# 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.

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

tel: +420-69-6160 234
fax: +420-69-6120 478
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e-mail: Vilem.Novak@osu.cz, novakv@osu.cz
WEB: http://www1.osu.cz/irafm
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