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It has nothing to do with Bayesian, we're talking logic here. An astrological sign would not fall under logic, but rather the domain of science where it can be

by jbjohns 13y ago

It has nothing to do with Bayesian, we're talking logic here. An astrological sign would not fall under logic, but rather the domain of science where it can be demonstrated to have no predictive power. A human can decide to stop lying, a sign can't decide to suddenly have predictive scientific properties. The village could certainly reason that the boy usually lied. But it is a fallacy to say "this argument is false because he is a liar". He might not be lying this time (indeed, the last time he was not). It would have been wise of them to get someone else to do the wolf watching, however, since they couldn't work with this boy.

lisper 13y ago
> It has nothing to do with Bayesian, we're talking logic here. You really don't understand this at all. There is no such thing as single Platonic "logic" independent of any qualifier. There are many different kinds of logic. There is propositional logic, first order logic, higher order logic(s), modal logics, extensional and intensional logics. Bayesian reasoning is a (particular kind of) logic. Specifically, it is a logic of probability, which is to say, the kind of logic that applies when you don't know for certain whether something is true of false. Which is to say, the only kind of logic that actually applies to real-world situations. > A human can decide to stop lying, Can they? All of them? Are you sure? There are humans who can't decide to (say) stop smoking, how can you be certain that there aren't humans who can't decide to stop lying? > a sign can't decide to suddenly have predictive scientific properties. Of course a sign can't "decide" anything because it doesn't have a brain, but that doesn't mean it couldn't suddenly start to have predictive power. You can't rule out the possibility that the laws of physics could change tomorrow on any logical basis. The best you can (logically) do is observe that there is a ton of EVIDENCE that thaw laws of physics don't change capriciously, and conclude that therefore the probability they will change tomorrow is low (and Bayes's theorem will tell you exactly how low if you want to crunch the numbers). Likewise, there is a ton of EVIDENCE to support the theory that the boy in the story is a pathological liar who is not capable of deciding not to lie, or for whatever reason chooses to lie notwithstanding that he might have the ability not to. The only issue is how many lies it would take before one's estimate of the posterior probability of the boy telling the truth was indistinguishable from zero. This has to do with one's Bayesian prior on the probability of a particular random individual being a pathological liar, but that's beside the point. The point is that there is some finite number of lies after which the theory that what the boy says is in any way correlated with the truth (except by chance) is no longer logically tenable.

by jbjohns 13y ago

lisper 13y ago

> It has nothing to do with Bayesian, we're talking logic here. You really don't understand this at all. There is no such thing as single Platonic "logic" independent of any qualifier. There are many different kinds of logic. There is propositional logic, first order logic, higher order logic(s), modal logics, extensional and intensional logics. Bayesian reasoning is a (particular kind of) logic. Specifically, it is a logic of probability, which is to say, the kind of logic that applies when you don't know for certain whether something is true of false. Which is to say, the only kind of logic that actually applies to real-world situations. > A human can decide to stop lying, Can they? All of them? Are you sure? There are humans who can't decide to (say) stop smoking, how can you be certain that there aren't humans who can't decide to stop lying? > a sign can't decide to suddenly have predictive scientific properties. Of course a sign can't "decide" anything because it doesn't have a brain, but that doesn't mean it couldn't suddenly start to have predictive power. You can't rule out the possibility that the laws of physics could change tomorrow on any logical basis. The best you can (logically) do is observe that there is a ton of EVIDENCE that thaw laws of physics don't change capriciously, and conclude that therefore the probability they will change tomorrow is low (and Bayes's theorem will tell you exactly how low if you want to crunch the numbers). Likewise, there is a ton of EVIDENCE to support the theory that the boy in the story is a pathological liar who is not capable of deciding not to lie, or for whatever reason chooses to lie notwithstanding that he might have the ability not to. The only issue is how many lies it would take before one's estimate of the posterior probability of the boy telling the truth was indistinguishable from zero. This has to do with one's Bayesian prior on the probability of a particular random individual being a pathological liar, but that's beside the point. The point is that there is some finite number of lies after which the theory that what the boy says is in any way correlated with the truth (except by chance) is no longer logically tenable.