Re: Misclassification of packages; "libs" and "doc" sections

[Eray Ozkural <erayo@cs.bilkent.edu.tr>]

"Thomas Bushnell, BSG" wrote:
> 
> Eray Ozkural <erayo@cs.bilkent.edu.tr> writes:
> 
> > You may still assert that Category Theory has nothing to with
> > the philosophy of Category, but that would imply that logic
> > has nothing to do with semantics, and so on. Which is a position
> > that I could not take as I've studied philosophy following the
> > analytic tradition. It's a rather personal choice I guess.
> 
> I think this paragraph exemplifies your confusion.
> 
[1]> I think that logic has a great deal to do with semantics.
   > 
[2]> I think that the mathematical notion Category Theory has a great deal
   >  to do with logic and semantics.
   > 
[3]> And I don't think that the mathematical notion "Category Theory" has a
   > great deal to do with the traditional philosophical notion of
   > "Category".

But I'm not saying this. It's about an analogy concerning a
mapping (meta)mathematics -> metaphysics [4]

[5] logicians do (meta)mathematics, and philosophers of language use it to
    describe their metaphysical theories of reference. (whenever you talk
    about words pointing to people, that's not very physical :) As a
    consequence, logic is close to metaphysics of language.

[6] category theorists do (meta)mathematics, and _some_ philosophers
    of category use it to describe their _analytical_ metaphysical
    theories; as in the example I gave about universals. As a consequence,
    category theory is close to metaphysics of categories.

This mapping is a simple argument schema:
[7] A do (meta)mathematics, and philosophers of B use it to
    describe their metaphysical theories. As a
    consequence, A is close to metaphysics of B.

In this sense, if this schema does hold then you shouldn't
be able to say that logic is very close to semantics while category
theory isn't close to metaphysics of category. I think either this
mapping holds or not. If it holds then analogous arguments [5] and [6]
must both hold or must both fail. I assume that it holds because I do
subscribe to certain semantic theories as in [5]. :) The critical point
here is " _some_ philosophers of category use it to describe their
 _analytical_ metaphysical theories". I think that's the case, there're
example works for that.

In other words, your argument would indeed indicate a contradiction
if I meant
  [1] and [2] entail not [3]

I instead mean
  [1] entails not [3]
because
   [1]
   it's not the case that [5] exclusive or [6] ( because schema [7] holds )
   [1] implies [5]
   [5]
   therefore [6]

I know it isn't a nice thing to assert something, but I don't know
at the moment how I could express this thought without resorting to
a schema. Perhaps the schema should read
[7] A do (meta)mathematics, and philosophers of B use it to
    _fully_ describe their metaphysical theories. As a
    consequence, A is close to metaphysics of B.

[2] is irrelevant in my paragraph.

[I'm regarding "I think" as "it's the case" and "I don't think" as
"it's not the case" in [1],[2],[3]  The odd notation is just coincidence,
I didn't want to do ASCII art again...]

I think you can simply say that such an homomorphism doesn't exist,
and then your position is consistent. Nevertheless, I believe
that there's such a correspondence which makes me consistent, too. :)

I just tried to show that there isn't confusion in that paragraph,
its meaning depends on the context which is a bit implicit as my
fault. I probably made it unnecessarily complicated, but I'm growing
sleepy. :)

> As I read this, I can only form a deep suspicion that you are not
> really familiar at all with the traditional notion of category, as
> exemplified by Aristotle and Kant.  Here's a definiton from the
> American Heritage Dictionary:
> 
> "Aristotle's modes of objective being, such as quality, quantity, or
> relation, that are inherent in everything....Kant's modes of
> subjective understanding, such as singularity, universality, or
> particularity, that organize perceptions into knowledge.".

Ah, yes I'm familiar with Aristotle's categories but I don't have
detailed knowledge about Kant because I know his category notion
only as a vague overview.

There was a slight misunderstanding here, but for the other
post I'll need some time to be able to reply as categories of
understanding seems to be the true basis of disagreement. [I predict
that you won't like my resolution, but anyway.]

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