Tag Archives: Mathematics

Riffs and Rotes • Happy New Year 2021

Posted on January 3, 2021 by Jon Awbrey

Apart from their abstract beauty, Riffs and Rotes are structures I discovered while playing around with Gödel numberings of graphs and digraphs.  To my way of thinking they bear a deep connection to the mathematical infrastructure of logic.  Here are … Continue reading →

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | Leave a comment

Sign Relations, Triadic Relations, Relation Theory • Discussion 4

Posted on December 31, 2020 by Jon Awbrey

Re: Previous Post Re: Cybernetics • Cliff Joslyn Dear Cliff, Many thanks for your thoughtful reply.  I copied a transcript to my blog to take up first thing next year.  Here’s hoping we all have a better one! Regards, Jon CJ: … Continue reading →

Posted in C.S. Peirce, Icon Index Symbol, Information, Inquiry Driven Systems, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity, Visualization | Tagged , , , , , , , , , , , , , , , | 9 Comments

Sign Relations, Triadic Relations, Relation Theory • Discussion 3

Posted on December 29, 2020 by Jon Awbrey

Re: Peirce List • Helmut Raulien HR: As Peircean semiotics is a three-valued logic, I think it bears relevance for the discussion about multiple-valued logic. Dear Helmut, The distinction between “k-adic” (involving a span of k dimensions) and “k-tomic” (involving … Continue reading →

Posted in C.S. Peirce, Icon Index Symbol, Information, Inquiry Driven Systems, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity, Visualization | Tagged , , , , , , , , , , , , , , , | 10 Comments

Survey of Inquiry Driven Systems • 3

Posted on December 27, 2020 by Jon Awbrey

This is a Survey of blog and wiki posts on Inquiry Driven Systems, material I plan to refine toward a more compact and systematic treatment of the subject. An inquiry driven system is a system having among its state variables … Continue reading →

Posted in Abduction, Action, Adaptive Systems, Aristotle, Artificial Intelligence, Automated Research Tools, Change, Cognitive Science, Communication, Cybernetics, Deduction, Descartes, Dewey, Discovery, Doubt, Education, Educational Systems Design, Educational Technology, Fixation of Belief, Induction, Information, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretation, Invention, Kant, Knowledge, Learning, Learning Theory, Logic, Logic of Science, Mathematics, Mental Models, Peirce, Pragmatic Maxim, Pragmatism, Process Thinking, Scientific Inquiry, Semiotics, Sign Relations, Surveys, Teaching, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments

Animated Logical Graphs • 52

Posted on December 21, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Future Of Mathematics? • Is The End Near? Re: Peirce List • Jon Alan Schmidt Peirce’s explorations in logic and the theory of signs opened several directions of generalization from logics of complete information … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Animated Logical Graphs • 51

Posted on December 20, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Future Of Mathematics? • Is The End Near? Synchronicity being what it is, a long-running discussion on the Peirce List just gave me a handy bridge to a topic I’ve been meaning to take … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 2

Posted on December 16, 2020 by Jon Awbrey

This is a Survey of blog and wiki posts on three elementary forms of inference, as recognized by a logical tradition extending from Aristotle through Charles S. Peirce.  Particular attention is paid to the way these inferential rudiments combine to … Continue reading →

Posted in Abduction, Aristotle, C.S. Peirce, Deduction, Dewey, Discovery, Doubt, Fixation of Belief, Functional Logic, Icon Index Symbol, Induction, Inference, Information, Inquiry, Invention, Logic, Logic of Science, Mathematics, Morphism, Paradigmata, Paradigms, Pattern Recognition, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Scientific Inquiry, Scientific Method, Semiotics, Sign Relations, Surveys, Syllogism, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Animated Logical Graphs • 50

Posted on December 5, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) (46) (47) (48) (49) In the last of our six ways of looking at the Peirce duality between entitative and existential interpretations, we consider … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Animated Logical Graphs • 49

Posted on December 3, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) (46) (47) (48) Dualities are symmetries of order two and symmetries bear on complexity by reducing its measure in proportion to their order.  The … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Animated Logical Graphs • 48

Posted on November 30, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) (46) (47) A more graphic picture of Peirce duality is given by the next Table, which shows how logical graphs map to venn diagrams … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments