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

From: Ellen Hisdal (ellen@ifi.uio.no)
Date: Mon May 21 2001 - 20:07:25 MET DST

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    Concerning the Law of Excluded Middle and Fuzzy Set Theory, see section 5 of

       author = {Hisdal, E.},
       title = {Open-Mindedness and Probabilities versus Possibilities},
       booktitle={Fuzzy Logic Foundations and Industrial Applications},
       publisher = {Kluwer Academic Publishers, Boston},
       year = {1996},
       editor = {Da Ruan},
       pages = {27-55}

    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'.
    We therefore do not expect the Law of the Excluded Middle to hold
    exactly in Fuzzy Set Theory.

    > Originator: fuzzy-mail@dbai.tuwien.ac.at
    > From: devoirc@biotronik.com (Chris De Voir)
    > I am not attacking the science of Fuzzy Theory, but I have had this nagging
    > thought about the excluded middle and other normative thinking rules. Does
    > anyone know of an examination of Fuzzy Theory from the perspective of
    > Cognitive Science? People are already susceptible to cognitive illusions
    > just doing work-aday thinking in the Crisp world using traditional logic.
    > Are there normative thinking rules for the Fuzzy World? Are there studies,
    > reviews, discussions etc. of cognitive illusions in Fuzzy?
    >
    > ["Inevitable Illusions - How Mistakes of Reason Rule Our Minds" by Massimo
    > Piattelli-Palmarini]
    >
    > Thanks for any URLs, references, or additional thoughts,
    > Chris De Voir.

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