (and everywhere else) would be improved if people didn't do that. I find nitpicking as unappealing as nose-picking.
Few enough that it's in the "barely worth mentioning" bracket, of course. (Under any kind of resource constraint, it wouldn't be mentioned at all, however that only relates to its infinitesimal weight, not the nature of what it is (evidence).)
You say that shouldn't be classified as evidence, I say it should. Note that the table is about strength of evidence.
Nitpicking is absolutely critical in any public forum. Maybe in private, with only people who you know well and have very strong reason to believe are very much more likely to misspeak than to misunderstand, nitpicking can be overlooked. Certainly, I don't nitpick every misspoken statement in private. But when those conditions do not hold, when someone is speaking on a subject I am not certain they know well, or when I do not trust that everyone in the audience is going to correctly parse the statement as misspoken and then correctly reinterpret the correct version, nitpicking is the only way to ensure that everyone involved hears the correct message.
Charitably I'll guess that you dislike nitpicking because you already knew all those minor points, they were obvious to anyone reading after all, and they don't have any major impact on the post as a whole. The problem with that is that not everyone who reads Less Wrong has a fully correct understanding of everything that goes into every post. They don't spot the small mistakes, whether those be inconsequential math errors or a misapplication of some minor rule or whatever. And the problem is that just because the error was small in this particular context, it may be a large error in another context. If you mess up your math when doing Bayes' Theorem, you may thoroughly confuse someone who is weak at math and trying to follow how it is applied in real life. In the particular context of this post, getting the direction of a piece of evidence wrong is inconsequential if the magnitude of that evidence is tiny. But if you are making a systematic error which causes you to get the direction of certain types of evidence, which are usually small in magnitude, wrong, then you will eventually make a large error. And unless you are allowed to call out errors dealing with small magnitude pieces of evidence, you won't ever discover it.
I'd also like to say that just because a piece of evidence is "barely worth mentioning" when listing out evidence for and against a claim, does not mean that that evidence should be immediately thrown aside when found. The rules which govern evidence strong enough to convince me that 2+2=3 are the same rules that govern the evidence gained from the fact that when I drop an apple, it falls. You can't just pretend the rules stop applying and expect to come out ok in every situation. In part you can gain practice from applying the rules to those situations, and in part it's important to remember that they do still apply, even if in the end you decide that their outcome is inconsequential.
I disagree. Not all things that are true are either relevant or important. Irrelevancies and trivialities lower discussion quality, however impeccable their truth. There is practically nothing that anyone can say, that one could not find fault with, given sufficient motivation and sufficient disregard for the context that determines what matters and what does not.
In the case at hand, "evidence" sometimes means "any amount whatever, including zero", sometimes "any amount whatever, except zero, including such quantities as 1/3^^^3", and sometimes "an amount worth taking notice of".
In practical matters, only the third sense is relevant: if you want to know the colour of crows, you must observe crows, not non-crows, because that is where the value of information is concentrated. The first two are only relevant in a technical, mathematical context.
The point of the Bayesian solution to Hempel's paradox is to stop worrying about it, not to start seeing purple zebras as evidence for black crows that is worth mentioning in any other context than talking about Hempel's paradox.
Yes, in a world in which Zeus existed, people would not proclaim the importance of faith in Zeus, anymore than they proclaim the importance of faith in elephants or automobiles. Everyone would just accept that they exist.
I don't know: consider the classic cargo cult. It proclaims the importance of faith in airplanes.
Or consider Christianity: people who fully believe in Jesus Christ (=from their point of view they live in the world in which Jesus exists) tend to proclaim the importance of faith in Jesus.
Yes, that's the point - people don't tend to proclaim the importance of faith in things that actually exist. You won't hear them say "have faith in the existence of tables" or "have faith in the existence of chairs".
I would suspect that this is because a) everybody believes in tables and chairs (with the exception of a few very strange people, who are probably easy enough to spot), and b) nobody (again with a few odd exceptions) believes in any sort of doctrine or plan of action for chair-and-table-believers, so faith doesn't have many consequences (except for having somewhere to sit and place things on).
We, on the other hand, proclaim the importance of confidence in rational thought, for the same reasons that theists proclaim the importance of belief in their god: it is a belief which is not universal in the population, and it is a belief which we expect to have important consequences and prescriptions for action.