(For undistorted figures, see the attached.)
Hi,
While preparing for my interdisciplinary lecture on complementarity to
first-year students at Rutgers, called a Byrne seminar, the following
thoughts occurred to me today that may help apply abstract mathematical
concepts to Peirces' triadic sign relation which is based on his triadic
metaphysics:
The Essentiality of Threeness:
(1) One has NO RELATION.
Two has only ONE RELATION.
Three is the minimum to give rise to a RELATION between RELATIONS.
The Essentiality of the Threeness for Semiosis or Communication:
(2) What characterizes the Peircean sign relation is the transfer of
information from the object to the interpretant mediated by the sign:
f g
Object ------> Sign ------> Interpretant
| ^
| |
|___________________________________|
h
Figure 1. The triadic sign relation of Peirce. f = sign generation; g =
information transfer from the utterer to the hearer; h = coincidence of
the original and the received information. Thus the composition condition
of the category theory in mathematics holds, i.e., f x g = h.
(3) What mathematicians call "a category" can be viewed as the
generalization of Peirce's triadic sign relation. Both are the mechanisms
or the devices for
transferring information from the source to the destination through an
intermediate.
(4) Both Pericean sign relation and mathematical category can be
represented as a diagram called the "ur-category":
f g
A -------> B -------> C
| ^
| |
|_______________________|
h
Figure 2. The ur-category to which all categories and triadic relations
belong. f = information preserving mapping (e.g., sign generation); g =
information-preserving mapping (e.g., Fourier transform, transcription of
DNA information to mRNA information, etc.); h = coincidence of the
information between its source and receiver or target.
(5) Words alone are insufficient to convey the basic ideas behind the
sign relations. The diagrams must be combined with words to adequately
represent the subtle ideas behind the sign relation and the mathematical
category and their mutual relations.
With all the best.
Sung
___________________________________________________
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
> Thread:
> GR:http://permalink.gmane.org/gmane.science.philosophy.peirce/14086
> JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14122
> GR:http://permalink.gmane.org/gmane.science.philosophy.peirce/14123
> JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/14124
>
> Gary & All,
>
> The k-identity relations over a given domain X belong to the panoply of
> fundamental structures in the general theory of relations, and the fact
> that
> 3-identity relations suffice to generate all the other k-identity
> relations is a
> fundamental fact of that theory. It goes without saying that such
> fundamental
> structures will find application in the theory of relations, and the
> theory of
> triadic sign relations in particular, but they are themselves cast in a
> more
> general sphere than semiotics itself.
>
> Regards,
>
> Jon
>
> --
>
> 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
>
Jon_09162014.pdf
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