Category Archives: Proof Theory

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

Problems In Philosophy • 3

Posted on February 8, 2016 by Jon Awbrey

Re: R.D. Mounce Making reality our friend is necessary to survival and finding good descriptions of reality is the better part of doing that, so I don’t imagine we have any less interest in truth than the Ancients.  From what … Continue reading →

Posted in Aesthetics, Computation, Computer Science, Ethics, Heap Problem, Logic, Mathematics, Model Theory, Normative Science, Paradox, Peirce, Philosophy, Pragmatism, Problem Solving, Proof Theory, Sorites | Tagged , , , , , , , , , , , , , , , | Leave a comment

Problems In Philosophy • 2

Posted on February 8, 2016 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • You Think We Have Problems Classical tradition views logic as a normative science, one whose object is truth.  This puts logic on a par with ethics, whose object is justice or morality in … Continue reading →

Posted in Aesthetics, Algorithms, Animata, Automata, Beauty, C.S. Peirce, Ethics, Inquiry, Justice, Logic, Model Theory, Normative Science, Peirce, Philosophy, Pragmatism, Problem Solving, Proof Theory, Summum Bonum, Truth, Virtue | Tagged , , , , , , , , , , , , , , , , , , , | 3 Comments

Animated Logical Graphs • 9

Posted on May 24, 2015 by Jon Awbrey

Re: Ken Regan • The Shapes of Computations The insight it takes to find a succinct axiom set for a theoretical domain falls under the heading of abductive or retroductive reasoning, a knack as yet refractory to computational attack, but … 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

Animated Logical Graphs • 8

Posted on May 23, 2015 by Jon Awbrey

Re: Ken Regan • The Shapes of Computations The most striking example of a “Primitive Insight Proof” (PIP❢) known to me is the Dawes–Utting proof of the Double Negation Theorem from the CSP–GSB axioms for propositional logic.  There is a … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments