An Alternative Reformulation of the Transformation Rules in the Beta Part of Peirce’s Existential Graphs

Shigeyuki Atarashi


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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