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 10:52:03 EST 1992
Article 7641 of comp.ai.philosophy:
Path: newshub.ccs.yorku.ca!torn!cs.utexas.edu!zaphod.mps.ohio-state.edu!wupost!waikato.ac.nz!aukuni.ac.nz!kcbbs!nacjack!codewks!system
Newsgroups: comp.ai.philosophy
Subject: Re: The Paradox of the Unexpected Hanging
Message-ID: <B147TB4w165w@CODEWKS.nacjack.gen.nz>
>From: system@CODEWKS.nacjack.gen.nz (Wayne McDougall)
Date: Fri, 13 Nov 92 08:56:10 NZST
References: <1992Nov9.161212.365@oracorp.com>
Organization: The Code Works Limited, PO Box 10 155, Auckland, New Zealand
Lines: 48

daryl@oracorp.com (Daryl McCullough) writes:

> >> The statement "You will be executed today, but you will not be able to
> >> figure out that you will be executed today" is *not*
> >> self-contradictory. Suppose the prisoner thinks the judge might be
> >> lying, then he can't figure out anything from what the judge says.
> >> Therefore the judge's second statement "...you will not be able to
> >> figure out that you will be executed today" will turn out to be true.
> >> If in addition, the judge *does* hang the prisoner, then the first
> >> statement "You will be executed today" will turn out to be true. If
> >> everything the judge says turns out to be true, then it can't be
> >> self-contradictory.
> >
[Other comments by Wayne McDougall deleted]

> >
> >How can you run logic in a system where some statements are false, and 
> >you are not allowed to collect sufficient information to eliminate 
> >false statements (contrasted with unproveable ones).
> 
> You only need to divide statements into classes: those known to be
> true, those known to be false, and those whose truth value is unknown.
> What's the problem?

Ok, so the judge's statement is NOT self-contradictory if you assume 
the truth-value of the statement is unknown. So we're saying it is 
either meaningless, or we don't know if it is true. We are also saying 
that we, as the prisoner, cannot believe ALL of the statement to be 
true. So the prisoner can conclude that either all or part of the 
statement is false. Having so concluded, it is now possible for the 
statement to be true. The prisoner is smart enough to realise this. I 
guess the Prisoner could now say, hey Judge you're wrong. I am going to 
be executed today AND I can figure out that I will.

Does this clean it up? Can, in your recast of the Prisoner problem, can 
the Prisoner say, you are wrong judge? No. Because the Prisoner still 
has no evidence about the truth or falsity of the first part of the 
Judge's statement. The Prisonder knows that the judge is at least part 
wrong, and may be fully wrong. Well fine. I would suggest that if you 
can take a statement and show that it is either fully or partly wrong, 
then that statement is self-contradictory.


-- 
  Wayne McDougall, BCNU
  This .sig unintentionally left blank.

Hello! I'm a .SIG Virus. Copy me and spread the fun.


