**From:** Eliezer S. Yudkowsky (*sentience@pobox.com*)

**Date:** Thu Sep 08 2005 - 09:52:56 MDT

**Next message:**Eliezer S. Yudkowsky: "Re: The Relevance of Complex Systems [was: Re: Retrenchment]"**Previous message:**Wei Dai: "Re: The Relevance of Complex Systems [was: Re: Retrenchment]"**In reply to:**Wei Dai: "Re: The Relevance of Complex Systems [was: Re: Retrenchment]"**Next in thread:**Wei Dai: "mathematical reasoning"**Reply:**Wei Dai: "mathematical reasoning"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Wei Dai wrote:

*>
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*>>> >> I bet that if you name three subtleties, I can
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*>>> >> describe how Bayes plus expected utility plus Solomonoff
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*>>> >> (= AIXI) would do it given infinite computing power.
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*>
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*> What about mathematics? I don't think we know how to do mathematics
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*> under a Bayesian framework, even with infinite computing power (since
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*> some mathematical statements can be neither proved nor disproved from
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*> the usual axioms). I noticed that nobody replied to my "uncertainty in
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*> mathematics" post (http://sl4.org/archive/0508/12022.html).
*

My challenge was meant for Loosemore alone; I didn't mean it as an open

invitation to the whole SL4 list! I'm working on two book chapters that

are due in October right now, and that would be a bit more than I can

handle.

Wei Dai, you are correct. Mathematical reasoning is not usually

regarded as the domain of probability theory. There are efforts to

extend standard decision theory to remove the assumption of logical

omniscience, under the heading of "impossible possible worlds".

Figuring out exactly how to integrate this is, in fact, one of the

things I'm currently doing some work on myself.

Now let's see *Loosemore* come up with an example.

-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence

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