Path: utzoo!attcan!uunet!lll-winken!ames!amdahl!pyramid!prls!philabs!linus!mbunix!bwk
From: bwk@mbunix.mitre.org (Barry W. Kort)
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Summary: "The current king of France is bald." is True.  Or not.
Keywords: Aristotelian Logic, Law of the Excluded Middle
Message-ID: <43843@linus.UUCP>
Date: 25 Jan 89 00:15:26 GMT
References: <479@aipna.ed.ac.uk> <3038@uhccux.uhcc.hawaii.edu>
Sender: news@linus.UUCP
Reply-To: bwk@mbunix.mitre.org (Barry Kort)
Organization: The Gallimaufrey, Atsea, UK
Lines: 39

Let's play with the assertion,

	"The current king of France is bald."

If we put this into symbolic logic notation, we get

	For all x, if x is the current king of France, then x is bald.

Or in slightly more melifluous English, 

	Every person who happens to be the current king of France
	also happens to be bald.

Now in Aristotelian Logic, the above is equivalent to the denial of
its negative:

	It is not the case that there is a non-bald individual
	who is the current king of France.

Or again, in clearer English,

	There is no one who is both non-bald and the current
	king of France.

I think we would all agree that the above statement is a meaningful
and accurate description of the French state of affairs. That is, the
assertion is True.

So if you believe in the Law of the Excluded Middle, the original
assertion and the denial of its negation have equivalent truth
values (namely True).

If this line of reasoning leaves you uneasy, consider the possibility
of throwing away the Law of the Excluded Middle.  Then we can no longer
transform an assertion into the denial of its negation, and we can
pleasantly argue over the category into which the "current bald
king of France" can be tossed.

--Barry Kort