Category Archives: Peirce

Wherefore Aught?

Posted on June 1, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Why Is There Something? Here is another one of those eternally recurring ideas echoed inimitably by C.S. Peirce in his sketch of a Cosmogonic Philosophy. It would suppose that in the beginning,—infinitely remote,—there was … Continue reading →

Posted in C.S. Peirce, Cosmogony, Evolution, Existence, Natural Law, Peirce, Philosophy, References, Sources | Tagged , , , , , , , , | 2 Comments

⚠ 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

Absurdum Quid

Posted on April 22, 2013 by Jon Awbrey

I am thus justified in saying that the feeling of absurdity does not spring from the mere scrutiny of a fact or an impression, but that it bursts from the comparison between a bare fact and a certain reality, between … Continue reading →

Posted in Absurdity, Albert Camus, Existentialism, Inquiry, Method, Peirce, Pragmatic Maxim, Pragmatism, Sisyphus, Tertium Quid, Thirdness, Triadicity | Tagged , , , , , , , , , , , | 1 Comment

Pragmatism Meets Absurdity

Posted on March 30, 2013 by Jon Awbrey

At the streetcorner … At any streetcorner the feeling of absurdity can strike any man in the face. As it is, in its distressing nudity, in its light without effulgence, it is elusive. But that very difficulty deserves reflection. It … Continue reading →

Posted in Absurdity, Albert Camus, Existentialism, Peirce, Pragmatic Maxim, Pragmatism, Sisyphus | Tagged , , , , , , | Leave a comment

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

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