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From: weltyc@cs.rpi.edu (Christopher A. Welty)
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Keywords: Aristotelian Logic, Law of the Excluded Middle
Message-ID: <374@rpi.edu>
Date: 27 Jan 89 21:03:56 GMT
References: <479@aipna.ed.ac.uk> <3038@uhccux.uhcc.hawaii.edu> <43843@linus.UUCP> <32698@tut.cis.ohio-state.edu>
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>In article <43843@linus.UUCP> bwk@mbunix.mitre.org (Barry Kort) writes:
> 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.
> 

And this statement, according to first order logic, is equivalent to :

	For all x, x is not the current king of france or x is bald

Which is true (when the or is understood not to be exclusive).

In article <32698@tut.cis.ohio-state.edu> Diana Smetters <diana@cis.ohio-state.edu> writes:>
>
> "There exists an x, such that x is the current king of France and x is bald."
> [which is false]

Actually I think this the correct (logic) interpretation of the
statement.  The problem is that the statement implies indirectly that
there exists a current king of france, in fact the statemnet assumes
this.  When this assumption is shown to be false, the statement
becomes false (according to logic).

But this is missing the point.  Two-valued logics can not deal with the
information in this sentence.  The truthness or falsness is not the
point, it's the meaninglessness.  The english statement does not say
`there is a current king of france', nor does it say `all people are
either the current king of france or bald'.  The point is that we, as
humans, are able to form sentences like this and understand that there
is no `truth value' associated with it - it's meaningless.  of course,
if you had a many-valued logic you might be able to have values for
things like meaningless (see the first posting on this subject).


Christopher Welty  ---  Asst. Director, RPI CS Labs
weltyc@cs.rpi.edu             ...!njin!nyser!weltyc