Category Archives: Relation Theory

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 →

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 , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Survey of Semiotics, Semiosis, Sign Relations • 4

Posted on April 5, 2023 by Jon Awbrey

C.S. Peirce defines logic as “formal semiotic”, using formal to highlight the place of logic as a normative science, over and above the descriptive study of signs and their role in wider fields of play.  Understanding logic as Peirce understands … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadicity | Tagged , , , , , , , , | 1 Comment

Survey of Pragmatic Semiotic Information • 6

Posted on April 4, 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

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 , , , , , , , , , , , , , , , , , , , , , , | 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 , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Cybernetics • 2

Posted on September 8, 2022 by Jon Awbrey

Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors? Plato • … 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

Sign Relations • Discussion 14

Posted on July 17, 2022 by Jon Awbrey

Re: Cybernetics • Cliff Joslyn (1) (2) (3) (4) Dear Cliff, A few examples of sign relations and triadic relations may serve to illustrate the problem of their demarcation. First, to clear up one point of notation, in writing there … Continue reading →

Posted in C.S. Peirce, Logic, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , | 6 Comments

Sign Relations • Discussion 13

Posted on July 17, 2022 by Jon Awbrey

Re: Cybernetics • Cliff Joslyn (1) (2) (3) Dear Cliff, Backing up a little — Whether a thing qualifies as a sign is not an ontological question, a matter of what it is in itself, but a pragmatic question, a … Continue reading →

Posted in C.S. Peirce, Logic, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , | 6 Comments

Sign Relations • Discussion 12

Posted on July 16, 2022 by Jon Awbrey

Re: Cybernetics • Cliff Joslyn CJ: For a given arbitrary triadic relation (let’s say that and are all finite, non‑empty sets), I’m interested to understand what additional axioms you’re saying are necessary and sufficient to make a sign relation.  I … Continue reading →

Posted in C.S. Peirce, Logic, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , | 6 Comments

Sign Relations • Discussion 11

Posted on July 13, 2022 by Jon Awbrey

Re: Cybernetics • Cliff Joslyn CJ: For a given arbitrary triadic relation (let’s say that and are all finite, non‑empty sets), I’m interested to understand what additional axioms you’re saying are necessary and sufficient to make a sign relation.  I … Continue reading →

Posted in C.S. Peirce, Logic, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , | 6 Comments