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From: smoliar@vaxa.isi.edu (Stephen Smoliar)
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Keywords: Aristotelian Logic, Law of the Excluded Middle
Message-ID: <7462@venera.isi.edu>
Date: 7 Feb 89 22:12:42 GMT
References: <479@aipna.ed.ac.uk> <3038@uhccux.uhcc.hawaii.edu> <43843@linus.UUCP>
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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.
>
>Or in slightly more melifluous English, 
>
>	Every person who happens to be the current king of France
>	also happens to be bald.
>
This is fine as far as it goes;  but, at least for the sake of argument, we
should acknowledge that this is NOT the approach which Bertrand Russell took
in his paper "On Denoting" (MIND, 1905).  There, Russell introduced a specific
denotation clause, that is, a form which explicitly stood for the denotation of
some entity;  so he was concerned with the interpretation of expressions which
used this form, such as using "C(the father of Charles II.)" to represent a
sentence about the father of Charles II.  Quoting from his paper:

	Observe that, according to the above interpretation, whatever
	statement C may be, "C(the father of Charles II.)" implies:--
	"It is not always flase of x that 'if y begat Charles II., y is
		identical with x' is always true of y,"
	which is what is expressed in common language by "Charles II.
	had one father and no more."  Consequently if this condition
	fails, EVERY proposition of the form "C(the father of Charles II.)"
	is false.  Thus e.g. every proposition of the form "C(the present
	King of France)" is false.

Most of the paper is concerned with justifying this rather convoluted
interpretation.  In a nutshell, the point is tries to make is the following:

	Thus "the present King of France," "the round square," etc.
	are supposed to be genuine objects.  It is admitted that such
	objects do not SUBSIST, but nevertheless they are supposed to
	be objects.  This is in itself a difficult view;  but the chief
	objection is that such objects, admittedly, are apt to infringe
	the law of contradiction.