Category Archives: Mathematics

Objects, Models, Theories • 2

Posted on November 20, 2013 by Jon Awbrey

Re: K.W. Regan • The Graph Of Math Re: Artem Kaznatcheev • Three Types Of Mathematical Models What — if anything — is the common sense that connects the different senses of the word model, as it has been used … Continue reading →

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 10 Comments

Alpha Now, Omega Later • 1

Posted on November 16, 2013 by Jon Awbrey

I am still in the middle of trying to catch up on some long put-off work but recent discussions of logical graphs and physics and the like on the Peirce List have bestirred me from my grindstone long enough to … Continue reading →

Posted in C.S. Peirce, Differential Logic, Dynamical Systems, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Semiotics, Sign Relations, Spencer Brown | Tagged , , , , , , , , , , , | 8 Comments

“What we’ve got here is (a) failure to communicate” • 6

Posted on November 15, 2013 by Jon Awbrey

Excerpt from Warren S. McCulloch, “What Is a Number, that a Man May Know It, and a Man, that He May Know a Number?” (1960) Please remember that we are not now concerned with the physics and chemistry, the anatomy … Continue reading →

Posted in Abduction, Amphecks, Aristotle, Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Combinatorics, Deduction, Duns Scotus, Induction, Leibniz, Logic, Logic of Relatives, Mathematics, Neural Models, Ockham, Peirce, Propositional Logic, Psychons, Relation Theory, Sources, Triadic Relations, Warren S. McCulloch, William James | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Peircean Semiotics and Triadic Sign Relations • 3

Posted on November 1, 2013 by Jon Awbrey

Having labored mightily to bring out a new edition of my article on sign relations, including material on the pivotal concept of semiotic equivalence relations which had fallen into obscurity elsewhere, I thought it worth the candle to post a … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Logic of Relatives, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | 2 Comments

Definition and Determination • 10

Posted on October 7, 2013 by Jon Awbrey

The moment, then, that we pass from nothing and the vacuity of being to any content or sphere, we come at once to a composite content and sphere.  In fact, extension and comprehension — like space and time — are … Continue reading →

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Indication, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Peirce, Semiotics, Sources | Tagged , , , , , , , , , , , , , , , , | 11 Comments

Definition and Determination • 9

Posted on September 12, 2013 by Jon Awbrey

Re: Cathy O’Neil • The Art of Definition In classical logical traditions the concepts of definition and determination are closely related and their bond acquires all the more force if you view the overarching concept of constraint from an information-theoretic … Continue reading →

Posted in C.S. Peirce, Definition, Determination, Inquiry, Logic, Mathematics, Peirce, Phenomenology, Semiotics | Tagged , , , , , , , , | 7 Comments

Objects, Models, Theories • 1

Posted on September 10, 2013 by Jon Awbrey

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839 Re: Artem Kaznatcheev • Three Types of Mathematical Models Comment 1 In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another.  Logicians … Continue reading →

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 11 Comments

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