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 Lines: 18 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