Tag Archives: Duality

Peirce’s 1870 “Logic of Relatives” • Comment 1

Posted on October 22, 2019 by Jon Awbrey

Peirce often stressed his Logic of Relatives as the key to unlocking many puzzles.  As I read him, it was Peirce’s drive to understand the Logic of Science that required the grounding of logic in the mathematical forms of triadic … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Peirce’s 1870 “Logic Of Relatives” • Discussion 1

Posted on September 30, 2019 by Jon Awbrey

Re: Ontolog Forum • John Bottoms Re: History View Blog • A Yukaghir Girl Writes A Love Letter Re: Peirce’s 1870 “Logic Of Relatives” • Proto-Graphical Syntax John Bottoms, writing in the Ontolog Forum, compared the graphic I drew for … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Peirce’s 1870 “Logic of Relatives” • Overview

Posted on September 24, 2019 by Jon Awbrey

My long ago encounter with Peirce’s 1870 paper, “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, was one of the events precipitating my return from the hazier … Continue reading →

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 19 Comments

Animated Logical Graphs • 31

Posted on September 1, 2019 by Jon Awbrey

Re: Systems Science • Aleksandar Malečić Re: Animated Logical Graphs • 21 AM: Each step on its own, as far as I can follow them, makes sense.  You are, if I understand it correctly, trying to figure out something fundamental, … 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 • 30

Posted on August 25, 2019 by Jon Awbrey

The duality between Entitative and Existential interpretations of logical graphs is a good example of a mathematical symmetry, in this case a symmetry of order two.  Symmetries of this and higher orders give us conceptual handles on excess complexity in … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 22 Comments

Animated Logical Graphs • 29

Posted on August 11, 2019 by Jon Awbrey

Re: Animated Logical Graphs • 21 Re: Ontolog Forum • Joseph Simpson JS: I tend to view equivalence and distinction as relationships as opposed to operations.  I do not know if this makes any significant difference in this context. Dear Joe, … 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 • 28

Posted on August 3, 2019 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Discrepancy Games and Sensitivity Re: Ontolog Forum • Joseph Simpson Re: Animated Logical Graphs • 24 I will have to focus on other business for a couple of weeks — so just by … 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 • 27

Posted on July 31, 2019 by Jon Awbrey

The rules given in the previous post for evaluating cactus graphs were given in purely formal terms, that is, by referring to the mathematical forms of cacti without mentioning their potential for logical meaning.  As it turns out, two ways … 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 • 26

Posted on July 28, 2019 by Jon Awbrey

This post and the next wrap up the Themes and Variations section of my speculation on Futures Of Logical Graphs.  I made an effort to “show my work”, reviewing the steps I took to arrive at the present perspective on … 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 • 25

Posted on July 26, 2019 by Jon Awbrey

Re: Animated Logical Graphs • 23 Let’s examine the Formal Operation Table for the third in our series of reflective forms to see if we can elicit the general pattern. Or, thinking in terms of the corresponding cactus graphs, writing for … 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