AlephNeil comments on Dutch Books and Decision Theory: An Introduction to a Long Conversation - Less Wrong

19 Post author: Jack 21 December 2010 04:55AM

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Comment author: taw 21 December 2010 05:33:36PM 0 points [-]

How, exactly, to deal with logical uncertainty is an unsolved problem, no?

Your choice is either accepting that you will be sometimes inconsistent, or accepting that you will sometimes answer "I don't know" without providing a specific number, or both.

There's nothing wrong with "I don't know".

It's not clear why it's more of a problem for Bayesian than anyone else.

For Perfect Bayesian or for Subjective Bayesian?

Subjective Bayesian does believe many statements of kind P(simple math step) = 1, P(X|conjunction of simple math steps) = 1, and yet P(X) < 1.

Comment author: AlephNeil 21 December 2010 06:57:07PM 0 points [-]

Subjective Bayesian does believe many statements of kind P(simple math step) = 1, P(X|conjunction of simple math steps) = 1, and yet P(X) < 1.

Well, they can wriggle out of this by denying P(simple math step) = 1, which is why I introduced this variation.

Comment author: taw 26 December 2010 12:34:15PM 0 points [-]

Well, they can wriggle out of this by denying P(simple math step) = 1

Doesn't this imply you'd be willing to accept P(2+2=5) on good enough odds?

This might be pragmatically a reasonable thing to do, but if you accept that all math might be broken, you've already given up any hope of consistency.