Re: Thomas' Fuzziness and Probability

From: Robert Dodier (robertd@athenesoft.com)
Date: Sun Aug 19 2001 - 13:02:09 MET DST

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    Stephan.Lehmke@cs.uni-dortmund.de (Stephan Lehmke) wrote:

    > Robert Dodier writes:
    > >
    > > Any such definition must ignore the relation between elements in a
    > > compound: if truth(B')=truth(B), then in any proposition containing
    > > A and B, I can swap in B' in place of B, and get exactly the same
    > > truth value for the compound; whether the elements are redundant,
    > > contradictory, or completely unrelated doesn't enter the calculation.
    >
    > It's exactly the same in two-valued logic. As fuzzy logic agrees with
    > classical logic on the extremal truth values, there is no way the
    > behaviour you observe can be avoided.

    Consider a less-extreme example, then: let A = "the mayor is tall",
    B = "the mayor is heavy", and B' = "the mayor is well-dressed". For the
    sake of argument suppose that truth(B)=truth(B'). Despite the fact that
    we know that there is some relation between height and weight, the
    truth value assigned to a compound containing A and B is just the same
    as what we get by putting B' in the place of B.

    > If _you_ have some additional knowledge about how eye colors usually
    > behave, you have to introduce this knowledge as an additional axiom,
    > exactly as you would do in two-valued logic.

    There is a two-fold drawback of defining truth value of a compound
    strictly as a function of truth values of its parts. (i) You cannot
    exploit information about the relation between A and B; even if you
    know what it is, there is simply no place to put it in the computation
    of the truth value of a compound proposition. (ii) The rules for computing
    truth value of the compound don't tell you when you need to supply
    some information about the relation between the parts. To draw a
    conclusion about a compound proposition, maybe you need to know something
    about the relation between the parts and maybe you don't, but there's
    no way to tell from the rules which is the case.

    Regards,
    Robert Dodier

    --
    ``Socrates used to meditate all day in the snow, but Descartes'
    mind worked only when he was warm.'' -- Bertrand Russell
    

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