Tag Archives: Semiotics

⚠ It’s A Trap ⚠

Posted on May 18, 2013 by Jon Awbrey

Re: Kenneth W. Regan • Graduate Student Traps The most common mathematical trap I run across has to do with Triadic Relation Irreducibility, as noted and treated by the polymath C.S. Peirce. This trap lies in the mistaken belief that every … Continue reading →

Posted in C.S. Peirce, Category Theory, Descartes, Error, Fallibility, Logic, Logic of Relatives, Mathematical Traps, Mathematics, Peirce, Pragmatism, Reductionism, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , | 5 Comments

Triadic Relation Irreducibility • 3

Posted on May 16, 2013 by Jon Awbrey

References Relation Theory OEIS Wiki • PlanetMath Triadic Relations OEIS Wiki • PlanetMath Sign Relations OEIS Wiki • PlanetMath Relation Composition OEIS Wiki • PlanetMath Relation Construction OEIS Wiki • PlanetMath Relation Reduction OEIS Wiki • PlanetMath Related Readings Notes … Continue reading →

Posted in C.S. Peirce, Category Theory, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Teridentity, Thirdness, Triadic Relations | Tagged , , , , , , , , , , , , , , , | 1 Comment

C.S. Peirce : Information = Comprehension × Extension

Posted on May 8, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • A Most Perplexing Mystery The inverse relationship between symmetry and diversity — that we see for example in the lattice-inverting map of a Galois correspondence — is a variation on an old theme … Continue reading →

Posted in C.S. Peirce, Comprehension, Diversity, Extension, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Peirce, Reciprocity, Semiotics, Sign Relations, Symmetry, Variety | Tagged , , , , , , , , , , , , , , , | 13 Comments

Finding a Needle in a Cactus Patch

Posted on April 30, 2013 by Jon Awbrey

Re: R.J. Lipton • Sex, Lies, And Quantum Computers Don’t know much about quantum computation, but my ventures in graphical syntaxes for propositional calculus did turn up a logical operator whose evaluation process reminded me a little of the themes … Continue reading →

Posted in Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Quantum Computing, Semiotics | Tagged , , , , , , , , , , , , | 4 Comments

I Wonder, Wonder Who

Posted on February 25, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? The question recalls recent discussions of discovery and invention in the mathematical field, bringing back to mind questions I’ve wondered about for as long as I can remember. Speaking … Continue reading →

Posted in Anamnesis, Aristotle, Boole, Boolean Functions, C.S. Peirce, Discovery, Invention, Learning, Logic, Mathematics, Meno, Model Theory, Peirce, Plato, Propositional Calculus, Recollection, Semiotics, Socrates, Teaching | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Theme One • A Program Of Inquiry 4

Posted on February 14, 2013 by Jon Awbrey

Re: Next Polymath Project • What, When, Where? Here’s a bit of data on the Theme One Program I worked on all through the 1980s.  My aim was to develop fundamental algorithms and data structures to support an integrated learning … 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, Peirce, Semiotics | Tagged , , , , , , , , , , , , , | 8 Comments

The Difference That Makes A Difference That Peirce Makes • 1

Posted on February 7, 2013 by Jon Awbrey

Being one who does not view Peirce’s work as a flickering foreshadowing of analytic philosophy, logical whatevism, or anything else you want to call it, but leans more to thinking of the latter philosophies as fumbling fallbacks losing what ground … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Philosophy, Pragmatism, Science, Scientific Method, Semiotics | Tagged , , , , , , , , | 1 Comment

Plato’s Puppet Returns

Posted on January 21, 2013 by Jon Awbrey

Re: Peter Cameron • Discovery and Invention Between the discovery and the invention, Falls the Shadow, who knows, you know, By tracking backward, retracing the steps Of the tourist, who comes not to conquer, But to enjoy the winding stair … Continue reading →

Posted in Anamnesis, Artificial Intelligence, Discovery, Education, Epistemology, Inquiry, Inquiry Driven Systems, Intelligent Systems, Invention, Learning, Meno, Philosophy, Plato, Psychology, Semiotics, Socrates, Teaching | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Triadic Relation Irreducibility • 2

Posted on January 18, 2013 by Jon Awbrey

Re: Peirce List • Matt Faunce • Jon Awbrey • Jon Awbrey Though my present object has more to do with the logical and mathematical aspects of triadic relations than it does with their psychological embodiments, the following exchange on … Continue reading →

Posted in C.S. Peirce, Category Theory, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Teridentity, Thirdness, Triadic Relations | Tagged , , , , , , , , , , , , , , , | 1 Comment

Triadic Relation Irreducibility • 1

Posted on January 17, 2013 by Jon Awbrey

The core insight of Peirce’s conceptual system is the recognition that triadic relations are sui generis, constituting a class by themselves.  Understanding the properties of triadic relations and the consequences of their irreducibility is critical to understanding Peirce’s thought and work.  … Continue reading →

Posted in C.S. Peirce, Category Theory, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Teridentity, Thirdness, Triadic Relations | Tagged , , , , , , , , , , , , , , , | 11 Comments