From: Michael Roy Ames (michaelroyames@yahoo.com)
Date: Thu Oct 21 2004 - 09:14:40 MDT
Eliezer: please give us your definition of the phrase "wrap-around
reflectivity".
Jeff Medina wrote:
> You won't ever find anything in the literature on how
> to prove that a system of proof is infallibily truth-
> producing outside of the context of said system of
> proof (or even how to prove that system-of-proof A is
> more consistently truth-producing than system-of-proof
> B; not outside of the context of system-of-proof A, B,
> or X) because even if someone were to come up with
> something that looked like a proof that "wraps around"
> as you put it, they (or the journal editors/referees)
> would reject it as unsound, due to a reductio ad
> absurdum. Namely, because it would contradict that
> which the rest of proof theory claims is true; that
> wrap around is impossible -- truth is forever uncertain
> at its base. We cannot avoid inserting potentially
> unsound assumptions."
That is an adamant statement and one that I would agree with (except perhaps
for the 'ever' part). The ability of humans to perform wrap-around
reflectivity (as I understand it) is an illusiary one. We perform the same
algorithmic techniques when working through proofs that a computer would
use, but fall back on heuristics quickly when we detect our own tower of
meta becoming absurd.
Michael Roy Ames
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