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Article #585

Re: recursive definitions and paradoxes

#585
From: Brendan Mahony
Date: Mon, 23 Nov 1992 01:26
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In <1992Nov20.155725.11719@guinness.idbsu.edu> holmes@garnet.idbsu.edu (Randall Holmes) writes:

>This is inaccurate.  Russell's paradox proves nothing except that
>there is no set which has exactly the sets which are not elements of
>themselves as members.

Come on Russel's `paradox' tells us that if we assume
 
	(RS \in RS) or \lnot (RS \in RS)
 
we are in lots of trouble.
   
--
When soldiers form lines or hollow squares, you call it reason.
When wild geese in flight take the form of a letter V, you say instinct.
When the homogeneous atoms of a mineral arrange themselves into shapes
mathematically perfect you have nothing to say. You have not even invented a name to conceal your heroic unreason."
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Path: arc1-ca.pugleaf.net!sparky!uunet!munnari.oz.au!bunyip.cc.uq.oz.au!uqcspe!cs.uq.oz.au!brendan
From: brendan@cs.uq.oz.au (Brendan Mahony)
Newsgroups: sci.logic
Subject: Re: recursive definitions and paradoxes
Message-ID: <11143@uqcspe.cs.uq.oz.au>
Date: 23 Nov 92 01:26:54 GMT
References: <26788@optima.cs.arizona.edu> <1992Nov19.215048.26539@CSD-NewsHost.Stanford.EDU> <1992Nov20.155725.11719@guinness.idbsu.edu>
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