Jeff, List,
Yes, these sorts of discussion have always been a RIOT (Radical Indeterminacy Of Translation), as
Quine more or less put it, between what seem to be practically incommensurable paradigms of thought.
At any rate, it looked for a moment there like we might actually be settling down to a serious
mathematical discussion of potential cross-pollinations between category theory and semiotics, all
of which inspired me to collect a sample of previously frayed threads for the benefit of those who
may have snoozed through them the first time around —
Precursors of Category Theory
=============================
http://intersci.ss.uci.edu/wiki/index.php/Precursors_of_Category_Theory
Category Theory (Phenomenology and the Categories)
==================================================
JA:http://web.archive.org/web/20140311054002/http://permalink.gmane.org/gmane.science.philosophy.peirce/12131
JA:http://web.archive.org/web/20140316160001/http://permalink.gmane.org/gmane.science.philosophy.peirce/12183
Category Theory, Relational Arrows, Sign Relations
==================================================
JA:http://web.archive.org/web/20140321150001/http://permalink.gmane.org/gmane.science.philosophy.peirce/12248
RM:http://web.archive.org/web/20140321150020/http://permalink.gmane.org/gmane.science.philosophy.peirce/12249
JA:http://web.archive.org/web/20140321152006/http://permalink.gmane.org/gmane.science.philosophy.peirce/12250
RM:http://web.archive.org/web/20140322021358/http://permalink.gmane.org/gmane.science.philosophy.peirce/12256
JA:http://web.archive.org/web/20140322021200/http://permalink.gmane.org/gmane.science.philosophy.peirce/12258
JA:http://web.archive.org/web/20140322140001/http://permalink.gmane.org/gmane.science.philosophy.peirce/12262
JA:http://web.archive.org/web/20140330033027/http://permalink.gmane.org/gmane.science.philosophy.peirce/12386
Category Theory In Math
=======================
JBD:http://web.archive.org/web/20140429200401/http://permalink.gmane.org/gmane.science.philosophy.peirce/12705
JA:http://web.archive.org/web/20140429201000/http://permalink.gmane.org/gmane.science.philosophy.peirce/12713
JBD:http://web.archive.org/web/20140430052801/http://permalink.gmane.org/gmane.science.philosophy.peirce/12715
JLRC:http://web.archive.org/web/20140430052522/http://permalink.gmane.org/gmane.science.philosophy.peirce/12719
JBD:http://web.archive.org/web/20140430054001/http://permalink.gmane.org/gmane.science.philosophy.peirce/12721
JA:http://web.archive.org/web/20140430152001/http://permalink.gmane.org/gmane.science.philosophy.peirce/12722
The main obstacles to advancing this discussion are a couple of recalcitrant category confusions,
one between the semiotic roles of syntactic means and objective ends and the other between different
levels of structure in the object domains, specifically. between the properties proper to individual
elements of sets and the properties proper to those sets themselves. But perhaps we can be just as
persistent in clearing up those confusions over time.
Regards,
Jon
Jeffrey Brian Downard wrote:
Hi Jon, List,
Thank you for sending the links -- especially to the discussion. It is helpful -- and quite funny.
For those who are a new to category theory, the explanation provided in the
Stanford Encyclopedia of philosophy is a pretty good place to start. The
section on the history of category theory provides context that is helpful for
seeing where the two works by Mac Lane, Lambeck and Scott that Jon refers us to
fit into the larger story. The bibliography is fairly comprehensive.
--Jeff
Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354
________________________________________
From: Jon Awbrey [[email protected]]
Sent: Tuesday, April 29, 2014 12:40 PM
To: Jeffrey Brian Downard
Cc: Peirce List
Subject: Re: category theory in math
Peircers,
Category theory, along with its applications to logic and computation, has been
a recurrent subject
of discussion in many online groups over the last 15 years or so, just since I
came online, anyway.
Here are excerpts from basic texts that served as springboards and resources
for these groups, along
with a few bits of associated commentary and discussion, that I archived at the
InterSciWiki site.
Perhaps a few readers on the Peirce List will find these of use by way of
informing their discussions.
Excerpts from Saunders Mac Lane (1971/1997), ''Categories for the Working
Mathematician''
=========================================================================================
☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_Awbrey/Mathematical_Notes#CAT._Category_Theory
☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_Awbrey/Mathematical_Notes#CAT._Category_Theory_.E2.80.A2_Discussion
Excerpts from J. Lambek and P.J. Scott (1986), ''Introduction To Higher Order
Categorical Logic''
=================================================================================================
☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_Awbrey/Mathematical_Notes#HOC._Higher_Order_Categorical_Logic
☞http://intersci.ss.uci.edu/wiki/index.php/User:Jon_Awbrey/Mathematical_Notes#HOC._Higher_Order_Categorical_Logic_.E2.80.A2_Discussion
Regards,
Jon
Jeffrey Brian Downard wrote:
Jerry, List,
We might add that category theory, as it has been developed in mathematics in
the 20th century, is a generalization upon the conception of a mathematical
group. Peirce was quite familiar with Klein's use of group structure as a
basis for exploring the relations between different areas of mathematics. As
such, we should not assume that the general idea of what is involved in the
conception of mathematical category is entirely foreign to Peirce.
Jeff
Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354
--
academia: http://independent.academia.edu/JonAwbrey
my word press blog: http://inquiryintoinquiry.com/
inquiry list: http://stderr.org/pipermail/inquiry/
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to [email protected] . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
