John and Azamat,
Lainaus "John F. Sowa" <sowa@xxxxxxxxxxx>:
> > What matters is the whole new idea of subjecting metaphysical
> > systems to axiomatization, the rigorous and systematic analysis
> > of a system from precise definitions, axioms and rules, what
> > Spinoza essayed in his philosophy.
> That is indeed an interesting idea. In mathematics, it has proved
> to be very valuable. But in the empirical sciences, even physics,
> it has had mixed results. Newton's achievements came from applying
> mathematical techniques to ideas that had been developed (with some
> use of mathematics) by Galileo and Kepler.
> As far as formalizing metaphysics, it is safe to say that there are
> *no* major insights that have resulted from the formalization. It
> is true that formal axioms are important for computer applications,
> since computers, by themselves, have no intuitions whatever. But
> the real insights have come from people whose intuitions were at
> the level of Galileo, Faraday, and Einstein. There are no formal
> achievements that are remotely comparable to the work of Newton,
> Maxwell, or Minkowski. (But there are insights into metaphysics
> that result from mathematical studies in physics, but the insights
> originated in physics, not formal philosophy.)
> In summary, the attempts by Spinoza and Descartes to formalize
> metaphysics were interesting failures. Even as late as the 20th
> century, when modern logic became available, attempts such as
> Carnap's Logische Aufbau were also interesting failures. Carnap
> was a good logician with a strong background in physics and
> mathematics. But his attempt was a dead end. Nelson Goodman
> made another interesting attempt, which developed some useful
> mathematics, but no new insights into metaphysics.
> Those of us who are working with logic and ontology hope thatWe have to separate two things:
> some kind of formalization will be useful for major applications.
> But so far, there have been *no* new insights into metaphysics that
> have come from the process of axiomatizing Cyc or any other formal
> system. On the contrary, the real insights have come from the same
> source as all the other insights since antiquity: dedicated study,
> observation, intuition, and discussion with teachers, students, and
> colleagues. The insights from formalization, if any, were modest
> at best.
To axiomatize something, does not mean that we have to impose
a horrible string of mathematical formulas upon it. In the
case of philosophical ontology (the best part of metaphysics),
plain text will do. Of course, some principles such as the
identity of indiscernibles and the indiscernibility of
identicals can be given in both ways, in text and in formulas,
and it helps understanding them. The act of axiomatization should
help understanding the subject, not to make it harder. Of course,
pictures and graphs help too.
To be clear, to state something axiomatically is clear, simply
because othervise it could be unclear. Over-formalization is a
threat that has to be avoided. The clearest cases of
over-formalization are the those where the thing that is
to be formalized, is actually required to understand the
formalization itself! Examples of these are e.g Frege-Russell,
von Neumann, and Zermelo -definitions of natural numbers.
> The largest of all attempts was the Cyc project, which many people
What good is it if you never use it?
> in AI regard as a failure. Cyc has had some useful applications,
> but none of them have been sufficiently successful to pay for the
> many millions of dollars that were invested in the project.
What good is it if you don't shake it,
be careful baby now and don't you break it!
What good is it, if I can't put it on a piece of bread?
It ain't no good to nobody!