Category Archives: Category Theory

Precursors Of Category Theory • Discussion 3

Take your place on The Great Mandala As it moves through your brief moment of time. Win or lose now you must choose now And if you lose you’re only losing your life. Peter Yarrow Re: Ontolog Forum • Alex … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 1 Comment

Precursors Of Category Theory • Discussion 2

Re: Ontolog Forum • Alex Shkotin AS: Looking at “categories, or types” in Precursors Of Category Theory • Hilbert and Ackermann what do you think of to say “Precursors Of Type Theory” as Category Theory is a math discipline?   … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 1 Comment

Survey of Precursors Of Category Theory • 2

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, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Precursors Of Category Theory • Discussion 1

Re: FB | Medieval Logic • EB • JA • JA • EB • JA • EB • JA • JA • EB JA:  In the logic of Aristotle categories are adjuncts to reasoning designed to resolve ambiguities and thus … Continue reading

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 1 Comment

Differential Logic, Dynamic Systems, Tangent Functors • Discussion 9

Re: FB | Systems Sciences • Kenneth Lloyd Dear Kenneth, Mulling over recent discussions put me in a pensive frame of mind and my thoughts led me back to my first encounter with category theory.  I came across the term … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Differential Logic, Dynamic Systems, Tangent Functors • Comment 1

Seeing as how quasi-neural models and the recurring issues of logical-symbolic vs. quantitative-connectionist paradigms have come round again, as they do every dozen or twenty years or so, I thought I might refer again to work I started initially in that … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Category Theory • Comment 1

I’m deep in the middle of upgrading my intro to sign relations and I am determined to stick to it this time but there will be a phase when it’s critical to bring category theory to bear on the development.  … Continue reading

Posted in Abstraction, C.S. Peirce, Category Theory, Differential Logic, Graph Theory, Group Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Categories, Research Technology, Scientific Method, Semiotics, Set Theory, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , | Leave a comment

Peirce’s Categories • 21

Re: Peirce List • Robert Marty Re: Peirce List • Robert Marty Dear Robert, Let’s go back to a point where paths diverged in the yarrow wood and a lot of synchronicity was lost … Variant understandings of words like … 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 , , , , , , , , , , , , , , , | 1 Comment

Differential Logic • Discussion 3

Re: R.J. Lipton • P<NP Instead of boolean circuit complexity I would look at logical graph complexity, where those logical graphs are constructed from minimal negation operators. Physics once had a frame problem (complexity of dynamic updating) long before AI … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Relation Theory • Discussion 1

Re: Cybernetics • Arthur Phillips Responding to what I’ll abductively interpret as a plea for relevance from the cybernetic galley, let me give a quick review of where we are in this many-oared expedition. Our reading of Ashby (see Survey … 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 , , , , , , , , , , , , , , , , , , , , , , | Leave a comment