Clark, list,
Sowa's note was forwarded to peirce-l by Gary Richmond as a comment on
Anellis's earlier peirce-l post on April 30, 2006
http://comments.gmane.org/gmane.science.philosophy.peirce/709 which said
the following:
[Quote Anellis]
I had earlier noted that, in going back to Herrlich & Strecker's
_Category Theory_, I was reminded that category theory permits
comparison of classes of any abstract mathematical structures with
any other class of abstract mathematical structure, e.g. the class
of all groups and their homomorphisms with the class of all
topological spaces and their continuous functions, and the
comparison of these with other classes of structured sets and
structure-preserving functions. A _/category/_ is the class of all
members of some kind of abstract mathematical entity (sets, groups,
rings, fields topological spaces, etc.) and all the functions that
hold between the class mathematical entity or structure being studied.
Whether this has any implications or significance for philosophers
-- other than perhaps philosophers of mathematics, I suggest that it
can be understood as a further development of Felix Klein's effort
in the Erlanger Programme to classify geometries according to their
algebraic groups, and CSP's contemporaneous work, in the appendix to
his father's work on Linear Nonassociative Algebra, to classify
those algebras in terms of his algebra of relatives, and followed by
Whitehead's efforts in the _Treatise on Universal Algebra_ at the
end of the nineteenth century, to bring together Boolean algebra,
linear and multilinear algebras, and Hermann Grassmann's
Ausdehnungslehre into a unified system. (It may not be amiss to
remind everyone that Whitehead's initial conception of the
_Principia Mathematica_ when he first joined forces with Russell to
write the latter, was as a second volume to his _Treatise_.) It is
also true that a number of mathematicians have seriously considered
using, and begun to develop, category theory as a foundation of
mathematics more felicitous than the discarded logicism of Frege,
Dedekind, and the Russell of the _Principles of Mathematics_ and the
_Principia_.
Irving H. Anellis
[End quote]
On 10/3/2014 2:57 PM, Clark Goble wrote:
On Oct 3, 2014, at 12:20 PM, Benjamin Udell <bud...@nyc.rr.com
<mailto:bud...@nyc.rr.com>> wrote:
On 10/3/2014 2:04 PM, Sungchul Ji wrote:
Ben, Jeff, Jon, lists,
1) Can we say that there can be many triads, depending one how one
defines them, but the Peircean triad is special and identical with a
mathematical category ?
Category theory is one of those things I’ve always wanted to learn and
never have had time. I can’t say much about it. However I did have
this in my notes. It’s from *way* back on May 1st, 2006 here on
Peirce-L. It’s from John Sowa whom I suspect most of us are familiar
with. This is him replying on connections between category theory and
Peirce.
I would say that the description of category theory by
Irving A. is a reasonable explanation of the subject.
But category theory wasn't invented until about 40 years
after Peirce died. Therefore, he wasn't aware of it.
On the other hand, I don't think that there's much point in
arguing "whether it can be connected to any part of the work
of Peirce in any significant way?" He probably would have
approved of it, but so what?
There are other developments, such as DNA and Heisenberg's
uncertainty principle in quantum mechanics, which are much
closer to themes that Peirce had discussed. Those could be
considered support for his positions, but I'd put category
theory into an area that is compatible with Peirce's views,
but not directly supportive of anything he said in particular.
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
