Diamond Semiotics

An interplay of semiotic and graphematic diamonds

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Some preliminary remarks about an interplay of semiotic and graphematic diamonds are sketched.


Abstract
A reconstruction of Alfred Toth’s semiotic constructions of diamonds with the help of different notations is introduced.
A distinction between the diamond properties of basic semiotic configurations and the composition of semiotic configurations as micro- and macro-analysis is proposed.
The as-abstraction for semiotic connections is introduced and a mechanism to complement semiotic figures is proposed.


Semiotics, again?

Thanks to the recent work of the semiotician Alfred Toth about mathematical semiotics and its application to polycontextural and kenogrammatic concepts, like chiasms and diamonds, a chapter of semiotization of diamonds and a diamondization of semiotics has to be added to the project of Short Studies.



This is a very first response to the profound work of Alfred Toth. It takes me back to the 70s/80s when I got involved in this headaching adventure of confronting Bense’s semiotics with Gunther’s polycontextural logic and kenogrammatics, both, at this time, quite in status nascendi, especially Gunther’s project.



Semiotics is defined by Peirce and is elaborated in extenso by Bense and Toth as a triadic-trichotomic system of semiosis, i.e. as a scheme of generating signs. Obviously, it has not to be confused with other sign theoretical projects, like semiology (de Saussure, Barthes) or the pre-war Semiotik for formal systems by Manfred Schröter and Hans Hermes.

Diamonds are not triadic-trichotomic but genuinely tetradic, chiastic, antidromic and 4-fold.

Hence, diamonds are not semiotical.



Are semiotic diamonds semiotical?



First diamondization: internal or micro


The semiotic sign relation is a product of semiosis which can be modeled as a categorical composition of elementary sign relations. Hence, a diamondization of semiotics is a diamondization of the semiotic composition operation of elementary sign relations. This kind of diamondization shall be called internal (micro) diamondization in contrast to the external (macro) diamondization of the composition of full sign systems.



Basic work to the study of diamonds of elementary semiotic compositions had been published by the semiotician Alfred Toth.
Toth gives a solution for the diamondization of sign systems with the help of the inversion operation (INV) he introduced.



Second diamondization: external or macro


A second kind of diamondization is introduced with the diamondization of the composition of signs as it occurs, i.e. in the constructions of iterative and accretive compositions of sign schemes, e.g. superposition and superisation of signs.



Transpositions, dualizations, inversions and compositions are semiotic operations, diamondization consists of difference, saltisitions, bridges and complementarity.




FULL TEXT
http://www.thinkartlab.com/pkl/lola/Diamond Semiotics/Diamond Semiotics.html
http://www.thinkartlab.com/pkl/lola/Diamond Semiotics/Diamond Semiotics.pdf
http://www.thinkartlab.com/pkl/lola/Diamond Semiotics/Diamond Semiotics.nb