Monthly Archives: January 2013

Duality Indicating Unity : 1

Re: Richard J. Lipton A formal duality points to a higher unity — a calculus of forms whose expressions can be read in two different ways by switching the meanings assigned to a pair of primitive terms. I just ran … Continue reading

Posted in Abstraction, Duality, Form, Indication, Interpretation, Unity | Tagged , , , , , | 5 Comments

Propositions As Types : 1

Re: Richard J. Lipton One of my favorite tricks — it seems almost too tricky to be true — is the Propositions As Types Analogy. And I seem to see hints that the 2-part analogy can be extended to a … Continue reading

Posted in Combinator Calculus, Combinatory Logic, Computation, Computer Science, Formal Language Theory, Graph Theory, Lambda Calculus, Logic, Logical Graphs, Mathematics, Programming Languages, Propositions As Types Analogy, Type Theory | Tagged , , , , , , , , , , , , | Leave a comment

Riffs and Rotes : 1

Re: Richard J. Lipton There is a study called generalized primes that investigates in a more general way the relationship between arbitrary elements called primes and all the composites that can be formed from them according to specified rules of … Continue reading

Posted in Algebra, Combinatorics, Graph Theory, Group Theory, Mathematics, Number Theory, Riffs and Rotes | Tagged , , , , , , | 1 Comment

repetition wears on the human soul

repetition wears on the human soul

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Plato’s Puppet Returns

Re: Peter Cameron Between the discovery and the invention, Falls the Shadow, who knows, you know, By tracking backward, retracing the steps Of the tourist, who comes not to conquer, But to enjoy the winding stair to the place. That … Continue reading

Posted in Artificial Intelligence, Discovery, Education, Epistemology, Inquiry, Inquiry Driven Systems, Intelligent Systems, Invention, Learning, Meno, Philosophy, Plato, Psychology, Semiotics, Socrates, Teaching | Tagged , , , , , , , , , , , , , , , | 3 Comments

Triadic Relation Irreducibility : 2

Though my present object has more to do with the logical and mathematical aspects of triadic relations than it does with their psychological embodiments, the following exchange on the matter of consciousness from earlier last Fall keeps intruding on my … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Philosophy, Pragmatism, Relation Theory, Triadic Relations | Tagged , , , , , , , , | 1 Comment

Triadic Relation Irreducibility : 1

The core insight of Peirce’s conceptual system is the recognition that triadic relations are sui generis.  Understanding the properties of triadic relations and the consequences of their irreducibility is critical to understanding Peirce’s thought and work.  Every attempt to reconstruct Peirce’s … Continue reading

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Philosophy, Pragmatism, Relation Theory, Triadic Relations | Tagged , , , , , , , , | 11 Comments