Path: utzoo!utgpu!utstat!jarvis.csri.toronto.edu!mailrus!ames!hc!pprg.unm.edu!unmvax!ncar!boulder!sunybcs!rutgers!att!whuts!homxb!genesis!hotlr!dave
From: dave@hotlr.ATT ( C D Druitt hotlk)
Newsgroups: comp.ai
Subject: Re: Natural Paradox
Message-ID: <538@hotlr.ATT>
Date: 7 Feb 89 19:08:34 GMT
References: <1706@tank.uchicago.edu> <17167@iuvax.cs.indiana.edu>
Reply-To: dave@hotlr.UUCP (54246 - C D Druitt hotlk)
Organization: AT&T-BL Holmdel NJ - Lab 5431
Lines: 45

In article <17167@iuvax.cs.indiana.edu> dave@duckie.cogsci.indiana.edu (David Chalmers) writes:
 > 
 > This is incoherent.  The "provability" of a statement is not dependent
 > upon the capacities of us limited human beings to find and construct
 > such a proof.  This applies even when the statement whose provability
 > we are investigating is of the form "Statement X is provable."
 > "Provability" is a well-defined mathematical notion that is
 > independent of arbitrary human exigencies, in the same way that,
 > say, "triangularity" is.  Just as the four-color theorem was in
 > fact TRUE even before 1974 (when some people found the proof), it was
 > also provable before then.  Upon Haken & Apell's proof in 1974, then
 > humans DISCOVERED for sure that not only was the theorem true, but
 > that it was provable, and that it was provable that it was provable, 
 > and so on.  But none of these are time-dependent concepts.
 > 
 > You've missed the point, or maybe I wasn't clear enough.  I was
 > That's absolutely right.  If we ever have a genuine paradox, grounded in a
 > well-defined system of reality (or mathematical reality), then our system
 > falls apart.  Given that we don't want our system to fall apart, then like
 > Russell we have to make damn sure that there aren't any real paradoxes.  The
 > usual way to do this is to deem statements like "This sentence is false"
 > ill-defined or meaningless.  Godel's great insight is that statements like
 > this (well, actually like "This statement is unprovable") can actually be 
 > grounded (with a lot of work) in concrete mathematical reality (if that's not
 > a contradiction in terms).  After he did this, the "meaningless" escape route
 > was no longer available, so people had to accept "true but unprovable"
 > statements.  Very annoying, but a small sacrifice to make to save all of
 > mathematics from destruction.  (See my last posting for more on Godel,
 > paradoxes and meaninglessness.) 
 > 				
 >                      Dave Chalmers
 >  


When I encounter something that doesn't make sense at first glance,
I have two choices:
File it away and keep listening or looking for further input to clarify
(passive) or request further input.
Seems to me that paradoxes and fuzzy sets are unavoidable.
Why not admit this and focus more on procedures for handling
them when they are encountered?

Dave Druitt
(the NODES)
(201) 949-5898