# Re: Thomas' Fuzziness and Probability

From: Stephan Lehmke (Stephan.Lehmke@cs.uni-dortmund.de)
Date: Mon Aug 20 2001 - 13:26:31 MET DST

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In article <23af61c2.0108180659.1cbf8b83@posting.google.com>, Robert Dodier writes:
> 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.

Again, i must ask whether the situation would change if two-valued
logic were employed? Otherwise, obviously it has to be the same in
fuzzy logic. Fuzzy logic is about vagueness, not telepathy (whatever I
know has to be reflected by the logical system, whether I care to
write it down or not).

Btw, I doubt that the fact that you know something is reflected by
probabilistic logic, without your formalizing it in any way.

> 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.

I think we're talking cross purposes here. Logic is not about
computing truth values, but about drawing conclusions from assertions.

Of course, it is perfectly possible to state the relations between A
and B it the form of axioms, as I have pointed out before.

> 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.

This statement is unintelligible to me. Could you elaborate?

regards
Stephan

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