Category Archives: Leibniz

Differential Logic • Overview

Posted on November 25, 2024 by Jon Awbrey

A reader once told me “venn diagrams are obsolete” and of course we all know how unwieldy they become as our universes of discourse expand beyond four or five dimensions.  Indeed, one of the first lessons I learned when I … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Functional Logic, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Time, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Survey of Differential Logic • 7

Posted on February 25, 2024 by Jon Awbrey

This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment. Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 41 Comments

Survey of Differential Logic • 6

Posted on November 10, 2023 by Jon Awbrey

This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment. Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Praeclarum Theorema • 3

Posted on October 15, 2023 by Jon Awbrey

Re: Praeclarum Theorema • (1) • (2) The steps of the proof are replayed in the following animation. Reference Leibniz, Gottfried W. (1679–1686?), “Addenda to the Specimen of the Universal Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966), Leibniz … Continue reading →

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 6 Comments

Praeclarum Theorema • 2

Posted on October 14, 2023 by Jon Awbrey

Re: Praeclarum Theorema • 1 And here’s a neat proof of that nice theorem — Reference Leibniz, Gottfried W. (1679–1686?), “Addenda to the Specimen of the Universal Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966), Leibniz : Logical Papers, … Continue reading →

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 8 Comments

Praeclarum Theorema • 1

Posted on October 13, 2023 by Jon Awbrey

The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus noted and named by G.W. Leibniz, who stated and proved it in the following manner. If a is b and d is c, then ad will be bc. This … Continue reading →

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 9 Comments

Praeclarum Theorema

Posted on October 5, 2023 by Jon Awbrey

Introduction The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus noted and named by G.W. Leibniz, who stated and proved it in the following manner. If a is b and d is c, then ad will be bc. … Continue reading →

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 8 Comments

Differential Logic • The Logic of Change and Difference

Posted on August 22, 2023 by Jon Awbrey

Differential logic is the logic of variation — the logic of change and difference. Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes … Continue reading →

Posted in Animata, Boolean Difference Calculus, Boolean Functions, C.S. Peirce, Differential Logic, Differential Propositions, Discrete Dynamical Systems, Leibniz, Logic, Logical Graphs, Minimal Negation Operators, Visualization | Tagged , , , , , , , , , , , | 6 Comments

Survey of Differential Logic • 5

Posted on April 25, 2023 by Jon Awbrey

This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment. Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Differential Logic • 4

Posted on November 20, 2022 by Jon Awbrey

This is a Survey of blog and wiki posts on Differential Logic, material I plan to develop toward a more compact and systematic account. Elements Differential Propositional Calculus Part 1 • Part 2 • Appendices • References Differential Logic • … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment