Tag Archives: Leibniz

Differential Logic • 2

Posted on March 23, 2020 by Jon Awbrey

Cactus Language for Propositional Logic The development of differential logic is facilitated by having a moderately efficient calculus in place at the level of boolean-valued functions and elementary logical propositions.  One very efficient calculus on both conceptual and computational grounds … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Differential Logic • 1

Posted on March 22, 2020 by Jon Awbrey

Introduction Differential logic is the component of logic whose object is the description of variation — for example, the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description.  A definition that broad naturally … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Differential Logic • Overview

Posted on March 20, 2020 by Jon Awbrey

The previous series of blog posts on Differential Propositional Calculus brought us to the threshold of the subject without quite stepping over but I wanted to lay out the necessary ingredients in the most concrete, intuitive, and visual way possible … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Survey of Differential Logic • 2

Posted on February 8, 2020 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 Logic • Introduction Differential Logic • Part 1 • Part 2 • Part 3 … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Differential Logic • Comment 4

Posted on January 4, 2020 by Jon Awbrey

Re: Cybernetic Communications • Stephen Paul King SPK: Is it possible that beliefs can propagate almost completely contrary to facts, seen by those that are not infected with those beliefs? Can we have complex waves in the domains of binary truth … Continue reading →

Posted in Adaptive Systems, Amphecks, Belief Systems, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Differential Logic, Discrete Dynamics, Fixation of Belief, Gradient Descent, Graph Theory, Hill Climbing, Hologrammautomaton, Inquiry, Inquiry Driven Systems, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Optimization, Painted Cacti, Peirce, Propositional Calculus, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Comments Off on Differential Logic • Comment 4

History, Its Arc, Its Tangents • 2

Posted on December 25, 2019 by Jon Awbrey

Re: Renaissance Mathematicus • Both Sides of History Are there watersheds in the history of science?  A continental divide between basins of right and wrong ideas?  I was pondering these questions when one of my favorite passages from Leibniz came … Continue reading →

Posted in Differential Calculus, History of Science, Hologrammautomaton, Leibniz, Thony Christie | Tagged , , , , | Leave a comment

¿Shifting Paradigms? • 6

Posted on October 17, 2017 by Jon Awbrey

Re: Peter Cameron • Infinity and Foundation C.S. Peirce is one who recognized the constitutional independence of mathematical inquiry, finding at its core a mode of operation tantamount to observation and more primitive than logic itself.  Here is one place … Continue reading →

Posted in Algorithms, Boole, C.S. Peirce, Combinatorics, Computation, Foundations of Mathematics, Inquiry, Laws of Form, Leibniz, Logic, Mathematics, Model Theory, Paradigms, Peirce, Proof Theory, Spencer Brown | Tagged , , , , , , , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 5

Posted on July 16, 2017 by Jon Awbrey

Re: Peter Cameron • Infinity and Foundation We always encounter a multitude of problems whenever we try to rationalize mathematics by reducing it to logic, where logic itself is reduced to a purely deductive style.  A number of thinkers have … Continue reading →

Posted in Algorithms, Boole, C.S. Peirce, Combinatorics, Computation, Foundations of Mathematics, Inquiry, Laws of Form, Leibniz, Logic, Mathematics, Model Theory, Paradigms, Peirce, Proof Theory, Spencer Brown | Tagged , , , , , , , , , , , , , , , | 4 Comments

The Present Is Big With The Future • Comment 2

Posted on June 9, 2017 by Jon Awbrey

My interest in this theme of Leibniz goes back to a time when I began exploring generalized measures of determination and qualitative analogues of differential calculus — doctrines of absolute determinism or predestination had long ago loosened their hold on … Continue reading →

Posted in C.S. Peirce, Determination, Differential Calculus, Differential Logic, Hologrammautomaton, Infinitesimals, Leibniz, Logic, Logical Graphs, Mathematics, Peirce, Preëstablished Harmony, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

The Present Is Big With The Future • Comment 1

Posted on June 2, 2017 by Jon Awbrey

Re: Peirce List • John Sowa Re: Peirce List • Jon Awbrey Here is a passage from Leibniz where he half decrypts half encrypts the big idea sparking his discovery of the differential calculus. The Present Is Big With The … Continue reading →

Posted in C.S. Peirce, Determination, Differential Calculus, Differential Logic, Hologrammautomaton, Infinitesimals, Leibniz, Logic, Logical Graphs, Mathematics, Peirce, Preëstablished Harmony, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , | 10 Comments