Tag Archives: Theorem Proving

Animated Logical Graphs • 13

Posted on May 24, 2019 by Jon Awbrey

Cf: Survey of Animated Logical Graphs The blog post linked above updates my Survey of Resources for Animated Logical Graphs.  It contains links to basic expositions and extended discussions of the graphs themselves, deriving from the Alpha Graphs C.S. Peirce used … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Survey of Animated Logical Graphs • 2

Posted on May 22, 2019 by Jon Awbrey

This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years.  After that I’ll look to organizing … Continue reading →

Posted in Abstraction, Amphecks, Animata, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Surveys, Theorem Proving, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 19 Comments

Animated Logical Graphs • 12

Posted on January 31, 2018 by Jon Awbrey

Re: Facebook Discussion • Meredith Bricken Mills I’ve always been fond of picture proofs — it was one of the things that drew me to graph theory, topology, and the logical graphs of C.S. Peirce and Spencer Brown in the first place.  … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Animated Logical Graphs • 11

Posted on January 30, 2018 by Jon Awbrey

Re: Richard Coyne • Inside Out Logic Venn diagrams make for very iconic representations of their universes of discourse.  That is one of the main sources of their intuitive utility and also the main source of their logical limitations — … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Charles Sanders Peirce, George Spencer Brown, and Me • 10

Posted on August 25, 2017 by Jon Awbrey

With any formal system it is easy to spend a long time roughing out primitives and reviewing first principles before getting on to practical applications, and logical graphs are no different in that respect.  But the promise of clearer and more … 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

Charles Sanders Peirce, George Spencer Brown, and Me • 9

Posted on August 22, 2017 by Jon Awbrey

Re: Boundary Logic A wider field of investigation opens up at this point, spanning the diversity of interactions among languages we use, and systems of signs in general, to the thoughts ever streaming through our heads, to the universes we … 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 • 8

Posted on August 22, 2017 by Jon Awbrey

Re: Boundary Logic For me, the heart of the matter is “what is the purpose of logic and what is the purpose of mathematics and what is their relationship?” There are semiotic situations which appear to violate the initial conditions … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 7 Comments

Charles Sanders Peirce, George Spencer Brown, and Me • 7

Posted on August 21, 2017 by Jon Awbrey

A statement that implies both and is called a false statement, and anyone can prove anything at all from a false statement, as we all too frequently observe on the political front these days. There is however a reasonable way … 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 • 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