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Journal of the International Association for Semiotic Studies / Revue de l'Association Internationale de Sémiotique

Editor-in-Chief: Danesi, Marcel

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Source Normalized Impact per Paper (SNIP) 2018: 0.478

Agenzia Nazionale di Valutazione del Sistema Universitario e della Ricerca: Classe A

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Volume 2015, Issue 207


Mathematics and Peirce’s semiotic

Ru Michael Sabre
Published Online: 2015-07-28 | DOI: https://doi.org/10.1515/sem-2015-0061


It is shown here that Peirce’s ten trichotomies, specifically art as discussed in Sabre (2014), provides a structure for presenting a mathematical conjecture and provide a heuristic for going about attempting a mathematical proof of the conjecture. The mathematics is presented through the work of the mathematical proof theorists George Polya and Daniel Solow. Here a geometric conjecture is shown to be true using a ten trichotomy context for a proof. Thus through the structure of mathematical proof the ten trichotomy structure validates itself.

Keywords: Peirce; semiotics; ten trichotomies; mathematical proof; George Polya; Daniel Solow


  • Polya, G. 1957. How to solve it, 2nd edn. Princeton: Princeton University Press.Google Scholar

  • Polya, George. 1962. Mathematical discovery. New York: John Wiley.Google Scholar

  • Sabre, Ru Michael. 2012. Peirce’s ten trichotomies: Metaphor, hypothesis, and decision. Semiotica 190(1/4). 139–155.Web of ScienceGoogle Scholar

  • Sabre, Ru Michael. 2014. Art, science, and value as found in Peirce’s ten trichotomies. Semiotica 200(1/4). 21–30.Web of ScienceGoogle Scholar

  • Solow, Daniel. 2010 [1976]. How to read and do proofs. New York: John Wiley.Google Scholar

About the article

Published Online: 2015-07-28

Published in Print: 2015-10-01

Citation Information: Semiotica, Volume 2015, Issue 207, Pages 175–183, ISSN (Online) 1613-3692, ISSN (Print) 0037-1998, DOI: https://doi.org/10.1515/sem-2015-0061.

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