Vladimir_Nesov comments on If a tree falls on Sleeping Beauty... - Less Wrong

83 Post author: ata 12 November 2010 01:14AM

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Tags: probability bayesian anthropic philosophy

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Comment author: Perplexed 12 November 2010 01:43:19AM *  4 points [-]

I tend to agree with you, but apparently E. T. Jaynes does not:

It has always seemed objectionable to some, including this writer, to base probability theory on such vulgar things as betting, expectation of profit, etc. We think that the principles of logic ought to be on a higher plane.

He then goes on to point out (rather illogically, I think) that if probability estimates actually do depend on how the wager is structured, then

a well posed question would have more than one "right" answer, with nothing to choose between them. This, in our view, is another aspect of the superiority of [the approach of PT:TLOS based on Cox's theorem] which stresses logical consistency instead and, just for that reason, is more likely to have a lasting place in probability theory.

Quotes from the final paragraph of Chapter 13 of PT:TLOS

Comment author: Vladimir_Nesov 12 November 2010 04:29:40PM *  7 points [-]

We have an apparently ambiguous word: "probability". That we accept it's ambiguous (the thesis of this post), means that there are situations where either of its multiple possibly contradictory meanings is intended. This doesn't negate a possibility of there being a concept that can be applied to most situations, doesn't itself suffer from ambiguity, and is usually referred to using the same word.

There is no apparent contradiction here: the disagreement you point out results from equivocating between the ambiguous word "probability" and (presumably) the more specific concept of probability that Jaynes refers to.

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