Monthly Archives: January 2013

Duality Indicating Unity • 1

Posted on January 31, 2013 by Jon Awbrey

Re: R.J. Lipton • Mathematical Tricks A formal duality points to a higher unity — a calculus of forms whose expressions can be read in two different ways by switching the meanings assigned to a pair of primitive terms. I … Continue reading →

Posted in Abstraction, C.S. Peirce, Duality, Form, Indication, Interpretation, Peirce, Unity | Tagged , , , , , , , | 19 Comments

Propositions As Types • 1

Posted on January 29, 2013 by Jon Awbrey

Re: R.J. Lipton • Mathematical Tricks One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy.  And I see hints the 2-part analogy can be extended to a 3-part … Continue reading →

Posted in Animata, C.S. Peirce, Combinator Calculus, Combinatory Logic, Curry–Howard Isomorphism, Graph Theory, Lambda Calculus, Logic, Logical Graphs, Mathematics, Proof Theory, Propositions As Types Analogy, Type Theory | Tagged , , , , , , , , , , , , | Leave a comment

Riffs and Rotes • 1

Posted on January 28, 2013 by Jon Awbrey

Re: Richard J. Lipton • Making Primes More Random There’s a study called generalized primes which investigates in a more general way the relationship between arbitrary elements called primes and the composites which can be formed from them according to … Continue reading →

Posted in Arithmetic, Combinatorics, Graph Theory, Group Theory, Logic, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , , | 2 Comments

repetition wears on the human soul

Posted on January 25, 2013 by Jon Awbrey

repetition wears on the human soul

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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

Why am I writing this question? here? to you?

Posted on January 16, 2013 by Jon Awbrey

Why can’t I write the answer? here? for you?

Posted in Ignorance, Inhibition, Inscription, Intention, Meditation, Question, Reflection, Reverie | Tagged , , , , , , , | Leave a comment

Tenacity, Authority, Plausibility, Inquiry

Posted on January 15, 2013 by Jon Awbrey

Re: Peter Cameron • Mathematics and Logic My favorite polymathematician, Charles Sanders Peirce, gave a fourfold classification of what he called “methods of fixing belief”, or “settling opinion”, most notably and seminally in his paper, “The Fixation of Belief” (1877).  … Continue reading →

Posted in Authority, Belief Fixation, C.S. Peirce, Fixation of Belief, Inquiry, Logic, Method, Peirce, Philosophy, Philosophy of Science, Plausibility, Science, Scientific Inquiry, Scientific Method, Tenacity, Uncertainty | Tagged , , , , , , , , , , , , , , , | 4 Comments

Paint Creek • 10 January 2013

Posted on January 10, 2013 by Jon Awbrey
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