From: Christian Szegedy (firstname.lastname@example.org)
Date: Thu Oct 21 2004 - 06:18:07 MDT
Eliezer Yudkowsky wrote:
> Presumably it also requires that the solution be correct.
Typical optimization probems come with another TM checking the
correctness. For example the graph coloring problem is defined
For each graph G, produce an output, for which the following
problem returns true.
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
> the system only produces correct theorems, so no proof system can
> prove the usefulness of a faster, rewritten proof system. Unless you
> specifically state that you're trying to prove admissibility in the
> old system, rather than correctness, usefulness, or other expected
> utility criteria on the object level. Hence the need to patch the
> Godel Machine.
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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