From newshub.ccs.yorku.ca!torn!cs.utexas.edu!uwm.edu!rpi!scott.skidmore.edu!psinntp!psinntp!scylla!daryl Tue Nov 24 10:52:15 EST 1992
Article 7658 of comp.ai.philosophy:
Newsgroups: comp.ai.philosophy
Path: newshub.ccs.yorku.ca!torn!cs.utexas.edu!uwm.edu!rpi!scott.skidmore.edu!psinntp!psinntp!scylla!daryl
>From: daryl@oracorp.com (Daryl McCullough)
Subject: Re: The Paradox of the Unexpected Hanging
Message-ID: <1992Nov16.124635.11533@oracorp.com>
Organization: ORA Corporation
Date: Mon, 16 Nov 1992 12:46:35 GMT
Lines: 33

In article <B147TB4w165w@CODEWKS.nacjack.gen.nz>,
system@CODEWKS.nacjack.gen.nz (Wayne McDougall) 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...

>Ok, so the judge's statement is NOT self-contradictory if you assume 
>the truth-value of the statement is unknown.

It isn't self-contradictory, in any case. It may be false, however.

>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.

No! Just because I cannot consistently *believe* that something is
true, does not mean that I must believe that it is false. For example,
PA cannot consistently prove the statement "PA is consistent" (coded
as an arithmetic statement), but that doesn't mean that the statement
is false, or that PA can prove that it is false.

The prisoner can neither consistently believe the judge, nor
consistently believe the judge is lying. That's why it is important to
partition sentences into those that you believe true, those you believe
false, and those whose truth values you can't determine (and may *never*
be able to determine).

Daryl McCullough
ORA Corp.
Ithaca, NY



