Category Archives: Logic

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 2

Posted on February 3, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives (cont.) §1. Individual and Simple Terms (concl.) 216.   Just as in mathematics we speak of infinitesimals and infinites, which are fictitious limits of continuous quantity, and every statement involving these expressions has its … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 11 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 1

Posted on February 1, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives §1. Individual and Simple Terms 214.   Just as we had to begin the study of Logical Addition and Multiplication by considering and terms which might have been introduced under the Algebra of the … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 10 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Preliminaries

Posted on January 30, 2015 by Jon Awbrey

Recurring questions about relations, especially triadic relations and sign relations, prompt a return to Peirce’s core papers on the logic of relative terms and the mathematics of relations in general.  I began a study of his Peirce’s 1870 “Logic of … Continue reading →

Posted in Algebra of Logic, Boolean Algebra, C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Mathematics, Relation Theory, Relational Algebra, Semiotics, Sign Relations, Theory of Limits, Triadic Relations | Tagged , , , , , , , , , , , , , | 9 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

Pragmatism About Theoretical Entities • 1

Posted on January 20, 2015 by Jon Awbrey

By theoretical entities I mean things like classes, properties, qualities, sets, situations, or states of affairs, in general, the putative denotations of theoretical concepts, formulas, sentences, terms, or treatises, in brief, the ostensible objects of signs. A conventional statement of … Continue reading →

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

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

Frankl, My Dear • 12

Posted on November 24, 2014 by Jon Awbrey

It is one of the rules of my system of general harmony, that the present is big with the future, and that he who sees all sees in that which is that which shall be. Leibniz • Theodicy Re: Dick … Continue reading →

Posted in Boolean Algebra, Boolean Functions, Computational Complexity, Differential Logic, Frankl Conjecture, Logic, Logical Graphs, Mathematics, Péter Frankl | Tagged , , , , , , , , | 10 Comments