Monthly Archives: July 2020

Differential Analytic Turing Automata • Discussion 2

Re: Scott Aaronson • The Busy Beaver Frontier Dear Scott, This discussion inspired me to go back and look at some of the work I did in the late 80s when I was trying to understand Cook’s Theorem.  One of … Continue reading

Posted in Algorithms, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Analytic Turing Automata, Differential Logic, Logic, Logical Graphs, Peirce, Propositional Calculus, Turing Machines | Tagged , , , , , , , , , , , | Leave a comment

Riffs and Rotes • 5

Re: Scott Aaronson • The Busy Beaver Frontier All my favorite integer sequences, some very fast growing, spring from the “lambda point” where graph theory, logic, and number theory meet.  My fascination with them goes back to a time when … Continue reading

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | 2 Comments

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

Sign Relations • Discussion 10

Anthesis • Definition • Signs and Inquiry • Examples Dyadic Aspects • Denotation • Connotation • Ennotation Semiotic Equivalence Relations • (1) • (2) Re: Cybernetics • Klaus Krippendorff • Bernard Scott Re: Ontolog • Mihai Nadin • John Sowa … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relations • Discussion 9

Re: Sign Relations • Ennotation Re: Peirce List • Helmut Raulien Dear Helmut, Thanks for your comments.  They prompt me to say a little more about the mathematical character of the sign relational models I’m using. Peirce without mathematics is … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relations • Semiotic Equivalence Relations 2

A few items of notation are useful in discussing equivalence relations in general and semiotic equivalence relations in particular. In general, if is an equivalence relation on a set then every element of belongs to a unique equivalence class under … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 1 Comment

Sign Relations • Discussion 8

Re: Sign Relations • Ennotation Re: Peirce List • Helmut Raulien Dear Helmut, The important thing now is to extend our perspective beyond one sign at a time and one object, sign, interpretant at a time to comprehending a sign … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 1 Comment

Sign Relations • Semiotic Equivalence Relations 1

A semiotic equivalence relation (SER) is a special type of equivalence relation arising in the analysis of sign relations.  Generally speaking, any equivalence relation induces a partition of the underlying set of elements, known as the domain or space of the … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 1 Comment