Author Archives: Jon Awbrey

Where Is Fancy Bred?

Posted on August 24, 2013 by Jon Awbrey

Re: Artem Kaznatcheev • Fitness Landscapes as Mental & Mathematical Models of Evolution The question of “mental models” has occupied my thoughts for quite a while. As intelligent agents with a capacity for inquiry, we have ways of forming and … Continue reading →

Posted in Adaptive Systems, Analogy, Artem Kaznatcheev, Artificial Intelligence, Biological Systems, Communication, Computational Complexity, Control, Evolution, Fitness Landscapes, Imagination, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Mathematical Models, Mental Models, Natural Intelligence, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , | 1 Comment

Ideas Demand Expression Always

Posted on August 7, 2013 by Jon Awbrey

Re: Quomodocumque What came of my morning meditation today — There is something about an idea that demands to be communicated. But what of bad ideas, fixed ideas, ideology? And again, is there really any such thing as a bad … Continue reading →

Posted in Meditation | Tagged | Leave a comment

Anamnesis, Maieusis, Monadology, Semeiosis

Posted on August 6, 2013 by Jon Awbrey

Anamnesis Learning = Recollection Maieusis Teaching = Midwifery Monadology Communication = Pre-Established Harmony Semeiosis Meaning = Interpretation

Posted in Anamnesis, Maieusis, Monadology, Semeiosis, Semiosis, Symbolism | Tagged , , , , , | Leave a comment

The Lambda Point • 1

Posted on August 1, 2013 by Jon Awbrey

A note on the title.  From long ago discussions with Harvey Davis, one of my math professors at Michigan State.  I remember telling him of my interest in the place where algebra, geometry, and logic meet, and he quipped, “Ah … Continue reading →

Posted in Algebra, Amphecks, Boolean Algebra, C.S. Peirce, Cactus Graphs, Geometry, Graph Theory, Lambda Point, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Peirce, Propositional Calculus, Topology | Tagged , , , , , , , , , , , , , , | Leave a comment

How To Succeed In Proof Business Without Really Trying

Posted on July 15, 2013 by Jon Awbrey

Re: R.J. Lipton • Surely You Are Joking? Comment 1 Even at the mailroom entry point of propositional calculus, there is a qualitative difference between insight proofs and routine proofs.  Human beings can do either sort, as a rule, but … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Automatic Theorem Proving, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Model Theory, Peirce, Praeclarum Theorema, Proof Theory, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 7 Comments

What Is A Theorem That A Human May Prove It?

Posted on June 19, 2013 by Jon Awbrey

Re: Gil Kalai • Why Is Mathematics Possible? • Tim Gowers’ Take On The Matter Comment 1 To the extent that mathematics has to do with reasoning about possible existence, or inference from pure hypothesis, a line of thinking going … Continue reading →

Posted in Abduction, Analogy, Aristotle, C.S. Peirce, Conjecture, Deduction, Epistemology, Hypothesis, Induction, Inquiry, Logic, Logic of Science, Mathematics, Peirce, Proof Theory, Retroduction, Theorem Proving, Warren S. McCulloch | Tagged , , , , , , , , , , , , , , , , , | 2 Comments

C.S. Peirce • The Proper Treatment of Hypotheses

Posted on June 19, 2013 by Jon Awbrey

Selection from C.S. Peirce, “Hume On Miracles” (1901), CP 6.522–547 530.   Now the testing of a hypothesis is usually more or less costly. Not infrequently the whole life’s labor of a number of able men is required to disprove a … Continue reading →

Posted in Abduction, Hypothesis, Inquiry, Logic of Science, Peirce, References, Retroduction, Sources | Tagged , , , , , , , | 1 Comment

Moneytheism

Posted on June 10, 2013 by Jon Awbrey

Re: Cathy O’Neil • Profit as Proxy for Value There is a deep and pervasive analogy between systems of commerce and systems of communication, turning on their near-universal use of symbola (images, media, proxies, signs, symbols, tokens, etc.) to stand … Continue reading →

Posted in Commerce, Communication, Economics, Moneytheism, Semiotics, Sign Relations | Tagged , , , , , | 6 Comments

Fourier Transforms of Boolean Functions • 2

Posted on June 4, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Twin Primes Are Useful Note.  Just another sheet of scratch paper, exploring possible alternatives to the Fourier transforms in the previous post.  As a rule, I like to keep Boolean problems in Boolean … Continue reading →

Posted in Boolean Functions, Computational Complexity, Fourier Transforms, Harmonic Analysis, Logic, Mathematics, Propositional Calculus | Tagged , , , , , , | Leave a comment

Wherefore Aught?

Posted on June 1, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Why Is There Something? Here is another one of those eternally recurring ideas echoed inimitably by C.S. Peirce in his sketch of a Cosmogonic Philosophy. It would suppose that in the beginning,—infinitely remote,—there was … Continue reading →

Posted in C.S. Peirce, Cosmogony, Evolution, Existence, Natural Law, Peirce, Philosophy, References, Sources | Tagged , , , , , , , , | 2 Comments