Category Archives: Category Theory

Semiotics, Semiosis, Sign Relations • Comment 1

Posted on August 9, 2021 by Jon Awbrey

I opened a topic on Sign Relations in the Logic stream of Category Theory Zulipchat to work on Peirce’s theory of triadic sign relations in a category-theoretic framework. I had been reading Peirce for a decade or more before I found … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 8 Comments

Relations & Their Relatives • Comment 3

Posted on August 6, 2021 by Jon Awbrey

Here’s a couple of selections from Peirce’s 1870 Logic of Relatives bearing on the proper use of individuals in mathematics, and thus on the choice between nominal thinking and real thinking. 😸 Mathematical Demonstration & the Doctrine of Individuals • … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 9 Comments

Relations & Their Relatives • Comment 2

Posted on August 5, 2021 by Jon Awbrey

Before I forget how I got myself into this particular briar patch — I mean the immediate occasion, not the long ago straying from the beaten path — it was largely in discussions with Henry Story where he speaks of … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 9 Comments

Relations & Their Relatives • Comment 1

Posted on August 2, 2021 by Jon Awbrey

I opened a topic on Relation Theory in the Logic stream of Category Theory Zulipchat to discuss the logic of relative terms and the mathematics of relations as they develop from Peirce’s first breakthroughs (1865–1870). As I have mentioned on … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 9 Comments

Notes On Categories • 2

Posted on July 31, 2021 by Jon Awbrey

Re: Category Theory • Joe Moeller JM: In category theory, we have this perspective that we should focus attention on maps, on the relationships between objects, rather than on the objects themselves.  What’s your favorite examples of people giving a … Continue reading →

Posted in Abstraction, Category Theory, Computing, Graph Theory, Logic, Mathematics, Relation Theory, Type Theory | Tagged , , , , , , , | Leave a comment

Differential Logic • 11

Posted on July 24, 2021 by Jon Awbrey

Transforms Expanded over Ordinary and Differential Variables As promised in Episode 10, in the next several posts we’ll extend our scope to the full set of boolean functions on two variables and examine how the differential operators and act on that … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Differential Logic • Discussion 14

Posted on July 23, 2021 by Jon Awbrey

Re: Differential Logic • Discussion • (12) (13) Re: FB | Peirce Society • Χριστο Φόρος Another bit of work I did toward a Psych M.A. was applying my Theme One program to a real-live dataset on family dynamics.  A … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Differential Logic • Discussion 13

Posted on July 22, 2021 by Jon Awbrey

Re: Differential Logic • Discussion 12 Re: FB | Peirce Society • Χριστο Φόρος Χριστο Φόρος asked whether the difference between qualitative and quantitative information was really all that much of a problem, especially in view of mixed datasets.  As I … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Differential Logic • Discussion 12

Posted on July 21, 2021 by Jon Awbrey

Re: Category Theory • John Baez (1) (2) JB: One thing I’m interested in is functorially relating purely qualitative models to quantitative ones, or mixed quantitative-qualitative models where you have some numerical information of the sort you describe, but not … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Differential Logic • Discussion 11

Posted on July 16, 2021 by Jon Awbrey

Re: Differential Logic • Discussion 9 Let’s look more closely at the “functor” from to and the connection it makes between real and boolean hierarchies of types.  There’s a detailed discussion of this analogy in the article and section linked … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments