Tag Archives: Algebra

Relation Theory • Discussion 1

Posted on May 18, 2020 by Jon Awbrey

Re: Cybernetics • Arthur Phillips Responding to what I’ll abductively interpret as a plea for relevance from the cybernetic galley, let me give a quick review of where we are in this many-oared expedition. Our reading of Ashby (see Survey … 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 Relation Theory • 4

Posted on May 15, 2020 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 , , , , , , , , , , , , , , , , , , , , , , | 14 Comments

Riffs and Rotes • 4

Posted on September 16, 2019 by Jon Awbrey

Prompted by a recent discussion of prime numbers and complex dynamics on one of the Santa Fe Institute’s FaceBook pages, I posted a link to an old project of mine, going back to a time when I was first learning programming … Continue reading →

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | Leave a comment

Survey of Relation Theory • 3

Posted on January 17, 2017 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 , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Riffs and Rotes • 3

Posted on February 3, 2016 by Jon Awbrey

Re: R.J. Lipton • Failure Of Unique Factorization My favorite question in this realm is how much of the linear ordering of the natural numbers is purely combinatorial, where we eliminate all the structure that isn’t purely combinatorial via the … Continue reading →

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | Leave a comment

Survey of Relation Theory • 2

Posted on November 30, 2015 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 , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Survey of Relation Theory • 1

Posted on May 16, 2015 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 , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Forest Primeval → Riffs & Rotes

Posted on August 17, 2014 by Jon Awbrey

Re: Shifting Paradigms? • (1) • (2) • (3) • (4) • (5) • (6) Prompted by the discussion of Catalan numbers on the Foundations Of Math List, I dug up a few pieces of early correspondence and later discussions that … Continue reading →

Posted in Algebra, Arithmetic, C.S. Peirce, Catalan Numbers, Combinatorics, Forest Primeval, Foundations of Mathematics, Gödel Numbers, Graph Theory, Group Theory, H.W. Gould, Integer Sequences, Logic, Martin Gardner, Mathematics, Neil Sloane, Number Theory, Paradigmata, Peirce, Planted Plane Trees, Programming, Riffs and Rotes | Tagged , , , , , , , , , , , , , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 2

Posted on August 6, 2014 by Jon Awbrey

Re: Timothy Chow • Shifting Paradigms? 2014 Jul 31 I can’t remember when I first started playing with Gödel codings of graph-theoretic structures, which arose in logical and computational settings, but I remember being egged on in that direction by … Continue reading →

Posted in Algebra, Arithmetic, Combinatorics, Foundations of Mathematics, Graph Theory, Group Theory, Inquiry, Logic, Mathematics, Model Theory, Number Theory, Paradigms, Peirce, Programming, Proof Theory, Riffs and Rotes | Tagged , , , , , , , , , , , , , , , | Leave a comment

The Lambda Point • 1

Posted on August 1, 2013 by Jon Awbrey

A note on the title.  From long ago discussions with Harvey Davis, one of my math professors at Michigan State.  I remember telling him of my interest in the place where algebra, geometry, and logic meet, and he quipped, “Ah … Continue reading →

Posted in Algebra, Amphecks, Boolean Algebra, C.S. Peirce, Cactus Graphs, Geometry, Graph Theory, Lambda Point, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Peirce, Propositional Calculus, Topology | Tagged , , , , , , , , , , , , , , | Leave a comment