Re: Fuzzy logic and Goedel's Theorems

From: P. Sarma (pramits@vsnl.com)
Date: Tue Jan 23 2001 - 15:22:40 MET

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    Prof. Penrose's "Emperor's New Mind" explores this to an extent, and is a
    thought provoking book.

    Perhaps it is worthwhile considering the nature of "consistency" itself?
    Isn't it, at one level above, also reducible to an axiom? In that case, is
    it not possible to argue that this logical requirement itself, perhaps,
    operates under unprovable conditions? It appears that the capacity to
    produce good results when used as a computing system should be given a
    priority to any logical system. The tangles created by the set theoretic
    constructs of Hilbert and Russell began, and ended, with the "need" to form
    a "complete" system, and was evidently the partial inspiration for Goedel.
    For if there are Logical systems which are tortuous simply to achieve
    "consistency", and are less used in systems (at some level or the other),
    and there are others which are "inconsistent" yet used from a middle level
    to a huge level with high degrees of success, then perhaps the definition
    of consistency may need a certain level of re-examination.

    Pramit

    "The absence of information is information in itself" - Sherlock Holmes

    -----Original Message-----
    From: Ulrich Bodenhofer <ulrich.bodenhofer@scch.at>
    To: Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>
    Date: Thursday, January 18, 2001 1:06 PM
    Subject: Re: Fuzzy logic and Goedel's Theorems

    >I would rather say that is Zadeh's opinion that he considers these
    >things unimportant in the context of fuzzy logic (without any particular
    >implications at first hand). In any case, we should not forget
    >that the notorious ignorance of logical foundations in combination
    >with the term "fuzzy logic" have led to the rejection of fuzzy logic by
    >a majority of logicians. However, some time has passed since then
    >and several people were very much engaged in bringing more light
    >into these questions. Please find enclosed three excellent
    >references in which these topics are discussed in very detail.
    >
    >Regards,
    >Ulrich
    >
    >--
    >
    >@book{Gottwald:01,
    > author = {S. Gottwald},
    > title = {A Treatise on Many-Valued Logics},
    > publisher = {Research Studies Press},
    > address = {Baldock},
    > year = {2001},
    > series = {Studies in Logic and Computation}
    >}
    >
    >@book{Hajek:98,
    > author = {P. H\'ajek},
    > title = {Metamathematics of Fuzzy Logic},
    > publisher = {Kluwer Academic Publishers},
    > volume = {4},
    > series = {Trends in Logic},
    > address = {Dordrecht},
    > year = {1998}
    >}
    >
    >@book{NovakPerfilievaMockor:99,
    > author = {V. Nov\'ak and I. Perfilieva and J. Mo\v{c}ko\v{r}},
    > title = {Mathematical Principles of Fuzzy Logic},
    > publisher = {Kluwer Academic Publishers},
    > address = {Boston},
    > year = {1999}
    >}
    >
    >
    >"Jonas Dagys" <jdagys@tennis.lt> wrote in message
    >news:LOBBINOMPFOEGKJEOAFDEEIICEAA.jdagys@tennis.lt...
    >> Dear All,
    >>
    >> I am referring to the following claim by Ch. Morgan in Routledge
    >> Encyclopedia of Philosophy:
    >> "Zadeh claimed that the standard metatheoretical notions such as
    >consistency
    >> and completeness are not relevant to fuzzy logic".
    >>
    >> Does that imply that fuzzy logic is somehow immune from Goedel's proofs
    of
    >> inconsistency and incompletness (which bear important consequences to AI,
    >as
    >> demonstrated by Lucas and Pernrose)?
    >> And if yes, in what sense it might be argued so?
    >>
    >> Would be grateful for any references as well.
    >>
    >> Regards,
    >>
    >> Jonas Dagys
    >> jpd@pieva.lt
    >>
    >>
    >>
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