Category Archives: Type Theory

Relation Theory • Discussion 5

Posted on April 22, 2023 by Jon Awbrey

Re: Survey of Relation Theory Re: Ontolog Forum • Ravi Sharma RS: Is there also an attempt at integrating these relation concepts? Like a meta‑model of relations? Dear Ravi, I haven’t run across the concept of a meta‑model before so … 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, Triadic Relations, Type Theory, Visualization | Tagged 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, Triadic Relations, Type Theory, Visualization | 1 Comment

Relation Theory • Discussion 4

Posted on April 19, 2023 by Jon Awbrey

Re: Survey of Relation Theory Re: Ontolog Forum • Ravi Sharma RS: Is there also an attempt at integrating these relation concepts? Like a meta‑model of relations? Dear Ravi, Thanks for the question. I believe I’d say yes to the … Continue reading →

Survey of Precursors Of Category Theory • 3

Posted on April 3, 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 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 | Leave a comment

Survey of Relation Theory • 6

Posted on April 1, 2023 by Jon Awbrey

In this Survey of blog and wiki posts on 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 of … 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 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 | 2 Comments

Survey of Relation Theory • 5

Posted on November 8, 2021 by Jon Awbrey

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 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 | Leave a comment

Relation Theory • Discussion 3

Posted on November 3, 2021 by Jon Awbrey

Re: Relation Theory • (1) • (2) • (3) • (4) • (5) Re: Laws of Form • James Bowery JB: Thanks for that very rigorous definition of “relation theory”. Its “trick” of including the name of the -relation in … Continue reading →

Relation Theory • Discussion 2

Posted on November 1, 2021 by Jon Awbrey

Re: Relation Theory • (1) • (2) • (3) • (4) Re: FB | Charles S. Peirce Society • Joseph Harry JH: These are iconic representations dealing with logical symbolic relations, and so of course are semiotic in Peirce’s sense, … Continue reading →

Notes On Categories • 2

Posted on July 31, 2021 by Jon Awbrey

Re: Category Theory • Joe Moeller JM: In category theory, we have this perspective that we should focus attention on maps, on the relationships between objects, rather than on the objects themselves. What’s your favorite examples of people giving a … Continue reading →

Posted in Abstraction, Category Theory, Computing, Graph Theory, Logic, Mathematics, Relation Theory, Type Theory | Tagged Abstraction, Category Theory, Computing, Graph Theory, Logic, Mathematics, Relation Theory, Type Theory | Leave a comment

C.S. Peirce and Category Theory • 8

Posted on July 2, 2021 by Jon Awbrey

Re: Category Theory • Henry Story Re: Laws of Form • Lyle Anderson LA: As I am trying to get “frame sync” on this discussion, as the satellite communications people say, I am taking clues from the introduction to the … Continue reading →

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Leave a comment

C.S. Peirce and Category Theory • 7

Posted on July 1, 2021 by Jon Awbrey

Re: Category Theory • Henry Story HS: I’d be very interested in the comments of people who know about Peirce on the two chapters in the book Diagrammatic Immanence I linked to above on “3. Peirce” and “4. Diagrams of Variation : … Continue reading →

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