Monthly Archives: July 2021

Notes On Categories • 2

Posted on July 31, 2021 by Jon Awbrey

Re: Category Theory • Joe Moeller JM: In category theory, we have this perspective that we should focus attention on maps, on the relationships between objects, rather than on the objects themselves.  What’s your favorite examples of people giving a … Continue reading →

Posted in Abstraction, Category Theory, Computing, Graph Theory, Logic, Mathematics, Relation Theory, Type Theory | Tagged , , , , , , , | Leave a comment

Logical Graphs • Discussion 3

Posted on July 31, 2021 by Jon Awbrey

Re: Peirce List • JFS • RM • ET • RM • JFS • JFS • RM Dear John, Robert, Edwina, The Peirce List discussion on “thinking in diagrams vs thinking in words” called to mind the time I spent … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Logical Graphs • Discussion 2

Posted on July 29, 2021 by Jon Awbrey

Re: Category Theory • Chad Nester CN: Recently a few of us have been using the “cartesian bicategories of relations” of Carboni and Walters, in particular their string diagrams, as syntax for relations.  The string diagrams in question are more … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • Discussion 1

Posted on July 28, 2021 by Jon Awbrey

Re: Laws of Form • John Mingers JM: I find it very frustrating not to be able to draw crosses and expressions within emails or Word documents.  Does anyone know of any software or apps that can do this?  If not, … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Inquiry Driven Systems • Discussion 9

Posted on July 26, 2021 by Jon Awbrey

Re: Laws of Form • Leon Conrad LC: As someone who has worked on, teaches, and uses the CoI [Calculus of Indications] to make classical syllogistic logic much easier to practice and more visually intuitive than any of the visualisations we … Continue reading →

Posted in Animata, Artificial Intelligence, C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Learning Systems, Logic, Logical Graphs, Peirce, Semiotics, Sign Relations, Visualization | Tagged , , , , , , , , , , , , , , | 4 Comments

Inquiry Driven Systems • Discussion 8

Posted on July 26, 2021 by Jon Awbrey

Re: Category Theory • Simon Burton SB: From what I’ve noticed there are two kinds of mathematical thinking:  manipulating abstract syntax, versus direct experience/perception of concrete mathematics.  These two are intertwined in various ways, but in my experience people generally … Continue reading →

Posted in Animata, Artificial Intelligence, C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Learning Systems, Logic, Logical Graphs, Peirce, Semiotics, Sign Relations, Visualization | Tagged , , , , , , , , , , , , , , | 4 Comments

Inquiry Driven Systems • Discussion 7

Posted on July 26, 2021 by Jon Awbrey

Re: Category Theory • Henry Story HS: I place Logic within Mathematics and modal logic is a field of Logic, and so of mathematics.  You will find that modal logic comes up a lot working with machines, programs, and all … Continue reading →

Posted in Animata, Artificial Intelligence, C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Learning Systems, Logic, Logical Graphs, Peirce, Semiotics, Sign Relations, Visualization | Tagged , , , , , , , , , , , , , , | 4 Comments

Inquiry Driven Systems • Discussion 6

Posted on July 25, 2021 by Jon Awbrey

Re: Category Theory • Henry Story HS: If one were to think about maths and children’s education one would need to look at the needs of other subjects too.  It should be easy for people here to work out how … Continue reading →

Posted in Animata, Artificial Intelligence, C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Learning Systems, Logic, Logical Graphs, Peirce, Semiotics, Sign Relations, Visualization | Tagged , , , , , , , , , , , , , , | 4 Comments

Inquiry Driven Systems • Discussion 5

Posted on July 25, 2021 by Jon Awbrey

Re: Laws of Form • Leon Conrad LC: As someone who has worked on, teaches, and uses the CoI [Calculus of Indications] to make classical syllogistic logic much easier to practice and more visually intuitive than any of the visualisations we … Continue reading →

Posted in Animata, Artificial Intelligence, C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Learning Systems, Logic, Logical Graphs, Peirce, Semiotics, Sign Relations, Visualization | Tagged , , , , , , , , , , , , , , | 4 Comments

Differential Logic • 11

Posted on July 24, 2021 by Jon Awbrey

Transforms Expanded over Ordinary and Differential Variables As promised in Episode 10, in the next several posts we’ll extend our scope to the full set of boolean functions on two variables and examine how the differential operators and act on that … 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