Tag Archives: Mathematics

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

Animated Logical Graphs • 47

Posted on November 27, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) (46) A logical concept represented by a boolean variable has its extension, the cases it covers in a designated universe of discourse, and its … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Animated Logical Graphs • 46

Posted on November 15, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) Another way of looking at Peirce duality is given by the following Table, which shows how logical graphs denote boolean functions under entitative and … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 14 Comments

Animated Logical Graphs • 45

Posted on November 12, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) There’s a nice interplay between geometric and logical dualities in C.S. Peirce’s graphical systems of logic, rooted in his discovery of the amphecks and and flowering … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments

Survey of Pragmatic Semiotic Information • 5

Posted on November 1, 2020 by Jon Awbrey

This is a Survey of previous blog and wiki posts on the Semiotic Theory Of Information.  All my projects are exploratory in essence but this line of inquiry is more open-ended than most.  The question is: What is information and how … Continue reading →

Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Theme One • A Program Of Inquiry 20

Posted on October 24, 2020 by Jon Awbrey

Re: Richard J. Lipton • Vaccines Are Not Developing Back in the day when I was making The Big Bucks (inflation-adjusted dollars) consulting on research statistics in bioscience-medical-nursing-public-health settings, I noticed a certain analogy between propositional calculus research (PCR0) and … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , | 7 Comments