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

From: Sidney Thomas (sf.thomas@verizon.net)
Date: Thu May 31 2001 - 15:23:03 MET DST

  • Next message: Sidney Thomas: "Re: Fuzzy proofs."

    ca314159 wrote:
    >
    > 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 ?

    This would be an inclusive or.

     
    Regards,
    S. F. Thomas

    ############################################################################
    This message was posted through the fuzzy mailing list.
    (1) To subscribe to this mailing list, send a message body of
    "SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
    (2) To unsubscribe from this mailing list, send a message body of
    "UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"
    to listproc@dbai.tuwien.ac.at
    (3) To reach the human who maintains the list, send mail to
    fuzzy-owner@dbai.tuwien.ac.at
    (4) WWW access and other information on Fuzzy Sets and Logic see
    http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info
    (5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html



    This archive was generated by hypermail 2b30 : Thu May 31 2001 - 15:50:25 MET DST