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Vaniver comments on Probability is in the Mind - Less Wrong

60 Post author: Eliezer_Yudkowsky 12 March 2008 04:08AM

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Comment author: Vaniver 24 May 2013 06:40:58PM 0 points [-]

I ought to assign high probability to P3 (since it's true of most statements that it's possible to construct) and consequently low probabilities to P1 and P2.

I don't think the logic in this part follows. Some of it looks like precision: it's not clear to me that P1, P2, and P3 are mutually exclusive. What about cases where 'my monitor is bamboozled' and 'my monitor is not bamboozled' are both true, like sets that are both closed and open? Later, it looks like you want P3 to be the reverse of what you have it written as; there it looks like you want P3 to be the proposition that it is a well-formed statement with a binary truth value.

Comment author: TheOtherDave 24 May 2013 07:04:08PM 1 point [-]

Blech; you're right, I incompletely transitioned from an earlier formulation and didn't shift signs all the way through. I think I fixed it now.

Your larger point about (p1 and p2) being just as plausible a priori is certainly true, and you're right that makes "and consequently low probabilities to P1 and P2" not follow from a properly constructed version of P3.

I'm not sure that makes a difference, though perhaps it does. It still seems that P(P1) > P(P2) is no more likely, given complete ignorance of the referent for "bamboozle", than P(P1) < P(P2)... and it still seems that knowing that otherwise sane people talk about whether monitors are bamboozled or not quickly makes me confident that P(P1 XOR P2) >> P((P1 AND P2) OR NOT(P1 OR P2))... though perhaps it ought not do so.