Peirce's tutorial on existential graphs
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John F. Sowa
Abstract
In his formal papers on existential graphs (EGs), Peirce tended to obscure the simplicity of EGs with distracting digressions. In MS 514, however, he presented his simplest introduction to the EG syntax, semantics, and rules of inference. This article reproduces Peirce's original words and diagrams with further commentary, explanations, and examples. Unlike the syntax-based approach of most current textbooks, Peirce's method addresses the semantic issues of logic in a way that can be transferred to any notation. The concluding section shows that his rules of inference can clarify the foundations of proof theory and relate diverse methods, such as resolution and natural deduction. To relate EGs to other notations for logic, this article uses the Existential Graph Interchange Format (EGIF), which is a subset of the CGIF dialect of Common Logic. EGIF is a linear notation that can be mapped to and from the Alpha, Beta, and Gamma variants of EGs. It can also be translated to or from other formalisms, algebraic or geometrical.
© 2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
Articles in the same Issue
- Introduction: Diagrammatical reasoning and Peircean logic representations
- Images, diagrams, and narratives: Charles S. Peirce's epistemological theory of mental diagrams
- The fine structure of Peircean ligatures and lines of identity
- When is a bunch of marks on paper a diagram? Diagrams as homomorphic representations
- Ligatures in Peirce's existential graphs
- Iconic thought and diagrammatical scripture: Peirce and the Leibnizian tradition
- Linear notation for existential graphs
- Peircean Algebraic Logic and Peirce's Reduction Thesis
- Remarks on the iconicity and interpretation of existential graphs
- Cognitive conditions of diagrammatic reasoning
- External diagrammatization and iconic brain co-evolution
- Computers as medium for mathematical writing
- Peircean diagrams of time
- Space, complementarity, and “diagrammatic reasoning”
- Diagrams, iconicity, and abductive discovery
- Moving pictures of thought II: Graphs, games, and pragmaticism's proof
- Peirce's alpha graphs and propositional languages
- Peirce's tutorial on existential graphs
- On operational and optimal iconicity in Peirce's diagrammatology
- Existential graphs and proofs of pragmaticism
Articles in the same Issue
- Introduction: Diagrammatical reasoning and Peircean logic representations
- Images, diagrams, and narratives: Charles S. Peirce's epistemological theory of mental diagrams
- The fine structure of Peircean ligatures and lines of identity
- When is a bunch of marks on paper a diagram? Diagrams as homomorphic representations
- Ligatures in Peirce's existential graphs
- Iconic thought and diagrammatical scripture: Peirce and the Leibnizian tradition
- Linear notation for existential graphs
- Peircean Algebraic Logic and Peirce's Reduction Thesis
- Remarks on the iconicity and interpretation of existential graphs
- Cognitive conditions of diagrammatic reasoning
- External diagrammatization and iconic brain co-evolution
- Computers as medium for mathematical writing
- Peircean diagrams of time
- Space, complementarity, and “diagrammatic reasoning”
- Diagrams, iconicity, and abductive discovery
- Moving pictures of thought II: Graphs, games, and pragmaticism's proof
- Peirce's alpha graphs and propositional languages
- Peirce's tutorial on existential graphs
- On operational and optimal iconicity in Peirce's diagrammatology
- Existential graphs and proofs of pragmaticism
