Path: utzoo!utgpu!water!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!mailrus!ames!umd5!mimsy!frabjous!nau
From: nau@frabjous (Dana Nau)
Newsgroups: comp.ai
Subject: Re: Fuzzy systems theory was (Re: Alternative to Probability)
Message-ID: <11782@mimsy.UUCP>
Date: 1 Jun 88 20:44:45 GMT
References: <4134%super.upenn.edu> <3200014@uiucdcsm> <1484@pt.cs.cmu.edu> <487@sequent.cs.qmc.ac.uk> <1073@usfvax2.EDU>
Sender: nobody@mimsy.UUCP
Reply-To: nau@frabjous.UUCP (Dana Nau)
Organization: U of Maryland, Dept. of Computer Science, College Pk., Md. 20742
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In article <1073@usfvax2.EDU> pollock@usfvax2.usf.edu.UUCP (Wayne Pollock) writes:
>On the other hand, set theory, which underlies much of current theory, is
>also based on fallacies; (given the basic premses of set theory one can
>easily derive their negation).

Not so.  Where in the world did you get this idea?  Admittedly, _naive_ set
theory leads to Russell's paradox--but this was the reason for the
development of axiomatic set theories such as Zermelo-Fraenkel set theory
(ZF).  The consistency of ZF is unproved--but this is a natural consequence
of Goedel's incompleteness theorem, and is much different from your
contention that set theory is inconsistent.  I suggest you read, for
example, Shoenfield's _Mathematical_Logic_ (Addison-Wesley, 1967), or
Rogers's _Theory_of_Recursive_Functions_and_Effective_Computability_
(McGraw-Hill, 1967).

Dana S. Nau				ARPA & CSNet:  nau@mimsy.umd.edu
Computer Sci. Dept., U. of Maryland	UUCP:  ...!{allegra,uunet}!mimsy!nau
College Park, MD 20742			Telephone:  (301) 454-7932