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

From: Gordon D. Pusch (gdpusch@NO.xnet.SPAM.com)
Date: Tue Jan 16 2001 - 03:53:44 MET

• Next message: albert@massivbau.tu-darmstadt.de: "Re: Fuzzy Implication Rules with Fuzzy Input"

Martine De Cock <Martine.DeCock@rug.ac.be> writes:

> Cristian Fabbi wrote:
>>
>> studied by FL? Why do we say that with Fuzzy Logic we will make
>> computers thinking like human?
>
> Because we believe "that humans deal with imprecision and uncertainty
> by using linguistic values and that they apply some kind of approximate
> reasoning techniques rather than exact numerical values and first order
> logic". (Fuzzy Sets and Approximate Reasoning, Etienne E. Kerre, Xian
> Jiaotong University Press, Xian (P.R. China), 1999).

It does not follow that because humans "deal with imprecision and uncertainty"
they must therefore be using the specific mathematical formalism called
``fuzzy logic'' to do so, or that machines using this mathematical formalism
will ``think'' exactly the same way humans think. Many different forms of
approximate, qualitative, and probabilistic reasoning methods have been
proposed in the literature; there is no evidence that the human reasoning
process uses _ANY_ of them.

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.)

-- Gordon D. Pusch

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