Tag Archives: Dyadic Relations

Relations & Their Relatives • Discussion 12

Posted on July 7, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien Definitions and examples for relation composition and the two most commonly arising types of relation reduction can be found in the following articles. Relation Composition Relation Reduction A previous post on this thread gives … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • Discussion 11

Posted on July 6, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien Cf: Relation Reduction • Examples of Projectively Reducible Relations I constructed the “Ann and Bob” examples of sign relations back at the beginning of my Systems Engineering program when I had to explain how … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 12 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

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

Survey of Precursors Of Category Theory • 1

Posted on May 15, 2015 by Jon Awbrey

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

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Sign Relations, Surveys, Triadic Relations, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.5

Posted on May 1, 2015 by Jon Awbrey

Suppose we add another individual to our initial universe of discourse, arriving at a three-point universe It might be thought that adding one more element to the universe of discourse would allow slightly more complicated relations to be compounded from … Continue reading →

Posted in Dyadic Relations, Graph Theory, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 10 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.4

Posted on April 24, 2015 by Jon Awbrey

Dyadic relations enjoy yet another form of graph-theoretic representation as labeled bipartite graphs or labeled bigraphs.  I’ll just call them bigraphs here, letting the labels be understood in this logical context. The figure below shows the bigraphs of the 16 … Continue reading →

Posted in Dyadic Relations, Graph Theory, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 9 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.3

Posted on April 23, 2015 by Jon Awbrey

Dyadic relations have graph-theoretic representations as labeled directed graphs with loops, also known as labeled pseudo-digraphs in some schools of graph theory.  I’ll just call them digraphs here, letting the labels and loops be understood in this logical context. The … Continue reading →

Posted in Dyadic Relations, Graph Theory, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 10 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2

Posted on April 19, 2015 by Jon Awbrey

Because it can sometimes be difficult to reconnect abstractions with their concrete instances, especially after the abstract types have become autonomous and taken on a life of their own, let us resort to a simple concrete case and examine the … Continue reading →

Posted in Dyadic Relations, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , | 11 Comments