Thread:
RM:http://permalink.gmane.org/gmane.science.philosophy.peirce/15206
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15211
JBD:http://permalink.gmane.org/gmane.science.philosophy.peirce/15230
Jeff,
Thanks for your detailed comments. It will probably be a while before I can get
back to Robert's paper with any level of concentration. Like Frederik's book it
raises many critical issues in the future development of Peirce's paradigm that
I believe could well occupy us for years to come.
But all I can hope to do with my idle time at present is to collect a passel of
links to ghosts of animadversions past, so I will do that by and by.
Regards,
Jon
Jeffrey Brian Downard wrote:
Jon, Robert, List,
The idea of a "sign relational manifold" is intriguing. One historical
approach to thinking about such matters is to take a cue from Kant's analysis of the
conditions necessary for our perceptions to form a manifold of experience that is--in one
way or another--brought into some kind of unity. The requirement that Kant fastens on is
that the manifold of your experience and my experience must involve a homogeneous
manifold. Peirce's early examination of the categories of experience seems to start with
these Kantian inquiries.
Daniel Sutherland has a couple of nice papers where he provides an
interpretation of Kant's approach to this issue. He reads Kant in light of the
history of geometry--including the classical geometry of Euclid and the
perspective geometry of Lambert. Here are the titles in case anyone is
interested:
1) "The Role of Magnitude in Kant's Philosophy of Geometry," Canadian J.
Phil., vol. 34.
2) "Kant's Philosophy of Mathematics and and the Greek Mathematical
Tradition," vol. 117
3) "Kant on Arithmetic, Algebra and the Theory of Proportions," J History of
Phil., vol. 44
One of the things I find particularly interesting about Peirce's approach to these
matters is the priority he gives to aesthetics over ethics and logic in the normative
sciences. The interpretative conjecture that Richard Smyth puts forward in
<Reading Peirce Reading> is that Peirce is coming at the problem of how we
might justify claims about the objectivity of our cognitions concerning what is real
by moving to weaker starting points about what, aesthetically considered, can be
justified as a matter of an intersubjectively valid claim about what is inherently
attractive (e.g., beautiful or sublime). These kinds of judgments are similar in
kind to the those that we make when we claim that something we have observed is
inherently worthy of our attention and seems to call out for some kind of explanation.
So, I'm wondering if Robert or Jon might have some suggestions to offer about
what we might learn from inquiries in mathematical category theory, topos
theory, etc. about the formal conditions necessary for making such aesthetic
evaluations of what is inherently attractive. My hunch is that Peirce seems to
be working on the idea that Kant's analysis in the third Critique of the
conditions necessary for valid aesthetic judgments is grounded on the same
kinds of assumptions about the homogeneity of the manifold of experience that
were needed in the analysis of objective cognition in the first Critique. In
effect, Peirce sees the advantages of grounding these assumptions
aesthetically--as conjectures that we make about the inherent attractiveness of
such features in our experience. Ultimately, the conjectures are grounded in
the deductive of taste by establish the right that each of us has to make
claims concerning the freedom of our imagination in judging such matters.
Robert, if you could point out any places in your paper where you might be
touching on these kinds of questions, I'd appreciate the assistance of being
pointed in the right direction. If you have the time, some fleshing out of the
formal ideas in simpler terms would be helpful for me given the fact that I'm
trying to learn enough category to follow the kinds of arguments that your
making--but I still have a long way to go.
--Jeff
Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354
________________________________________
From: Jon Awbrey [[email protected]]
Sent: Saturday, December 20, 2014 8:01 AM
To: Peirce List; Robert Marty
Subject: [PEIRCE-L] Algebraic Formalization of Phaneroscopy and Semiotics
Robert,
Many thanks for your very stimulating paper.
http://hardsemiotics.net/HARD/MISCELLANEOUS/algebraic%20formalization%20of%20semiotics.pdf
I am traveling today and otherwise diverted until the new year but I will drop
this topic anchor as a reminder to return to it. Just offhand from a casual
scan it appears to resonate with the work I've been trying to do with “sign
relational manifolds”.
http://inquiryintoinquiry.com/category/mathematics/manifolds/
Regards,
Jon
--
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