Newsgroups: comp.ai.philosophy,sci.logic
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From: jeff@festival.ed.ac.uk (J W Dalton)
Subject: Re: Putnam reviews Penrose.
References: <3ss4sm$cjd@mp.cs.niu.edu> <3ts2mt$aa3@netnews.upenn.edu> <jqbDBIrMr.HGx@netcom.com> <3tttjh$j5p@netnews.upenn.edu> <3u101c$efu@sun001.spd.dsccc.com>
Message-ID: <DBnsFp.5r6@festival.ed.ac.uk>
Organization: Edinburgh University
Date: Thu, 13 Jul 1995 14:33:24 GMT
Lines: 39
Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:30070 sci.logic:12302

afargnol@spd.dsccc.com (Al Fargnoli) writes:

>Ah, but Weiner's logic is intellectually dishonest.  

Sure, keep the insults going.

>Weiner seems to be arguing that humans don't have Goedel sentences
>because none have been determined/found. 

That's not it.  The argument is that it's an empirical observation
that human mathematicians can see that certain unprovable statements
are in fact true.  This is positive evidence, not the negative
evidence that no Goedel limits on humans have been found.

How do humans do it?  Here's the suggestion:

   Subject: Re: Putnam reviews Penrose.
   Message-ID: <3trap1$em9@netnews.upenn.edu>
   From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
   Date: 10 Jul 1995 13:42:57 GMT

   In article <95Jul10.044337edt.6061@neat.cs.toronto.edu>, cbo@cs (Calvin Bruce Ostrum) writes:
   >To repeat the original point, the problem with these attempts to
   >show man surpasses machine is that they equivocate on the nature of
   >proof.  They insist that a machine use the "impoverished" formal
   >notion of proof,

   [...]

   >		  whereas man is entitled to use a richer "informal"
   >kind of proof. 

   It is not that we are "entitled".  It is an empirical observation that
   we seem to really on this richer informal kind of proof.  I would call
   it inductive logic on a platonic realm.

-- jd


