Monthly Archives: May 2013

Special Classes of Propositions

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, Functional Logic, Logic, Mathematics, Propositional Calculus | Tagged , , , , , , | 2 Comments

Fourier Transforms of Boolean Functions : 1

Re: Another Problem 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 is given by: where is if is odd, … Continue reading

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

Strangers In Paradise

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 ⚠

Re: Kenneth W. Regan 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 3-place (triadic or ternary) … Continue reading

Posted in Error, Fallibility, Logic, Logic of Relatives, Mathematical Traps, Mathematics, Peirce, Philosophy, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , | 5 Comments

Triadic Relation Irreducibility : 3

References Note. The PlanetMath pages are messed up at present on account of a system changeover and switching from LaTeX to MathJerX, but I’ll leave the links here for now against the day when the site gets back in gear. … Continue reading

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Philosophy, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , | 1 Comment

grabitational singularity

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?

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