Category Archives: Combinatorics

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

Relations & Their Relatives • Discussion 10

Posted on July 2, 2015 by Jon Awbrey

Re: Peirce List Discussion • Helmut Raulien The facts about relational reducibility are relatively easy to understand and I included links to relevant discussions in my earlier survey of relation theory. The following article discusses relational reducibility and irreducibility in … Continue reading →

Posted in C.S. Peirce, Combinatorics, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • Discussion 9

Posted on July 2, 2015 by Jon Awbrey

Re: Peirce List Discussion • Jeffrey Brian Downard In viewing the structures of relation spaces, even the smallest dyadic cases we’ve been exploring so far, no one need feel nonplussed at the lack of obviousness in this domain.  Anyone who … Continue reading →

Posted in C.S. Peirce, Combinatorics, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • Discussion 8

Posted on June 30, 2015 by Jon Awbrey

Re: Peirce List Discussion • Jeffrey Brian Downard In discussing the “combinatorial explosion” of dyadic relations that takes off in passing from a universe of two elements to a universe of three elements, I made the following observation: Looking back … Continue reading →

Posted in Combinatorics, Graph Theory, Group Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 13 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 … Continue reading →

Posted in Algebra, Animata, 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, Planted Plane Trees, 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

“What we’ve got here is (a) failure to communicate” • 6

Posted on November 15, 2013 by Jon Awbrey

Excerpt from Warren S. McCulloch, “What Is a Number, that a Man May Know It, and a Man, that He May Know a Number?” (1960) Please remember that we are not now concerned with the physics and chemistry, the anatomy … Continue reading →

Posted in Abduction, Amphecks, Aristotle, Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Combinatorics, Deduction, Duns Scotus, Induction, Leibniz, Logic, Logic of Relatives, Mathematics, Neural Models, Ockham, Peirce, Propositional Logic, Psychons, Relation Theory, Sources, Triadic Relations, Warren S. McCulloch, William James | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment