From newshub.ccs.yorku.ca!torn!cs.utexas.edu!zaphod.mps.ohio-state.edu!caen!umeecs!dip.eecs.umich.edu!marky Tue Nov 24 10:51:53 EST 1992
Article 7625 of comp.ai.philosophy:
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>From: marky@dip.eecs.umich.edu (Mark Anthony Young)
Subject: Re: The Paradox of the Unexpected Hanging
Message-ID: <1992Nov12.210042.6205@zip.eecs.umich.edu>
Sender: news@zip.eecs.umich.edu (Mr. News)
Organization: University of Michigan EECS Dept., Ann Arbor
References: <1992Nov3.051001.21374@oracorp.com> <2217@sdrc.COM> <BxHv6w.KJu@ns1.nodak.edu>
Date: Thu, 12 Nov 1992 21:00:42 GMT
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%r vender@plains.NoDak.edu (Does it matter?)
>Just a note in passing:  The statements
>    B: "A always lies"
>    A: "I am telling a lie"
>result in an unresolvable problem, quite similar to a halting problem.

The problem of A's statement (B's statement being irrelevent) is _not_
that it has no resolution, but that it has too many.

There are (at least) two ways that someone can say X when (not X) is the
way things are:

    1) they can be lying--saying something they believe to be false; or
    2) they can be mistaken--believing what they say is true.

There is also the chance that the speaker is merely insincere--saying
something they do not believe to be true, without actually believing
that it is false, either.

So:

If A believes that A is lying, then A's statement is true, so A is
    mistaken.
If A believes that A is not lying, then A's statement is false, so
    A is again mistaken.

If A has no idea whether A is lying, then A's statement is insincere,
    and so false (unless insincere statements are lies, in which case
    it's true).

If A has reasoned this all out, then A knows that none of the above
    three states are stable, and so the statement must be paradoxical.  
    Therefore, the only reason for A to make this statement is to mess
    around with other people's minds.

We now have four ways to understand A's statement.  Which one we choose
will depend on what we think of A's reasoning powers.

...mark young



