Abstract
The aim of this paper is to reformulate the transformation rules presented by Peirce in the Beta part of Existential Graphs, in a different way from the rules systemized by Roberts and Shin. Existential Graphs provides an iconic system of logic. In other words, it visualizes logical reasonings by using diagrammatic representations. Specifically, a graph represents a situation occurring in a certain universe of discourse. In addition, Peirce introduced a line of identity and a cut. The former is a thick line that affirms the identity of two particulars signified by its two ends. The latter is a closed curve that is drawn with a thin line. By enclosing a graph entirely by a cut, the content represented by the graph is denied. Peirce forbid a line of identity from crossing a cut, yet both Roberts and Shin presumed that a line of identity can cross a cut. Hence, this paper eliminates that presumption completely and shows an alternative reformulation of the transformation rules in the Beta part of Existential Graphs.
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References
Burch, R.W.: The fine ftructure of Peircean ligatures and lines of identity. Semiotica 186, 21–68 (2011)
Charles Sanders Peirce: Collected Papers of Charles Sanders Peirce. The Belknap Press of Harvard University Press, Cambridge, MA (1974)
Roberts, D.D.: The Existential Graphs of Charles S. Peirce. Mouton, The Hague (1973)
Shin, S.-J.: The Iconic Logic of Peirce’s Graphs. A Bradford Book, Cambridge (2003)
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Atarashi, S. (2020). An Alternative Reformulation of the Transformation Rules in the Beta Part of Peirce’s Existential Graphs. In: Pietarinen, AV., Chapman, P., Bosveld-de Smet, L., Giardino, V., Corter, J., Linker, S. (eds) Diagrammatic Representation and Inference. Diagrams 2020. Lecture Notes in Computer Science(), vol 12169. Springer, Cham. https://doi.org/10.1007/978-3-030-54249-8_15
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DOI: https://doi.org/10.1007/978-3-030-54249-8_15
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