Category Archives: Boole

Differential Logic • Comment 7

Posted on September 17, 2021 by Jon Awbrey

Re: John Baez • Cyclic Identity for Partial Derivatives • Maxwell’s Relations (1) (2) (3) Much fun can be had by trying to do differentials and partial differentials over the boolean domain instead of the reals I took a first whack … 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 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 | Comments Off

Differential Logic • Comment 6

Posted on July 7, 2021 by Jon Awbrey

Cf: Category Theory • Jon Awbrey I opened a topic in the “logic” stream of “category theory.zulipchat” to discuss differential logic in a category theoretic environment and began by linking a few basic resources. The topic on logical graphs introduced … Continue reading →

Differential Logic • Comment 5

Posted on May 14, 2021 by Jon Awbrey

Re: Peirce List • John Sowa : “Modal Logic Is An Immense Swamp” Dear John, Best title I’ve read in a long time! But the really immense swamp critter here is the Naturally Evolved Organon known as ornery natural language which … Continue reading →

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 →

Survey of Animated Logical Graphs • 2

Posted on May 22, 2019 by Jon Awbrey

This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years. After that I’ll look to organizing … Continue reading →

Posted in Abstraction, Amphecks, Animata, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Surveys, Theorem Proving, Visualization, Zeroth Order Logic | Tagged Abstraction, Amphecks, Animata, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Surveys, Theorem Proving, Visualization, Zeroth Order Logic | 19 Comments

Indicator Functions • Discussion 1

Posted on October 10, 2018 by Jon Awbrey

Peter Smith, on his Logic Matters blog, asks the question, “What Is A Predicate?”, and considers a number of answers. There are of course other possible answers, and one I learned quite early on, arising very naturally in applying mathematical … Continue reading →

Posted in Boole, Boolean Functions, C.S. Peirce, Category Theory, Indication, Indicator Functions, Logic, Mathematics, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Set Theory, Venn Diagrams | Tagged Boole, Boolean Functions, C.S. Peirce, Category Theory, Indication, Indicator Functions, Logic, Mathematics, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Set Theory, Venn Diagrams | 1 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 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 | 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 →

Survey of Animated Logical Graphs • 1

Posted on May 10, 2015 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 9.4

Posted on February 27, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 9.4 Boole rationalizes the properties of what we now call boolean multiplication, roughly equivalent to logical conjunction, by means of his concept of selective operations. Peirce, in his turn, taking a radical step … Continue reading →

Posted in Boole, Boolean Algebra, C.S. Peirce, Logic, Logic of Relatives, Mathematics, Relation Theory, Visualization | Tagged Boole, Boolean Algebra, C.S. Peirce, Logic, Logic of Relatives, Mathematics, Relation Theory, Visualization | 6 Comments

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