Category Archives: Relation Theory

Inquiry Into Inquiry • Discussion 8

Posted on August 18, 2023 by Jon Awbrey

Re: Inquiry Into Inquiry • Discussion 7 Re: Academia.edu • Milo Gardner MG: Peirce sensed that bivalent syntax was superceded by trivalent syntax, but never resolved that nagging question. The main thing is not a question of syntax but a … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Compositionality, Formal Languages, Inference, Information, Information Fusion, Initiative, Inquiry, Logic, Relation Theory, Semiotics, Triadic Relation Irreducibility, Visualization | Tagged , , , , , , , , , , , , , , | 5 Comments

Inquiry Into Inquiry • Discussion 7

Posted on August 17, 2023 by Jon Awbrey

Dan Everett has prompted a number of discussions on Facebook recently which touch on core issues in Peirce’s thought — but threads ravel on and fray so quickly in that medium one rarely gets a chance to fill out the … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Compositionality, Formal Languages, Inference, Information, Information Fusion, Initiative, Inquiry, Logic, Relation Theory, Semiotics, Triadic Relation Irreducibility, Visualization | Tagged , , , , , , , , , , , , , , | 5 Comments

Survey of Precursors Of Category Theory • 4

Posted on August 1, 2023 by Jon Awbrey

A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of resources on … Continue reading →

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Relation Theory • 7

Posted on July 26, 2023 by Jon Awbrey

In the present Survey of blog and wiki resources for Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set‑theoretic constructions, many … Continue reading →

Posted in Algebra, Algebra of Logic, C.S. Peirce, Category Theory, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Graph Theory, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Pragmatic Semiotic Information • 7

Posted on July 23, 2023 by Jon Awbrey

This is a Survey of blog and wiki posts on a theory of information which grows out of pragmatic semiotic ideas.  All my projects are exploratory in character but this line of inquiry is more open‑ended than most.  The question … Continue reading →

Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Systems of Interpretation • 9

Posted on June 17, 2023 by Jon Awbrey

Re: Peirce List • Jerry Chandler It is above all important to understand that Peirce’s concept of a sign relation is defined at a higher order of abstraction than any notion of causal or temporal order. A sign relation is … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 6 Comments

Systems of Interpretation • 8

Posted on June 16, 2023 by Jon Awbrey

Re: Peirce List • Kirsti Määttänen One of the chief advantages of Peirce’s systems of logical graphs, entitative and existential, is the way they escape the bounds of 1‑dimensional syntax and thus make it clear that many constraints of order imposed … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Systems of Interpretation • 7

Posted on June 15, 2023 by Jon Awbrey

Re: Peirce List • Gary Fuhrman Peirce’s existential graphs are a general calculus for expressing the same subject matter as his logic of relative terms and thus they serve to represent the structures of many‑place relations.  Cast at that level … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Systems of Interpretation • 6

Posted on June 14, 2023 by Jon Awbrey

Re: Peirce List • Jon Awbrey • John Collier JA: Questions about the meaning of the “central hub” in the “three‑spoked” picture of an elementary sign relation have often come up.  The central “spot”, as Peirce called it in his … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Systems of Interpretation • Discussion 1

Posted on June 12, 2023 by Jon Awbrey

Re: FB | Systems Sciences • Esteban Trev ET: What is the difference between sign and symbol? In Peirce’s usage, “sign” is the generic term, covering all species or types of signs.  Signs are “symbolic” to the extent they mean … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments