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Category Archives: Mathematics
⚠ 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 Error, Fallibility, Logic, Logic of Relatives, Mathematical Traps, Mathematics, Peirce, Philosophy, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity
4 Comments
Triadic Relation Irreducibility : 3
References Relation Theory MyWikiBiz PlanetMath Sign Relations MyWikiBiz PlanetMath Triadic Relations MyWikiBiz PlanetMath Relation Composition MyWikiBiz PlanetMath Relation Construction MyWikiBiz PlanetMath Relation Reduction MyWikiBiz PlanetMath Related Readings Notes on Peirce’s 1870 Logic of Relatives Interpretation as Action : The Risk … Continue reading
Posted in Logic, Logic of Relatives, Mathematics, Peirce, Philosophy, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity
Tagged Logic, Logic of Relatives, Mathematics, Peirce, Philosophy, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity
1 Comment
Finding a Needle in a Cactus Patch
Re: 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 involved in the … Continue reading
Infinite Uses → Finite Means
The idea that a language is based on a system of rules determining the interpretation of its infinitely many sentences is by no means novel. Well over a century ago, it was expressed with reasonable clarity by Wilhelm von Humboldt … Continue reading
Posted in Chomsky, Finite Means, Formal Language Theory, Formal Languages, Foundations of Mathematics, Generative Grammar, Infinite Use, Linguistics, Pigeonhole Principle, Recursion, Syntax, Wilhelm von Humboldt
Tagged Chomsky, Finite Means, Formal Language Theory, Formal Languages, Foundations of Mathematics, Generative Grammar, Infinite Use, Linguistics, Pigeonhole Principle, Recursion, Syntax, Wilhelm von Humboldt
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What It Is
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 Change, Heraclitus, Infinity, Logic, Mathematics, Motion, Paradox, Parmenides, Phenomenology, Zeno
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Slip Slidin’ Away
Re: Zeno Proof Paradox 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 … Continue reading
Posted in Albert Camus, Change, Infinity, Lewis Carroll, Logic, Mathematics, Meno, Modus Ponens, Motion, Paradox, Peirce, Phenomenology, Sisyphus, Syllogism, Zeno
Tagged Albert Camus, Change, Infinity, Lewis Carroll, Logic, Mathematics, Meno, Modus Ponens, Motion, Paradox, Peirce, Phenomenology, Sisyphus, Syllogism, Zeno
2 Comments
The Present Is Big With The Future
Now that I have proved sufficiently that everything comes to pass according to determinate reasons, there cannot be any more difficulty over these principles of God’s foreknowledge. Although these determinations do not compel, they cannot but be certain, and they … Continue reading
Posted in Determination, Determinism, Differential Calculus, Differential Logic, Hologrammautomaton, Infinitesimals, Leibniz, Universal Harmony
Tagged Determination, Determinism, Differential Calculus, Differential Logic, Hologrammautomaton, Infinitesimals, Leibniz, Universal Harmony
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Riffs and Rotes : 2
Re: Peter Cameron 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 with these enigmas led me to the … Continue reading
Quotiens?
How many times do I repeat the same experience? Before I come to see it as the same experience?
Posted in Algorithms, Anamnesis, Arithmetic, Deja Vu, Education, Epistemology, Eternal Return, Inquiry, Learning, Meno, Music, Pattern Recognition, Plato, Poetry, Recursion, Repetition, Rhythm, Teaching
Tagged Algorithms, Anamnesis, Arithmetic, Deja Vu, Education, Epistemology, Eternal Return, Inquiry, Learning, Meno, Music, Pattern Recognition, Plato, Poetry, Recursion, Repetition, Rhythm, Teaching
2 Comments
I Wonder, Wonder Who
Re: 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 as an unreconstructed Platonic realist, I … Continue reading
Posted in Anamnesis, Aristotle, Boole, Boolean Functions, Discovery, Invention, Learning, Logic, Mathematics, Meno, Model Theory, Peirce, Plato, Propositional Calculus, Recollection, Semiotics, Socrates, Teaching
Tagged Anamnesis, Aristotle, Boole, Boolean Functions, Discovery, Invention, Learning, Logic, Mathematics, Meno, Model Theory, Peirce, Plato, Propositional Calculus, Recollection, Semiotics, Socrates, Teaching
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