Accessible Requires Authentication Published by De Gruyter Mouton March 27, 2019

The trichotomic machine

Robert Marty
From the journal Semiotica

Abstract

The formal analysis of the principles leading the classification of the hexadic, decadic, and triadic signs from C. S. Peirce especially, gives rise to a general methodology allowing to systematically classify any n-adic combinatory named “protosign.” Basic concepts of the algebraic theory regarding the categories and functors will be used. That formalization provides an additional benefit by highlighting and systematizing formal immanent relationships between the classes of protosigns (or signs). Well known hierarchical structures (lattices) are then obtained. Thanks to the contribution of specific concepts in the Homological Algebra, new methodologies of analysis and creation of significations can be introduced.

A Appendix

Figure 19: Copy of the result of the generator of latttices by Patrick Benazet for n=6. Every arrow represents a natural transformations of functors, that is to say, in this case 6 morphisms.

Figure 19:

Copy of the result of the generator of latttices by Patrick Benazet for n=6. Every arrow represents a natural transformations of functors, that is to say, in this case 6 morphisms.

B Appendix

Figure 20: Copy of the result of the generator of lattices by Patrick Benazet for n=10. Every arrow represents a natural transformations of functors, that is to say, in this case 10 morphisms.

Figure 20:

Copy of the result of the generator of lattices by Patrick Benazet for n=10. Every arrow represents a natural transformations of functors, that is to say, in this case 10 morphisms.

References

Marty, R. 1990. L’algèbre des signes: Essai de semiotique scientifique d’après C. S. Peirce. Amsterdam & Philadelphia: John Benjamins. Search in Google Scholar

Marty, R. 2011. Seventy-six definitions of the sign by C. S. Peirce. http://www.iupui.edu/~arisbe/rsources/76DEFS/76defs.HTM (accessed 11 February 2019). Search in Google Scholar

Peirce, Charles S. 1931–1966. The collected papers of Charles S. Peirce, vol. 8. C. Hartshorne, P. Weiss & A. W. Burks (eds.). Cambridge: Harvard University Press. [Reference to Peirce’s papers will be designated CP followed by volume and paragraph number.]. Search in Google Scholar

Peirce, Charles S. 1976. The new elements of mathematics, vol. 4. C. Eisele (ed.). Berlin & New York: Mouton de Gruyter. Atlantic Highlands, NJ: Humanities Press. [Reference to Peirce’s New Elements will be designated NEM followed by volume and page number]. Search in Google Scholar

Peirce, Charles S. & Lady Victoria Welby. 1977. Semiotic and significs. Charles S. Hardwick (ed.). Bloomington: Indianapolis University Press. [Reference to this work will be designated SS followed by page number]. Search in Google Scholar

Published Online: 2019-03-27
Published in Print: 2019-05-07

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