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Peirce’s Diagrammatic Logic in IF Perspective

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Diagrammatic Representation and Inference (Diagrams 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2980))

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Abstract

This paper presents a topological and game-theoretic extension of the system of Existential Graphs (eg). Egs were Charles S. Peirce’s diagrammatic and iconic approach to logic. By scribing the graphs on assertion spaces of higher dimensions, this extension provides the precise iconic counterpart to the Independence-Friendly (if) restatement of first-order logic suggested by Hintikka. Consequently, the if extension completes the project that Peirce initiated: it breaks off from the linear confines of language by diagrams that extend to three dimensions, which Peirce predicted to be necessary and sufficient for the expression of all assertions. Apart from improved ways of performing conceptual modelling on natural-language expressions, this extension reveals the true proportions of Peirce’s sign- and model-theoretic thinking in plunging into the notions of identity, negation, continuity and quantification.

Supported by the Academy of Finland and the Hungarian Academy of Sciences (Project No. 104262: Communications in the 21st Century: The Relevance of C.S. Peirce).

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Author information

Authors and Affiliations

  1. Department of Philosophy, University of Helsinki, P.O. Box 9, FIN-00014

    Ahti-Veikko Pietarinen

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  1. Ahti-Veikko Pietarinen
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Editors and Affiliations

  1. Computer Laboratory, University of Cambridge, CB3 0FD, Cambridge, UK

    Alan F. Blackwell

  2. Clayton School of IT Monash University, 3800, Australia

    Kim Marriott

  3. Faculty of Culture and Information Science, Doshisha University, Japan

    Atsushi Shimojima

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Pietarinen, AV. (2004). Peirce’s Diagrammatic Logic in IF Perspective. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds) Diagrammatic Representation and Inference. Diagrams 2004. Lecture Notes in Computer Science(), vol 2980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25931-2_11

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  • DOI: https://doi.org/10.1007/978-3-540-25931-2_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21268-3

  • Online ISBN: 978-3-540-25931-2

  • eBook Packages: Springer Book Archive

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