Re: Do we have proofs that human think in a fuzzy (logic) way?

From: Vilem Novak (NovakV@dynami.osu.cz)
Date: Tue Jan 16 2001 - 14:35:04 MET

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    > Moreover, Cox's Theorem [Cox, R.T.: ``Probability, frequency, and
    > reasonable expectation,'' Am. J. Phys. v.14, pp.1--13 (1946)] proves
    > conclusively that =ALL= possible approximate reasoning methods other than
    > Bayesian Probability Theory fail to be logically self-consistent in some
    > way or other --- and that includes fuzzy logic. Hence, if any method of
    > approximate reasoning is to be preferred, it would have to be Bayesian
    > reasoning. (This is =NOT= to say that _humans_ use Bayesian reasoning,
    > but only that _if_ we wish our machines to think in a way compatible with
    > logic, Bayesian reasoning has been mathematically proved to be the =ONLY=
    > approximate reasoning method that is capable of doing so. Any other method
    > --- including Fuzzy Logic --- will necessarily yield logical paradoxes
    > and inconsistencies under certain circumstances.)

    ??????????????? - this is very strange and clear nonsense.
    Please, read the basic books on fuzzy logic:

    A Treatise on Many-Valued Logics.
    Research Studies Press Ltd., Baldock, Herfordshire, UK (to
    appear).

    H\'ajek, P.: Metamathematics of fuzzy logic. Kluwer, Dordrecht
    1998.
     
    Nov\'ak, V., Perfilieva I. and J. Mo\v{c}ko\v{r}:
    Mathematical Principles of Fuzzy Logic. Kluwer, Boston 1999.

    Turuen, E.: Mathematics Behind Fuzzy Logic. Springer, Heidelberg
    1999.

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    Vilem Novak, DSc., Associate Professor
    University of Ostrava
    IRAFM (Institute for Research and Applications of Fuzzy Modeling)
    30. dubna 22
    701 03 Ostrava 1
    Czech Republic

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