Category Archives: Category Theory

Peirce’s 1870 “Logic Of Relatives” • Discussion 1

Posted on September 30, 2019 by Jon Awbrey

Re: Ontolog Forum • John Bottoms Re: History View Blog • A Yukaghir Girl Writes A Love Letter Re: Peirce’s 1870 “Logic Of Relatives” • Proto-Graphical Syntax John Bottoms, writing in the Ontolog Forum, compared the graphic I drew for … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Peirce’s 1870 “Logic of Relatives” • Overview

Posted on September 24, 2019 by Jon Awbrey

My long ago encounter with Peirce’s 1870 paper, “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, was one of the events precipitating my return from the hazier … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 19 Comments

Differential Logic and Dynamic Systems • Overview

Posted on September 10, 2019 by Jon Awbrey

In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade‑off between dynamic paradigms and symbolic paradigms.  Dynamic models take their cue from physics, using … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Semiotics, Semiosis, Sign Relations • Discussion 1

Posted on April 29, 2019 by Jon Awbrey

Re: Semiotic Triangle • John Corcoran Concepts for Peirce are mental symbols, so they fall under the general designation of signs.  For triadic sign relations in general, then, we are dealing with a triadic relation among (1) objects of signs, … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 15 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 8

Posted on December 24, 2018 by Jon Awbrey

Re: Systems Science • Len Troncale It’s been a while since I started this thread, with many sidetrips and tangents, so let me go back to the top and expand on the motivations I expressed there, addressing a few issues … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 7

Posted on December 20, 2018 by Jon Awbrey

Re: Systems Science • JS Let’s stand back from the picture and see how the dimensions of syntax, semantics, and pragmatics look from a pragmatic semiotic or sign relational perspective. is an object domain, a set of elements under view … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 6

Posted on December 19, 2018 by Jon Awbrey

Re: Systems Science • JS A few of my readers are racing well ahead of me, exploring a range of different roads, but I’ll be making a dogged effort to stick to my math-bio-graphical narrative this time around, and try … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 5

Posted on December 18, 2018 by Jon Awbrey

Re: Systems Science • JS Yes, all these strands are strongly entangled. I had already spent a full decade wrestling with the works of Charles Sanders Peirce and George Spencer Brown before my need to figure out what they were … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 4

Posted on December 17, 2018 by Jon Awbrey

Re: Systems Science • LT To clarify my previous remark about General Systems Theory, I wasn’t trying to define a whole field but merely to describe my experience in forums like these, where it took me a while to realize … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 3

Posted on December 12, 2018 by Jon Awbrey

Re: Systems Science • (1) • (2) • (3) Various discussions in various places bring back to mind this thread from early this fall, prompting me to make a try at continuing it.  Here’s a series of blog posts where … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments