Enhancing Existential Graphs: Peirce's Late Improvements

Charles Peirce developed Existential Graphs as a diagrammatic syntax for representing and reasoning about propositions, with three parts: Alpha for propositional logic, Beta for first-order predicate logic, and Gamma for aspects of modal logic, second-order logic, and metalanguage. He made several a...

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Bibliographic Details
Published inTransactions of the Charles S. Peirce Society Vol. 60; no. 2; pp. 187 - 204
Main Author Schmidt, Jon Alan
Format Journal Article
LanguageEnglish
Published Indiana University Press 22.03.2024
Subjects
Analysis
Criticism and interpretation
Existentialism
Graphic methods
Peirce, Charles Sanders
Philosophers
United States
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Summary:Charles Peirce developed Existential Graphs as a diagrammatic syntax for representing and reasoning about propositions, with three parts: Alpha for propositional logic, Beta for first-order predicate logic, and Gamma for aspects of modal logic, second-order logic, and metalanguage. He made several adjustments between 1909 and 1911 that merit further consideration: using heavy lines to denote possible states of things in which attached propositions would be true, drawing a red line just inside the edge of a page and writing postulates in the resulting margin, shading oddly enclosed areas instead of drawing thin lines as their boundaries, and using multiple sheets of paper to represent different subjects within the overall universe of discourse. These modifications can be combined to constitute a plausible candidate for Delta, a fourth part that Peirce intended to add but never spelled out. It implements modern formal systems of modal propositional logic in accordance with a version of possible worlds semantics in which the laws for the actual state of things are facts in every possible state of things.
ISSN:0009-1774
1558-9587
1558-9587
DOI:10.2979/csp.00026