Monthly Archives: May 2013

Special Classes of Propositions

Posted on May 31, 2013 by Jon Awbrey

Adapted from Differential Propositional Calculus • Special Classes of Propositions A basic proposition, coordinate proposition, or simple proposition in the universe of discourse is one of the propositions in the set Among the propositions in are several families of propositions … Continue reading →

Posted in Boolean Functions, Computational Complexity, Differential Logic, Equational Inference, Functional Logic, Indication, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , | 2 Comments

Fourier Transforms of Boolean Functions • 1

Posted on May 30, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Twin Primes Are Useful The problem is concretely about Boolean functions of variables, and seems not to involve prime numbers at all. For any subset of the coordinate [indices], the corresponding Fourier coefficient … Continue reading →

Posted in Boolean Functions, Computational Complexity, Fourier Transforms, Harmonic Analysis, Logic, Mathematics, Propositional Calculus | Tagged , , , , , , | 1 Comment

Strangers In Paradise

Posted on May 22, 2013 by Jon Awbrey

Re: Kilvington’s Sophismata Comment 1 On the one hand Aristotle gives us the logic of analogy (παραδειγμα). On the other hand he cautions us that different paradigms may have no common measure. It seems these Immortals are always getting ahead … Continue reading →

Posted in Albert Camus, Analogy, Aristotle, Differential Logic, Eleatic Stranger, Heraclitus, Incommensurability, Logic, Metabasis, Paradigmata, Paradox, Parmenides, Plato, Richard Kilvington, Sisyphus, Sophismata, Thomas Kuhn, Zeno | Tagged , , , , , , , , , , , , , , , , , | Leave a comment

⚠ 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

grabitational singularity

Posted on May 16, 2013 by Jon Awbrey

the trouble with a bubble on a pyramid top is the point when it pop ⚠ ⚠⚠ ⚠⚠⚠ ⚠⚠⚠⚠ ⚠⚠⚠⚠⚠ ⚠⚠⚠⚠⚠⚠

Posted in Grabitational Singularity, Singularity, Verse | 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

Rock On

Posted on May 6, 2013 by Jon Awbrey

Elsewhere I have brought out the fact that human will had no other purpose than to maintain awareness.  But that could not do without discipline.  Of all the schools of patience and lucidity, creation is the most effective.  It is … Continue reading →

Posted in Absurdity, Albert Camus, Diversity, Existentialism, Freedom, Myth, Oedipus, Passion, Revolt, Sisyphus | Tagged , , , , , , , , , | 13 Comments