From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!usc!cs.utexas.edu!uunet!mcsun!sunic2!sics.se!sics.se!torkel Sun May 31 19:04:48 EDT 1992
Article 5978 of comp.ai.philosophy:
Newsgroups: comp.ai.philosophy
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!usc!cs.utexas.edu!uunet!mcsun!sunic2!sics.se!sics.se!torkel
>From: torkel@sics.se (Torkel Franzen)
Subject: Re: penrose
In-Reply-To: costello@CS.Stanford.EDU's message of Fri, 29 May 1992 11:27:49 GMT
Message-ID: <1992May29.125208.13752@sics.se>
Sender: news@sics.se
Organization: Swedish Institute of Computer Science, Kista
References: <atten.706786286@groucho.phil.ruu.nl>
	<1992May29.053625.6202@sics.se>
	<1992May29.112749.14160@CSD-NewsHost.Stanford.EDU>
Date: Fri, 29 May 1992 12:52:08 GMT
Lines: 19

In article <1992May29.112749.14160@CSD-NewsHost.Stanford.EDU> costello@
CS.Stanford.EDU (T Costello) writes:

   >Thus I claim that your reflection principle does not hold in general.

  Ok, I'll spell it out. Of the axioms used to derive the contradiction,

      B( B x \supset x)  

does not hold if we are speaking about provability in T (for the T at issue).
Indeed, by Loeb's theorem, if "if B(+A+) then A" is provable in T, so is A.

  Frankly, I'm a bit surprised at your persistence, since the
extension I described added to the theory only axioms that are
obviously true (given that T is sound).



  


