[FOM] 23 syllables

Hartley Slater slaterbh at cyllene.uwa.edu.au
Tue Dec 12 18:45:11 EST 2006

At 3:20 PM -0800 12/12/06, Bill Greenberg wrote:
>The standard definition of heterlogicality entails.
>2) -(G)(Des('Het',G) <-> Het=G)
>Does the plausibility of this definition provide more warrant for (2)
>than the 'plausibility' of unrestricted comprehension provides for the
>existence of the Russell Set?
>Or do you hold that "{x: x in x and -x in x}" is not univocal?

The cases are exactly parallel - and both are covered in the Journal 
of the IGPL piece I previously mentioned, as well as, for example, 'A 
Poor Concept Script', Australasian Journal of Logic 2004 
(http://www.philosophy. unimelb.edu.au/ajl/2004/2004_4.pdf), and 
'Choice and Logic', Journal of Philosophical Logic. 43 (2005) 
207-216..  The Russell case is also the sole subject of 'Frege's 
Hidden Assumption', just out in Critica 38.113.

The Reductios yielding (2) and its parallel in the Russell case, are 
indirect proofs of course.  More interesting are the direct proofs, 
which I first published in MIND 1973, and which I discussed not only 
in  the above papers, but also on the FOM list quite recently.  The 
point is that the predicates 'is not self applicable', 'is not a 
member of itself' and (for good measure also, Quine's) 'generates a 
falsehood when appended to its own quotation' all contain pronouns, 
which are contextual elements without a determinate referent in 
themselves.  So these and similar predicates do not express constant 
properties.  What is a set a member of if it is not a member of 
itself?  It is a member of its complement.
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater

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