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Article 5934 of comp.ai.philosophy:
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>From: torkel@sics.se (Torkel Franzen)
Subject: Re: penrose
In-Reply-To: costello@CS.Stanford.EDU's message of Tue, 26 May 1992 22:52:20 GMT
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Date: Wed, 27 May 1992 08:01:14 GMT
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In article <1992May26.225220.18126@CSD-NewsHost.Stanford.EDU> 
costello@CS.Stanford.EDU (T Costello) writes:

   >The set of theorems of the above progression includes all true sentences of
   >elementary number theory.  The progression through the ordinals has order
   >type less than omega one.

  You haven't, of course, introduced the very technical concept of
"progression" used in Feferman's paper, and your remarks may be misleading.
It should be emphasized that there is nothing in this work that implies
that the set of theorems "humanly provable" by reflection is not
recursively enumerable.

  What is epistemologically interesting and (by Godel's theorem) at
least potentially useful is the informal reflection principle
"if a theory T is sound, any extension by reflection of T is also sound".
This is not a formal principle, but there is nothing about it that
suggests that it should be peculiarly unimplementable on a machine.


