Re: Misclassification of packages; "libs" and "doc" sections
"Thomas Bushnell, BSG" wrote:
>
> Yes... but nothing to do with "category" in metaphysics.
>
I don't agree with this.
> The mathematical notion of category is important for many things, some
> of them philosophical. But it simply doesn't mean anything really
> like the same thing as category in metaphysics.
You should be approaching from the point of view of continental philosophy
or theology in order to say that the category in metaphysics is so much
different from category in mathematics. I'm simply saying that you
can devise a philosophy of "category" based on the mathematical theory.
Next, one could claim that formal semantics has nothing to do with the
philosophy of language which does include metaphysical theories such as
those of "reference". Such a claim would be plain wrong.
I don't know if you want to go into details, but I suggest that all
the senses and components of traditional "Category" do exist in
Category Theory and thus the term was chosen on purpose.
* Ontology: Categories
* Predication: Function/Argument distinction (or the more primitive
Predicate/Subject) present as arrows, and other sorts of morphisms
(functors, etc)
* Universals/Particulars: Categories are universals, Objects are
particulars. Also abstract/concrete categories...
* Category Hierarchy: Categories of Categories. (A category may
be an object in another category)
* Cross-Categorial Predication: functors, natural transformations, etc.
Tentatively compared to slightly modernized versions of
Aristotle's "Category". I wanted to show that Category
Theory is powerful enough to express every formal statement
made about "Category" in metaphysics and more. Some of the
more fuzzy metaphysical theories would not be expressible;
of course they _aren't_ interesting to an analytic philosopher.
I view it as just another language to talk of the same problem,
though a more refined and exact language.
This is rather like Frege's approach to philosophy of language
rather than late Wittgenstein's aprroach to the same matter.
Note also that meta-mathematics is very close to meta-physics :)
Some mathematicians would say that Category Theory shouldn't
be a part of "real" mathematics :), they find it too philosophical.
[Rather like C coders despising higher-level languages. :)]
> I fully grant that the mathematical notion of category should be
> important to philosophers. Even if it were the most important thing
> possible, with ramifications in every conceivable area of philosophy,
> that *still* doesn't make it similar to the traditional metaphysical
> notion of "category".
>
> I *completely* agree that the mathematical notion of category theory
> is important. All you've done (and others) is repeat how very totally
> important it is. Great! That doesn't make it the same thing as the
> traditional notion of "category", anymore than it makes it the same
> thing as the traditional notion of "fish", "sophistry", or
> "pythagoreanism".
That's exactly where we disagree.
For a relevant analogy, I'd say that "Suppose the mind is a computational
phenomenon. In that case, if one devises a theory which explains all
important phenomena relating to mind in computational terms then that
theory has to explain all philosophy of mind. And of course, a working
model would be required :)" In other words, there isn't an impenetrateable
border between science and philosophy. I suppose that's where our
real difference lies. [Might it be related to incompatibility of
our views on theology?]
An interesting work may be:
Ellerman, D., 1987, "Category Theory and Concrete Universals", Synthese, 28, 409-429.
Sincerely,
--
Eray (exa) Ozkural
Comp. Sci. Dept., Bilkent University, Ankara
e-mail: erayo@cs.bilkent.edu.tr
www: http://www.cs.bilkent.edu.tr/~erayo
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