SUO: Re: Plea for Relements
Jon,
There is a difference:
JS>>There is a very big difference between fuzzy logic and
>>fuzzy sets. I approve of fuzziness in set membership,
>>but not fuzziness in truth value.
>
JA> No argument there. The same thing applies to many-valued logics.
Peirce also noted the need for a third truth value, Unknown,
between T and F. And I approve of Cyc's 5 truth values:
Certainly T; T by default; Unknown; F by default; Certainly F.
But those values can be introduced without destroying
the relationship between the logic and the model theory.
None of the many formulas for computing fuzzy truth values
are compatible with any reasonable version of model theory.
JA> The important thing is not the multitude M of functional values that
> we use in making decisions or in expressing propositions f : X -> M,
> which need for analytic purposes, and can without loss of generality,
> be constructed from distinctions of the form f : X -> B = {0, 1}, but
> the arity, dimensionality, or valence of the relations that we use to
> model the realities behind the phenomena. And here I think it is way
> past time to put the interpreter back into the picture of logic and
> semiotics, as they were forced to even in physics, long long ago.
Yes. The 5 truth values of Cyc can be interpreted as the
result of a triadic relation that relates (1) a proposition,
(2) a model, and (3) some interpreter:
- T, F, and Unknown represent the interpreter's
knowledge about how the proposition is related
to the model.
- T or F by default represent the interpreter's
presupposition in terms of some default model,
which the statisticians call the "null hypothesis".
My quarrel with the fuzzy logicians is that they ignore
the complex relationships between the logic, the model
the interpreter, and the world.
I have brought such issues to the attention of several
fuzzy proponents. Their answer is that they do take
such matters into account in their applications. That
is why they are able to demonstrate useful applications
of their theory.
That response, however, turns fuzzy practice into an
art rather than a science. Since the theory does not
show the relationships explicitly, there is no "official"
interpretation of what the truth numbers are supposed to
mean. By long experience, some fuzzy artists get better
results than others because they have more experience
in applying the mysterious numbers to an application.
This all gets back to my point about the fallacy of
misplaced fuzziness. T and F are the result of a
binary relation between a theory and the model.
When you bring the real world into account, you
need a triadic relation between the theory, the
model, and the world.
You can add the interpreter to that triad to make
it a tetrad -- but then, as Peirce observed, you
could break the tetrad into two triads. In any case,
you have to go beyond two.
The fuzzy theorists have been trying to go beyond
T and F while sticking with just a dyadic relation
between a proposition and the world. That doesn't
work as a science, and it only works as an art
when the artist makes some unstated assumptions.
Bottom line: The fuzzy people need to study
Peirce in order to learn how to make the implicit
relationships explicit.
John Sowa