Sidney Thomas wrote:
> Ellen Hisdal wrote:
> > 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
> mu[NOT TALL] > 0,
> but for _all_ x,
> mu[TALL AND NOT TALL](x) = 0,
> mu[TALL OR NOT TALL](x) = 1.
Is this an exclusive or (xor), xor an inclusive or (ior);
disjunctive xor conjunctive ?
The Xor problem:
> 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
> S. F. Thomas
> PS. Good seeing you here again, Prof. Hisdal.
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