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thomblake comments on A Parable On Obsolete Ideologies - Less Wrong
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It is, actually. It's the Bayesian definition that evidence for X is something more likely to be true in a universe where X than in a universe where -X.
Part of the point of Bayes' Theorem is that correction for the base rate fallacy is baked in. That's a large part of what separates Bayesian rationality from irrationality,
What you're saying here is that you use Bayes' theorem to inform your definition of "evidence".
If I used a different definition of evidence, that doesn't mean I'm saying something about Bayes' theorem. That simply means I use the word differently.
When it comes to evidence, I don't believe Bayes' theorem deals with the real-world problems that arise when considering a hypothesis. For example, it doesn't deal with the "garbage in, garbage out" problem.
As I said, we might plug the number of calls Uri Geller got into Bayes' theorem and because of the answer believe that supernatural events did actually occur. But that would be an incorrect conclusion because we have based our conclusion on the faulty premise that more calls means supernatural events are more likely to have occurred.
If you mean things like the base rate fallacy, then yes it does. If you mean that putting in random numbers for your priors doesn't solve your problems, then there isn't any method of considering evidence that fixes that in principle.
In the paragraph after the one you quoted, I gave an example of what I was discussing.
You can check the source of the evidence and try to make sure that you're not putting in random numbers but reliable data.
When considering hypotheses in the real world -- like "Does God exist?" or "Is my wife cheating on me?"-- Bayes' theorem doesn't encapsulate all the skills you need to arrive at a trustworthy answer. You must clearly understand what it is you're trying to establish -- Aquinas's conception of God is very different from your average Christian's. You must be willing to question beliefs that you are attached to or identify with -- maybe your wife is sleeping with anything that moves, or maybe you're a needlessly jealous, insecure husband. You must gather as much evidence as possible, including the evidence that you might initially deem to be irrelevant. You must be diligent, fastidious, and detached when performing the investigation -- not hiding behind "Oh, my wife would never do that" or allowing your emotions to effect your judgment.
People will have done all the above and still arrived at erroneous conclusions. Such is the difficulty of testing a hypothesis.