Category Archives: Mathematics

Theme One • A Program Of Inquiry 8

Posted on March 10, 2018 by Jon Awbrey

Coding Logical Graphs My earliest experiments coding logical graphs as dynamic “pointer” data structures taught me that conceptual and computational efficiencies of a critical sort could be achieved by generalizing their abstract graphs from trees to the variety graph theorists … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Theme One • A Program Of Inquiry 7

Posted on March 3, 2018 by Jon Awbrey

Re: Peirce List • (1) • (2) Discussion arose in the Laws Of Form Group about computational explorations of George Spencer Brown’s calculus of indications. Readers of Peirce are generally aware Spencer Brown revived certain aspects of Peirce’s logical graphs, focusing on … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Theme One • A Program Of Inquiry 6

Posted on February 28, 2018 by Jon Awbrey

Programs are algorithms operating on data structures (Niklaus Wirth).  How do we turn abstract graphs like those used by Charles S. Peirce and G. Spencer Brown into concrete data structures algorithms can manipulate?  There are many ways to do this, but one … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Survey of Theme One Program • 2

Posted on February 25, 2018 by Jon Awbrey

This is a Survey of blog and wiki posts relating to the Theme One Program I worked on all through the 1980s.  The aim was to develop fundamental algorithms and data structures to support an integrated learning and reasoning interface, … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 20 Comments

Sign Relations • Comment 12

Posted on February 17, 2018 by Jon Awbrey

Re: Ontolog Discussion • HP In the Peirce universe “the role that human institutions play in establishing grounding and associated frames of reference and standards” (Hans Polzer) is articulated by reference to “communities of inquiry” and “communities of interpretation”.  Invoking … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic of Relatives, Peirce, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | 16 Comments

Sign Relations • Comment 11

Posted on February 14, 2018 by Jon Awbrey

Re: Peirce List • Jon Alan Schmidt When you ask a question about what something is, you are asking a question about its ontology.  But signhood is not a matter of ontology, it is a form of relation. Re: Peirce … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic of Relatives, Peirce, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | 15 Comments

Sign Relations • Comment 10

Posted on February 9, 2018 by Jon Awbrey

Re: Peirce List • John Sowa Three-Headed Dogs and Triadic Sign Relations Peirce’s “Sop to Cerberus” got tossed about quite a bit in our discussions across the Web this millennium.  Here’s a record of one occasion from the days when … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic of Relatives, Peirce, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | 16 Comments

{ Information = Comprehension × Extension } • Discussion 7

Posted on February 2, 2018 by Jon Awbrey

Re: Joselle DiNunzio Kehoe • Information and Questions of Consciousness C.S. Peirce put forth the idea that what he called “the laws of information” were key to solving “the puzzle of the validity of scientific inference” and thus to understanding … Continue reading →

Posted in Abduction, C.S. Peirce, Comprehension, Consciousness, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Peirce, Peirce's Categories, Scientific Method, Semiotic Information, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Animated Logical Graphs • 12

Posted on January 31, 2018 by Jon Awbrey

Re: Facebook Discussion • Meredith Bricken Mills I’ve always been fond of picture proofs — it was one of the things that drew me to graph theory, topology, and the logical graphs of C.S. Peirce and Spencer Brown in the first place.  … 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

Animated Logical Graphs • 11

Posted on January 30, 2018 by Jon Awbrey

Re: Richard Coyne • Inside Out Logic Venn diagrams make for very iconic representations of their universes of discourse.  That is one of the main sources of their intuitive utility and also the main source of their logical limitations — … 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