Tag Archives: Mathematics

Animated Logical Graphs • 54

Re: Peter Cameron • Doing Research Re: Gil Kalai • Chomskian Linguistics Oneirocritical Interlude Speaking of dreams, the night before last I had a dream where I was listening to a lecturer and something he said made me think of … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Charles Sanders Peirce, George Spencer Brown, and Me • 13

Re: Laws of Form • Dirk Baecker DB: I guess you know Fernando Zalamea’s work on Peirce.  He thinks that all of GSB’s important ideas are already in Peirce’s Existential Graphs. I think he may be right, but then there … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Charles Sanders Peirce, George Spencer Brown, and Me • 12

Re: Laws of Form • Dirk Baecker DB: Thanks to James Bowery for inviting me to this group.  Maybe it is not exactly what I am looking for, since I am interested in a sociological reading of LoF.  Which means … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Animated Logical Graphs • 53

Much of the work I do on the C.S. Peirce/Spencer Brown approach to “mathematical hypostases underlying logic” now goes under the heading of Animated Logical Graphs.  There’s a Survey of related resources I update from time to time at 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 , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Charles Sanders Peirce, George Spencer Brown, and Me • 11

There’s a new Laws of Form group in town.  James Bowery et al. have just revived the earlier group on a new platform and everything looks pretty handy so far.  There’s an honest-to-goodness 60s vibe about it for me since … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Sign Relations, Triadic Relations, Relation Theory • Discussion 5

Re: Cybernetics • Cliff Joslyn Re: Sign Relations, Triadic Relations, Relation Theory • Discussion (3) (4) Dear Cliff, I’m still collecting my wits from the mind-numbing events of the past two weeks so I’ll copy your last remarks here and … 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 , , , , , , , , , , , , , , , | Leave a comment

Riffs and Rotes • Happy New Year 2021

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

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 , , , , , , , , , , , , , , , | 2 Comments

Sign Relations, Triadic Relations, Relation Theory • Discussion 3

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 , , , , , , , , , , , , , , , | 3 Comments

Survey of Inquiry Driven Systems • 3

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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment