Category Archives: Diagrammatic Reasoning

Animated Logical Graphs • 8

Posted on May 23, 2015 by Jon Awbrey

Re: Ken Regan • The Shapes of Computations The most striking example of a “Primitive Insight Proof” (PIP❢) known to me is the Dawes–Utting proof of the Double Negation Theorem from the CSP–GSB axioms for propositional logic.  There is a … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 7

Posted on May 22, 2015 by Jon Awbrey

Re: Ken Regan • The Shapes of Computations There are several issues of computation shape and proof style that raise their heads already at the logical ground level of boolean functions and propositional calculus.  From what I’ve seen, there are … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • Discussion 4

Posted on March 19, 2015 by Jon Awbrey

Re: Peirce List Discussion • Howard Pattee We use this or that species of diagrams to represent a fraction of the properties, hardly ever all the properties, of the objects in an object domain.  The diagrams that Peirce developed to … Continue reading →

Posted in Diagrammatic Reasoning, Diagrams, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 6

Posted on March 13, 2015 by Jon Awbrey

Re: Peirce List Discussion • Jim Willgoose At root we are dealing with a genre of very abstract formal systems.  They have grammars that determine their well-formed expressions and rules that determine the permissible transformations among expressions, but they lack … Continue reading →

Posted in Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Graph Theory, Iconicity, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 5

Posted on January 28, 2015 by Jon Awbrey

Re: Peirce List Discussion • HP A computational problem is defined as a set of problem instances with specified properties.  An algorithm solves a problem if it computes the correct answer to every problem instance in that set. The use … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 4

Posted on January 27, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien It’s fair to say most of my university coursework leaned to the theoretical side but I did cobble together a respectable enough background in computing, statistics, and industrial-organizational styles of systems and simulation that … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 3

Posted on January 26, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien I have a little more leisure now to start climbing back into the saddle, so let me see where we left off … Try looking into the article I linked before: Logical Graphs Or … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 2

Posted on January 14, 2015 by Jon Awbrey

Re: Peirce List • Jim Willgoose It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 1

Posted on January 8, 2015 by Jon Awbrey

For Your Musement … Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic. ☞ Proof Animations See the following article for a full … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Logical Graphs • Introduction

Posted on July 29, 2008 by Jon Awbrey

A logical graph is a graph-theoretic structure in one of the styles of graphical syntax that Charles Sanders Peirce developed for logic. Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 43 Comments