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ChristianKl comments on Rationality Quotes April 2014 - LessWrong
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You are making a mistake in reasoning if you don't change your belief through that evidence. Your belief should change by orders of magnitude. A change from 10^{-18} to 10^{-15} is a strong change.
The central reason to believe that Zeus doesn't exist are weak priors.
Skeptics have ideas that someone has to prove something to them for them to believe it. In the Bayesian worldview you always have probabilities for your beliefs. Social obligations aren't part of it. "Good" evidence means that someone fulfilled a social obligation of providing a certain amount of proof. It doesn't refer to how strongly a Bayesian should update after being exposed to a piece of evidence.
There are very strong instincts for humans to either believe X is true or to believe X is false. It takes effort to think in terms of probabilities.
Where do those numbers come from?
In this case they come from me. Feel free to post your own numbers.
The point of choosing Zeus as an example is that it's a claim that probably not going to mindkill anyone. That makes it easier to talk about the principles than using an example where the updating actually matters.
I agree with this comment, but I want to point out that there may be a problem with equating the natural language concept "strength of evidence" with the likelihood ratio.
You can compare two probabilities on either an additive or multiplicative scale. When applying a likelihood ratio of 1000, your prior changes by a multiplicative factor of 1000 (this actually applies to odds rather than probabilities, but for low probability events, the two approximate each other). However, on an additive scale, a change from 10^{-18} to 10^{-15} is really just a change of less than 10^{-15} , which is negligible.
The multiplicative scale is great for several reasons: The likelihood ratio is suggested by Bayes' theorem, it is easy to reason with, it does not depend on the priors, several likelihood ratios can easily be applied sequentially, and it is suitable for comparing the strength of different pieces of evidence for the same hypothesis.
The additive scale does not have those nice properties, but it may still correspond more closely to the natural language concept of "strength of evidence"
I have not said that it's strong evidence. I said it's evidence.
Yes, that is probably clear to most of us here. But, in reality, I and most likely also you discount probabilities that are very small, instead of calculating them out and changing our actions (we'll profess 'this is very unlikely' instead of 'this is not true', but what actually happens is the same thing). There's a huge amount of probability 10^{-18} deities out there, we just shrug and assume they don't exist unless enough strong (or 'good', I still don't see the difference there) evidence comes up to alter that probability enough so that it is in the realm of probabilities worth actually spending time and effort thinking about.
This hypothetical skeptic, if pressed, would most likely concede that sure, it is /possible/ that Zeus exists. He'd even probably concede that it is more likely that Zeus exists than that a completely random other god with no myths about them exists. But he'd say that is fruitless nitpicking, because both of them are overwhelmingly unlikely to exist and the fact that they still might exist does not change our actions in any way. If you wish to argue this point, then that is fine, but if we agree here then there's no argument, just a conflict of language.
I'm trying to say that where you would say "Probability for X is very low", most people who have not learned the terminology here would normally say "X is false", even if they would concede that "X is possible but very unlikely" if pressed on it.
Given that someone like Richard Kennaway who's smart and exposed to LW thinking (>10000 karma) doesn't immediately find the point I'm making obvious, you are very optimistic.
People usually don't change central beliefs about ontology in an hour after reading a convincing post on a forum. A hour might be enough to change the language you use, but it's not enough to give you a new way to relate to reality.
The probability that an asteroid destroys humanity in the next decade is relatively small. On the other hand it's still useful for our society to invest more resources into telescopes to have all near-earth objects covered. The same goes for Yellowstone destroying our civilisation.
Our society is quite poor at dealing with low probability high impact events. If it comes to things like Yellowstone the instinctual response of some people is to say: "Extraordinary claims require extraordinary evidence."
That kind of thinking is very dangerous given that human technology get's more and more powerful as time goes on.
I would say the probability of Yellowstone or meteor impact situation are both vastly higher than something like the existance of a specific deity. They're in the realm of possibilities that are worth thinking about. But there are tons of other possible civilization-ending disasters that we don't, and shouldn't, consider, because they have much less evidence for them and thus are so improbable that they are not worth considering. I do not believe we as humans can function without discounting very small probabilities.
But yeah, I'm generally rather optimistic about things. Reading LW has helped me, at that - before, I did not know why various things seemed to be so wrong, now I have an idea, and I know there are people out there who also recognize these things and can work to fix them.
