Tag Archives: Logic

⚠ 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

What part do arguments from authority play in mathematical reasoning?

Posted on May 14, 2013 by Jon Awbrey

In forming your answer you may choose to address any or all of the following aspects of the question: Descriptive What part do arguments from authority actually play in mathematical reasoning? Normative What part do arguments from authority ideally play … Continue reading →

Posted in Artificial Intelligence, Authority, Control, Control Theory, Cybernetics, Fixation of Belief, History of Mathematics, History of Science, Information, Information Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intuition, Logic, Logic of Science, Mathematical Intuition, Mathematical Reasoning, Operations Research, Optimal Control, Optimization, Philosophy of Science, Scientific Method | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

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

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