Jim:
On May 2, 2006, at 1:06 AM, Peirce Discussion Forum digest wrote:
Irving:
On May 1, 2006, at 1:06 AM, Peirce Discussion Forum digest wrote:
A _category_ is the class of all members of some =
kind of abstract mathematical entity (sets, groups, rings, fields
topologic=
al spaces, etc.) and all the functions that hold between the class
mathema=
tical entity or structure being studied.
I find category theory to be somewhat of a conundrum.
From the perspective of language, how is it possible to
conceptualize
both the subject and the copula for a category?
If so defined, would you say that category theory is a sort of sortal
logic over mathematical objects? Even metaphorically?
Cheers
Jerry
Dear Folks,
Yes, this is what is puzzling me -- seems that the fundamental
rules or
notions that relate the categories are in effect a definition of the
categories themselves. So for me the question becomes as I think
Jerry is
asking -- how do we have both entities and relations. Seems to me
that one
or the other is not fundamental. I think the Piercean approach
that all
being is merely relations is more satisfying. Some of these
relations (of
relations) we relate to as objects, collateral objects, etc. The
fundamental
categories are themselves relations. I take that to be one of
Peirce's main
contributions to the theory of categories.
Sort of . . .
Cheers,
Jim Piat
I purposefully stated my sentence in ordinary language (grammar) to
avoid the possible confusion in technical language.
It seems to me that category theory bears a different relation to
language than does ordinary calculations.
I have not found a way to express this sentiment but I feel it deeply.
The deeply checkered philosophical history of the concept of a
"category" does not provide significant guidance to me.
Cheers
Jerry
---
Message from peirce-l forum to subscriber archive@mail-archive.com