As for the note about changing their central beliefs, I agree on that. What I meant to say was that the central beliefs of this hypothetical skeptic are not actually different from yours in this particular regard, he just uses different terminology. That is, his thinking goes 'This has little evidence for it and is a very strong claim that contradicts a lot of the evidence we have' -> 'This is very unlikely to be true' -> 'This is not true' and what happens in his brain is he figures it's untrue and does not consider it any further. I would assume that your thinking goes something along the lines of 'This has little evidence for it and is a very strong claim that contradicts a lot of the evidence we have' -> 'This is very unlikely to be true', and then you skip that last step, but what still happens in your brain is that you figure it is probably untrue and don't consider it any further.
And both of you are most likely willing to reconsider should additional evidence present itself.
Careful there. Our intuition of what's in the "realm of possibilities that are worth thinking about" doesn't correspond to any particular probability, rather it is based on whether the thing is possible based on our current model of the world and doesn't take into account how likely that model is to be wrong.
If I understand you correctly, then I agree. However, to me it seems clear that human beings discount probabilities that seem to them to be very small, and it also seems to me that we must do that, because calculating them out and having them weigh our actions by tiny amounts is impossible.
The question of where we should try to set the cut-off point is a more difficult one. It is usually too high, I think. But if, after actual consideration, it seems that something is actually extremely unlikely (as in, somewhere along the lines of 10^{-18} or whatever), then we treat it as if it is outright false, regardless of whether we say it is false or say that it is simply very unlikely.
And to me, this does not seem to be a problem so long as, when new evidence comes up, we still update, and then start considering the possibilities that now seem sufficiently probable.
Of course, there is a danger in that it is difficult for a successive series of small new pieces of evidence pointing towards a certain, previously very unlikely conclusion to overcome our resistance to considering very unlikely conclusions. This is precisely because I don't believe we can actually use numbers to update all the possibilities, which are basically infinite in number. It is hard for me to imagine a slow, successive series of tiny nuggets of evidence that would slowly convince me that Zeus actually exists. I could read several thousand different myths about Zeus, and it still wouldn't convince me. Something large enough for a single major push to the probability to force me to consider it more thoroughly, priviledge that hypothesis in the hypothesis-space, seems to be the much more likely way - say, Zeus speaking to me and showing off some of his powers. This is admittedly a weakness, but at least it is an admitted weakness, and I haven't found a way to circumvent it yet but I can at least try to mitigate it by consciously paying more attention than I intuitively would to small but not infinitesimal probabilities.
Anyway, back to the earlier point: What I'm saying is that whether you say "X is untrue" or "X is extremely unlikely", when considering the evidence you have for and against X, it is very possible that what happens in your brain when thinking about X is the same thing. The hypothetical skeptic who does not know to use the terminology of probabilities and likelihoods will simply call things he finds extremely unlikely 'untrue'. And then, when a person who is unused to this sort of terminology hears the words 'X is very unlikely' he considers that to mean 'X is not unlikely enough to be considered untrue, but it is still quite unlikely, which means X is quite possible, even if it is not the likeliest of possibilities'. And here a misunderstanding happens, because I meant to say that X is so unlikely that it is not worth considering, but he takes it as me saying X is unlikely, but not unlikely enough not to be worth considering.
Of course, there are also people who actually believe in something being true or untrue, meaning their probability estimate could not possibly be altered by any evidence. But in the case of most beliefs, and most people, I think that when they say 'true' or 'false', they mean 'extremely likely' or 'extremely unlikely'.
Disagree. Most people use "unlikely" for something that fits their model but is unlikely, e.g., winning the lottery, having black come up ten times in a row in a game of roulette, two bullets colliding in mid air. "Untrue" is used for something that one's model says is impossible, e.g, Zeus or ghosts existing.
I am confused now. Did you properly read my post? What you say here is 'I disagree, what you said is correct.'
To try and restate myself, most people use 'unlikely' like you said, but some, many of whom frequent this site, use it for 'so unlikely it is as good as impossible', and this difference can cause communication issues.
My point is that in common usage (in other words from the inside) they distinction between "unlikely" and "impossible" doesn't correspond to any probability. In fact there are "unlikely" events that have a lower probability than some "impossible" events.
Assuming you mean that things you believe are merely 'unlikely' can actually, more objectively, be less likely than things you believe are outright 'impossible', then I agree.