The fine structure of Peircean ligatures and lines of identity
Abstract
Lines of identity in Peirce's existential graphs (beta) are logically complex structures that comprise both identity and existential quantification. Yet geometrically they are simple: linear continua that cannot have “furcations” or cross “cuts.” By contrast Peirce's “ligatures” are geometrically complex: they can both have furcations and cross cuts. Logically they involve not only identity and existential quantification but also negation. Moreover, Peirce makes clear that ligatures are composed of lines of identity by virtue of the fact that such lines can be “connected” with one another and can “abut upon” one another at a cut. This paper shows in logical detail how ligatures are composed and how they relate to identity, existential quantification, and negation. In so doing, it makes use of Peirce's non-standard account of the linear continuum, according to which, when a linear continuum is separated into two parts, (1) the parts are symmetric rather than (as the standard account of Dedekind holds) asymmetric, and (2) the one point at which separation occurs actually becomes two points, each of which is a Doppelgänger of the other.
© 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
