Category Archives: Category Theory

Peirce’s Categories • 18

Posted on May 12, 2020 by Jon Awbrey

Re: Peirce’s Categories • 15 In These Uncertain Times, as people keep saying, it’s become even harder to concentrate than usual and I keep losing track of tricky points coming up in discussion which cry out for further discussion but … Continue reading →

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 6 Comments

Peirce’s Categories • 17

Posted on May 7, 2020 by Jon Awbrey

I’ve been too immersed in the Peirce List discussion of Robert Marty’s “Podium” paper to write much here — before I lose track of what I’ve been thinking the last several days I’ll need to ravel up my off-the-cuff remarks … Continue reading →

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 6 Comments

Peirce’s Categories • 16

Posted on May 4, 2020 by Jon Awbrey

Re: Peirce’s Categories • 15 Re: Robert Marty • The Podium of the Universal Categories of C.S. Peirce A feature of particular interest to me in Robert Marty’s paper is the resonance he finds between category theory, as it’s known in … Continue reading →

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Mathematics, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Universals | Tagged , , , , , , , , , , , , | 9 Comments

Peirce’s Categories • 15

Posted on May 1, 2020 by Jon Awbrey

Re: Peirce List • Robert Marty RM: I submit for your review this preprint which is awaiting publication: The Podium of the Universal Categories of C.S. Peirce Abstract This article organizes Peirce’s universal categories and their degenerate forms from their presupposition … Continue reading →

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 13 Comments

Differential Logic • 10

Posted on April 25, 2020 by Jon Awbrey

It’s been a while, so let’s review … Tables A1 and A2 showed two ways of organizing the sixteen boolean functions or propositional forms on two variables, as expressed in several notations.  For ease of reference, here are fresh copies … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Peirce’s Categories • 14

Posted on April 16, 2020 by Jon Awbrey

Re: Peirce List • Robert Marty RM: What do you think of the presuppositions between the levels? Do they make sense to you? At this point I have mostly questions, which would take further research to answer, not to mention … Continue reading →

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 7 Comments

Peirce’s Categories • 13

Posted on April 15, 2020 by Jon Awbrey

Re: Peirce List • Robert Marty With a few choice exceptions I have always found Peirce’s earlier writings on categories, relations, and semiotics to be more clear, exact, and fruitful in practice than his last attempts to explain himself without … Continue reading →

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 7 Comments

Differential Logic • Discussion 2

Posted on April 14, 2020 by Jon Awbrey

Re: Peirce List • Edwina Taborsky I first encountered Peirce’s Collected Papers sometime during my freshman year in one of the quieter corners of the Michigan State Math Library where I used to hide out to study and shortly after … 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

Semiotics, Semiosis, Sign Relations • Discussion 6

Posted on April 12, 2020 by Jon Awbrey

Re: Peirce List • Jon Alan Schmidt Just a note to record this citation by Jon Alan Schmidt of an important theme in Peirce.  It touches on one of those recurring questions which has come up time and again on the … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 12 Comments

Differential Logic • 9

Posted on April 11, 2020 by Jon Awbrey

Propositional Forms on Two Variables Table A2 arranges the propositional forms on two variables according to another plan, sorting propositions with similar shapes into seven subclasses.  Thereby hangs many a tale, to be told in time. Table A2.  Propositional Forms … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments