From newshub.ccs.yorku.ca!torn!cs.utexas.edu!zaphod.mps.ohio-state.edu!wupost!waikato.ac.nz!aukuni.ac.nz!kcbbs!nacjack!codewks!system Tue Nov 24 10:52:04 EST 1992
Article 7642 of comp.ai.philosophy:
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Newsgroups: comp.ai.philosophy
Subject: Re: The Paradox of the Unexpected Hanging
Message-ID: <Hq57TB5w165w@CODEWKS.nacjack.gen.nz>
>From: system@CODEWKS.nacjack.gen.nz (Wayne McDougall)
Date: Fri, 13 Nov 92 09:11:52 NZST
References: <1992Nov10.030302.44285@Cookie.secapl.com>
Organization: The Code Works Limited, PO Box 10 155, Auckland, New Zealand
Lines: 29

frank@Cookie.secapl.com (Frank Adams) writes:

> 
> There are two forms of the unexpected hanging problem: one where the judge
> says "... you will be surprised ...", and the other where he says "... you
> will not be able to prove ...".  Both really work the same in the stripped-
> down version as when multiple days are involved.
> 
> In the proof-theoretic version, the judge's statements (together with the
> fact that he makes them to the prisoner) *are* contradictory.  There is
> potentially a problem with levels, since formal systems in general can't
> deal with statements about what they are able to prove.  But in any context
> where they can be accepted, they are contradictory; hence you can prove
> anything from them; so in particular the second statement is false (since
> you can prove anything from a contradiction, you *can* prove that it will
> occur on whatever day it actually does occur).
> 
Doesn't a lot hinge on WHEN the Prisoner is allowed to contrsuct their 
proof? If they have to decide, fixed and forever, the day on which the 
judgement is given, then yes, it could be any day. But isn't the whole 
point is that the Prisoner must logically wake up each day and say, 
well it MUST be today and it CAN'T be today.


-- 
  Wayne McDougall, BCNU
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