Category Archives: Logic

Objects, Models, Theories : 4

Posted on November 27, 2013 by Jon Awbrey

I need to stay with this problem a while … What are objects, models, theories, and how do they relate to one another? In contemplating this problem I always find it helpful to ruminate on the diagram shown above — … Continue reading →

Posted in Adaptive Systems, Analogy, Aristotle, Artificial Intelligence, Biological Systems, C.S. Peirce, Computational Complexity, Evolution, Gödel, Information, Information Theory, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mental Models, Model Theory, Natural Intelligence, Paradigms, Peirce, Pragmata, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Objects, Models, Theories : 3

Posted on November 21, 2013 by Jon Awbrey

Re: Peirce List Discussion • Tom Gollier Here my task is to build bridges between several different classical and contemporary uses of the word model, so I don’t have the luxury of complete control over the words in play but … Continue reading →

Posted in Adaptive Systems, Analogy, Aristotle, Artificial Intelligence, Biological Systems, C.S. Peirce, Computational Complexity, Evolution, Gödel, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mental Models, Model Theory, Natural Intelligence, Peirce, Pragmata, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

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, Aristotle, Artificial Intelligence, Biological Systems, C.S. Peirce, Computational Complexity, Evolution, Gödel, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mental Models, Model Theory, Natural Intelligence, Peirce, Pragmata, Semiotics | Tagged , , , , , , , , , , , , , , , , , , , , , | 8 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

Differential Analytic Turing Automata • Discussion 1

Posted on October 14, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Proving Cook’s Theorem Synchronicity Rules❢ I just started reworking an old exposition of mine on Cook’s Theorem, where I borrowed the Parity Function example from Wilf (1986), Algorithms and Complexity, and translated it … Continue reading →

Posted in Algorithms, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Analytic Turing Automata, Differential Logic, Logic, Logical Graphs, Peirce, Propositional Calculus, Turing Machines | 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 , , , , , , , , , , , , , , , , , , | 8 Comments