**From:** Christian Szegedy (*szegedy@or.uni-bonn.de*)

**Date:** Thu Oct 21 2004 - 06:18:07 MDT

**Next message:**Jeff Medina: "Re: [agi] A difficulty with AI reflectivity"**Previous message:**Christian Szegedy: "Re: [agi] A difficulty with AI reflectivity"**In reply to:**Eliezer Yudkowsky: "Re: [agi] A difficulty with AI reflectivity"**Next in thread:**Jeff Medina: "Re: [agi] A difficulty with AI reflectivity"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Eliezer Yudkowsky wrote:

*>
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*> Presumably it also requires that the solution be correct.
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Typical optimization probems come with another TM checking the

correctness. For example the graph coloring problem is defined

by:

For each graph G, produce an output, for which the following

problem returns true.

----------------- Progam:

Check whether the input is a valid coloring

-----------------

This is the whole idea of the NP complexity class: the class

of those problems, for which the correctness of solutions can

be checked in polynomial time.

*> This is a problem because no consistent proof system can prove that
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*> the system only produces correct theorems, so no proof system can
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*> prove the usefulness of a faster, rewritten proof system. Unless you
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*> specifically state that you're trying to prove admissibility in the
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*> old system, rather than correctness, usefulness, or other expected
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*> utility criteria on the object level. Hence the need to patch the
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*> Godel Machine.
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You will never be able to prove absolute consistency in a formal fashion.

Absolute consistency is always a hypothesis. In fact it is a physical

statement, not a mathematical one.

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