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

**Date:** Thu Oct 21 2004 - 15:21:51 MDT

**Next message:**Slawomir Paliwoda: "Re: Donate Today and Tomorrow"**Previous message:**Paul Fidika: "Re: [agi] A difficulty with AI reflectivity"**In reply to:**Jeff Medina: "Re: [agi] A difficulty with AI reflectivity"**Next in thread:**Christian Szegedy: "Re: [agi] A difficulty with AI reflectivity"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Jeff Medina wrote:

*> Eliezer said: "Thank you for your suggested reading, but I'm already
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*> quite extremely aware that no consistent formal system can prove its own
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*> consistency. If you're not clear on why this presents a unique
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*> challenge for reflective theorem provers, I recommend John Harrison's
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*> "Metatheory and Reflection in Theorem Proving: A Survey and Critique." "
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*>
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*> I neither suggested any readings, nor made mention of the fact that no
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*> consistent formal system can prove its own consistency (which is such a
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*> fundamental and widely known result, I take that it goes without saying
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*> on such a mailing list). Perhaps the flurry of replies resulted in my
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*> name being included in a reply intended for a different commenter. If
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*> not, I'm baffled as to how any of what you've said applies to my recent
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*> message.
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Jeff Medina wrote:

*>
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*> You won't ever find anything in the literature on how to prove that a
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*> system of proof is infallibily truth-producing outside of the context of
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*> said system of proof (or even how to prove that system-of-proof A is
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*> more consistently truth-producing than system-of-proof B; not outside of
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*> the context of system-of-proof A, B, or X) because even if someone were
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*> to come up with something that looked like a proof that "wraps around"
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*> as you put it, they (or the journal editors/referees) would reject it as
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*> unsound, due to a reductio ad absurdum. Namely, because it would
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*> contradict that which the rest of proof theory claims is true; that wrap
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*> around is impossible -- truth is forever uncertain at its base. We
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*> cannot avoid inserting potentially unsound assumptions.
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If you meant something else by this than that no consistent system can

prove its own consistency, then sorry for the misattribution. I also

acknowledge that you did not suggest any specific literature.

I wish people would realize that I know the basics, but sometimes I do make

embarassing mistakes, as with the recent discussion of fleeing an UFAI at

near-lightspeed. (It's not that I didn't know the math, it's that I

guessed intuitively, instead of taking ten seconds to derive quantitatively

the subjective lifespan of the escapee... stupid of me.)

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

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