hairyfigment comments on Gödel and Bayes: quick question - Less Wrong

1 Post author: hairyfigment 14 April 2011 06:12AM

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Comment author: DanielLC 14 April 2011 06:27:49AM *  1 point [-]

From what I understand we could write a version of the Gödel statement for the axioms of probability theory,

It only works on sufficiently complex systems. Basically, anything with addition and multiplication. None of the probability axioms involve multiplication.

I could be wrong about this not being complex enough, though.

So, can we or can't we write a mathematically meaningful version of the statement, "This statement has less than .5 probability within the system"?

No. Probability can't be easily applied to mathematical statements. Either it's provable or it's not.

Comment author: hairyfigment 14 April 2011 06:35:44AM 0 points [-]

None of the probability axioms involve multiplication.

The product rule does, and in any case I mean to include all the rules of arithmetic that we use to apply Bayes.

Comment author: DanielLC 14 April 2011 06:40:37AM *  0 points [-]

The product rule does

It's not an axiom. I think it might be the definition of "given".

and in any case I mean to include all the rules of arithmetic that we use to apply Bayes.

Then you're talking about math, not probability. The fact that you can't prove or disprove Goedel's sentence doesn't change the probability of a hypothesis.

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