Tag Archives: Visualization

Objects, Models, Theories • 1

Posted on September 10, 2013 by Jon Awbrey

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839 Re: Artem Kaznatcheev • Three Types of Mathematical Models Comment 1 In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another.  Logicians … Continue reading →

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 8 Comments

How To Succeed In Proof Business Without Really Trying

Posted on July 15, 2013 by Jon Awbrey

Re: R.J. Lipton • Surely You Are Joking? Comment 1 Even at the mailroom entry point of propositional calculus, there is a qualitative difference between insight proofs and routine proofs.  Human beings can do either sort, as a rule, but … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Automatic Theorem Proving, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Model Theory, Peirce, Praeclarum Theorema, Proof Theory, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 7 Comments

Special Classes of Propositions

Posted on May 31, 2013 by Jon Awbrey

Adapted from Differential Propositional Calculus • Special Classes of Propositions A basic proposition, coordinate proposition, or simple proposition in the universe of discourse is one of the propositions in the set Among the propositions in are several families of propositions … Continue reading →

Posted in Boolean Functions, Computational Complexity, Differential Logic, Equational Inference, Functional Logic, Indication, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , | 2 Comments

Indicator Functions • 1

Posted on March 13, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? One of the things it helps to understand about 19th Century mathematicians, and those who built the bridge to the 20th, is that they were capable of high abstraction … Continue reading →

Posted in Abstraction, Boole, Boolean Functions, C.S. Peirce, Category Theory, Characteristic Functions, Euler, Indicator Functions, John Venn, Logic, Mathematics, Peirce, Propositional Calculus, Set Theory, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , | Leave a comment

Theme One • A Program Of Inquiry 1

Posted on December 20, 2012 by Jon Awbrey

Re: Peirce List • Jerry Chandler • Jon Awbrey • Gary Richmond • Christophe Menant I view psychology, throughout its many branches, as a fascinating and compelling collection of subjects, so much so I spent one of my parallel lives … Continue reading →

Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Semiotics, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

Sign Relational Manifolds • 5

Posted on November 1, 2012 by Jon Awbrey

Let me try to say in intuitive terms what I think is really going on here. The problem we face is as old as the problem of other minds, or intersubjectivity, or even commensurability, and it naturally involves a whole … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • 4

Posted on October 30, 2012 by Jon Awbrey

Another set of notes I found on this theme strikes me as getting to the point more quickly and though they read a little rough in places I think it may be worth the effort to fill out their general … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 4 Comments

Sign Relational Manifolds • 3

Posted on October 23, 2012 by Jon Awbrey

I’m not sure when it was I first noticed the relationship between manifolds and semiotics but I distinctly recall the passage in Serge Lang’s Differential and Riemannian Manifolds which brought the triadic character of tangent vectors into high relief.  I … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Intentionality, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • 2

Posted on October 22, 2012 by Jon Awbrey

A sense of how manifolds are applied in practice may be gleaned from the set of excerpts linked below, from Doolin and Martin (1990), Introduction to Differential Geometry for Engineers, which I used in discussing differentiable manifolds with other participants … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relational Manifolds • 1

Posted on October 22, 2012 by Jon Awbrey

Riemann’s concept of a manifold, especially as later developed, bears a close relationship to Peirce’s concept of a sign relation. I will have to wait for my present train of thought to stop at a station before I can hop … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | 2 Comments