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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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Volume 2011, Issue 186 (Jan 2011)


Peirce's alpha graphs and propositional languages

Sun-Joo Shin
  • Professor at Yale University.
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Published Online: 2011-08-08 | DOI: https://doi.org/10.1515/semi.2011.059


Many do not doubt that Peirce's Existential Graphs are diagrammatic, as opposed to symbolic. However, when we are pressured to draw a distinction between the two different forms of representation, we find ourselves at a loss and our intuition quite vague. In this paper, I locate fundamental differences between two logically equivalent systems, Peirce's Alpha system and propositional languages. Suppose we have only two sentential connectives, ¬ and ̂. In spite of its truth-functional completeness, we don't want to use this language for the translation of English sentences or as a deductive calculus. We would adopt this language only when we intend to develop logical theories. That is, it is convenient to have fewer connectives for a meta-theory, but not for practical use. So, there seems to be a trade-off between a language with fewer connectives and a language with more connectives. This view has been accepted without question. In this paper, I will argue that this trade-off is limited to linear symbolic systems and that we could have a diagrammatic system with fewer operations but no need to suffer from problems like those of a sentential language with fewer connectives. How is that possible? A comparison between Peirce's Alpha system and a propositional language is presented to answer this question. The case study identifies the following unique property of a non-linear diagrammatic system as a main source of the discrepancy between two different types of representation: One and the same diagram can be read off in more than one way by carving it up in many ways, but without ambiguity.

Keywords:: logic; diagrams; Peirce; Alpha graphs; propositional logic; multi-model reasoning

About the article

Published Online: 2011-08-08

Published in Print: 2011-08-01

Citation Information: Semiotica, ISSN (Online) 1613-3692, ISSN (Print) 0037-1998, DOI: https://doi.org/10.1515/semi.2011.059. Export Citation

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