Category Archives: Model Theory

Charles Sanders Peirce, George Spencer Brown, and Me • 6

Posted on August 18, 2017 by Jon Awbrey

The formal system of logical graphs is defined by a foursome of formal equations, called initials when regarded purely formally, in abstraction from potential interpretations, and called axioms when interpreted as logical equivalences.  There are two arithmetic initials and two … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Charles Sanders Peirce, George Spencer Brown, and Me • 5

Posted on August 12, 2017 by Jon Awbrey

Here are blog and wiki versions of an article I wrote on Peirce’s Law, an axiom or theorem (depending on your choice of logical basis) which distinguishes classical from intuitionistic propositional calculus.  Aside from its pivotal logical status it affords … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Charles Sanders Peirce, George Spencer Brown, and Me • 4

Posted on August 6, 2017 by Jon Awbrey

Two things impacting my studies of Peirce and Spencer Brown over the years were my parallel studies in mathematics and computer science.  In the overlap between those areas came courses in logic, mathematical linguistics, and the theory of formal languages, … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Charles Sanders Peirce, George Spencer Brown, and Me • 3

Posted on July 31, 2017 by Jon Awbrey

Re: Laws of Form There are a number of “difficulties at the beginning” that arise here.  I’ve been trying to get to the point where I can respond to James Bowery’s initial comments and also to questions about the relation … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Charles Sanders Peirce, George Spencer Brown, and Me • 2

Posted on July 21, 2017 by Jon Awbrey

Re: Laws of Form I’m making an effort to present this material in a more gradual and logical order than I’ve ever managed to do before.  There are issues about the relationship between episodic and semantic memory that are giving … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Charles Sanders Peirce, George Spencer Brown, and Me • 1

Posted on July 20, 2017 by Jon Awbrey

It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown’s Laws of Form in … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Peirce, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Charles Sanders Peirce, George Spencer Brown, and Me

Posted on July 19, 2017 by Jon Awbrey

James Bowery left a comment on my blog and opened a thread in the Yahoo! group devoted to discussing the mathematics of George Spencer Brown’s Laws of Form.  I’ve been meaning to join that discussion as soon as I could work … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Analytic Turing Automata, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

¿Shifting Paradigms? • 5

Posted on July 16, 2017 by Jon Awbrey

Re: Peter Cameron • Infinity and Foundation We always encounter a multitude of problems whenever we try to rationalize mathematics by reducing it to logic, where logic itself is reduced to a purely deductive style.  A number of thinkers have … Continue reading →

Posted in Algorithms, Boole, C.S. Peirce, Combinatorics, Computation, Foundations of Mathematics, Inquiry, Laws of Form, Leibniz, Logic, Mathematics, Model Theory, Paradigms, Peirce, Proof Theory, Spencer Brown | Tagged , , , , , , , , , , , , , , , | 4 Comments

Animated Logical Graphs • 10

Posted on March 3, 2017 by Jon Awbrey

Re: Peirce List Discussion • Charles Pyle Let’s consider Peirce’s logical graphs at the alpha level, the abstract forms of which can be interpreted for propositional logic.  I say “can be interpreted” advisedly because the system of logical graphs itself … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Homunculomorphisms • 2

Posted on February 12, 2016 by Jon Awbrey

Re: John Baez • The Internal Model Principle There’s a far-ranging discussion that takes off from this point, touching on links among analogical reasoning, arrows and functors, cybernetic images, iconic versus symbolic representations, mental models, systems simulations, etc., and just … Continue reading →

Posted in Analogy, Ashby, Automata, Control Systems, Cybernetics, Homunculi, Homunculomorphisms, Iconicity, Information Theory, Inquiry, Inquiry Driven Systems, Intentionality, Internal Models, Logic, Logic of Science, Mathematics, Mental Models, Model Theory, Optimal Control, Peirce, Semiotics, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , | 1 Comment