Re: "Inevitable Illusions", Law of Excluded Middle etc.

From: ca314159 (ca314159@bestweb.net)
Date: Mon May 28 2001 - 12:27:24 MET DST

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    Sidney Thomas wrote:
    >
    > Ellen Hisdal wrote:
    > <snip>
    > > It is shown there that when a subject takes the possibility of the
    > > presence of fuzziness into account, then he realizes that an object
    > > whose height is near the lower threshold for 'tall' may, in the presence
    > > of fuzziness (e.g. errors of measurement; these are one example of fuzziness),
    > > sometimes be labeled `tallī, and sometimes `NOT tall'.
    >
    > I would expect that to be true.
    >
    > > We therefore do not expect the Law of the Excluded Middle to hold
    > > exactly in Fuzzy Set Theory.
    >
    > It can be. The problem of fuzziness and LEM is resolved in my opinion
    > with rules for AND, OR and NOT which yield the following result:
    > There exist x such that both
    >
    > mu[TALL](x) > 0
    >
    > and
    >
    > mu[NOT TALL] > 0,
    >
    > but for _all_ x,
    >
    > mu[TALL AND NOT TALL](x) = 0,
    >
    > and
    >
    > mu[TALL OR NOT TALL](x) = 1.

     Is this an exclusive or (xor), xor an inclusive or (ior);
     disjunctive xor conjunctive ?

    The Xor problem:
    http://www.google.com/search?q=xor+problem

    Quantum superpositions:
    http://search.cpan.org/doc/DCONWAY/Quantum-Superpositions-1.03/lib/Quantum/Superpositions.pm

    >
    > THis reflects the common-sense observation that the fuzziness in the
    > term "tall", for example, would not rescue a witness from the
    > derision of the court were she to say "the perpetrator was tall and
    > not tall." In other words, LEM and law of contradiction may still
    > hold under a fuzzy set theory, and without doing away with the
    > fuzziness. This result is developed in some detail in my _Fuzziness
    > and Probability_ (ACG Press, 1995). LEM and LC of course do not hold
    > if AND and OR are modeled exclusively by the min and max operators
    > respectively.
    >
    > Regards,
    > S. F. Thomas
    >
    > PS. Good seeing you here again, Prof. Hisdal.

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