Tag Archives: Mathematics

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

What It Is

Posted on April 13, 2013 by Jon Awbrey

Re: Gil Kalai If I remember my long ago readings well enough, Jimmy the Ancient Greek could lay odds as well as any modern bookmaker on the outcomes of Olympic contests, but that was not really the point of Zeno’s … Continue reading →

Posted in Change, Heraclitus, Infinity, Logic, Mathematics, Motion, Paradox, Parmenides, Phenomenology, Zeno | Tagged , , , , , , , , , | Leave a comment

Slip Slidin’ Away

Posted on April 11, 2013 by Jon Awbrey

And you give me the choice between a description that is sure but that teaches me nothing and hypotheses that claim to teach me but that are not sure. — Albert Camus • The Myth of Sisyphus Re: R.J. Lipton … Continue reading →

Posted in Albert Camus, C.S. Peirce, Change, Differential Logic, Infinity, Lewis Carroll, Logic, Mathematics, Meno, Modus Ponens, Motion, Paradox, Phenomenology, Sisyphus, Syllogism, Time, Zeno | Tagged , , , , , , , , , , , , , , , , | 3 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

Riffs and Rotes • 2

Posted on March 3, 2013 by Jon Awbrey

Re: Peter Cameron • Addition and Multiplication of Natural Numbers The interaction between addition and multiplication in the natural numbers has long been an interest of mine, leading to broader questions about the relationship between algebra and combinatorics.  My gropings … Continue reading →

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

Notes On Categories • 1

Posted on February 22, 2013 by Jon Awbrey

Continued from “Notes On Categories” (14 Jul 2003) • Inquiry List • Ontology List NB.  This page is a work in progress.  I will have to dig up some still older notes from the days of pen and paper before … Continue reading →

Posted in Abstraction, Category Theory, Computing, Graph Theory, Logic, Mathematics, Relation Theory, Type Theory | Tagged , , , , , , , | 10 Comments

Château Descartes

Posted on February 14, 2013 by Jon Awbrey

But if we are to select those dimensions which will be of the greatest assistance to our imagination, we should never attend to more than one or two of them as depicted in our imagination, even though we are well … Continue reading →

Posted in Analytic Geometry, Cartesian Coordinate System, Cartesian Philosophy, Cartesian Product, Descartes, Dualism, Dyadicism, Inquiry, Logic, Mathematics, Philosophy, Reductionism, Relation Theory | Tagged , , , , , , , , , , , , | 3 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

Propositions As Types Analogy • 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 … 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 , , , , , , , , , , , , | 3 Comments