Monthly Archives: February 2021

Animated Logical Graphs • 62

Posted on February 28, 2021 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (57) • (58) • (59) • (60) • (61) Another way of looking at the dual interpretation of logical graphs from a group-theoretic point of view … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 15 Comments

Animated Logical Graphs • 61

Posted on February 26, 2021 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (57) • (58) • (59) • (60) Anything called a duality is naturally associated with a transformation group of order 2, say a group acting on … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 16 Comments

Animated Logical Graphs • 60

Posted on February 21, 2021 by Jon Awbrey

Re: Laws of Form • Lyle Anderson Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (57) • (58) • (59) LA: Definition 1.  A group is a set together with a binary operation satisfying … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments

Animated Logical Graphs • 59

Posted on February 21, 2021 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (57) • (58) Returning to the theme of duality and more general group-theoretic symmetries in logical graphs, here’s an improved version of the introduction I gave two … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments

Double Negation • 3

Posted on February 19, 2021 by Jon Awbrey

Re: Double Negation • (1) • (2) The steps of the proof of double negation are replayed in the following animation. Resources Logic Syllabus Logical Graphs • Informal Introduction • Formal Development • Proof Animations Futures Of Logical Graphs Propositional … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Double Negation • 2

Posted on February 18, 2021 by Jon Awbrey

If we stand back for a moment to regard the structure of an implicational logic, such as Whitehead and Russell’s, we see that it is fully contained in that of an equivalence logic.  The difference is in the kind of … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Double Negation • 1

Posted on February 14, 2021 by Jon Awbrey

The article and section linked below introduce the Double Negation Theorem (DNT) in the manner described as Consequence 1 or Reflection by Spencer Brown. Logical Graphs • Double Negation Converting the planar figures used by Peirce and Spencer Brown to the … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Animated Logical Graphs • 58

Posted on February 11, 2021 by Jon Awbrey

Re: Laws of Form • Lyle Anderson Re: Brading, K., Castellani, E., and Teh, N., (2017), “Symmetry and Symmetry Breaking”, The Stanford Encyclopedia of Philosophy (Winter 2017), Edward N. Zalta (ed.).  Online. Dear Lyle, Thanks for the link to the … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 19 Comments

Animated Logical Graphs • 57

Posted on February 11, 2021 by Jon Awbrey

All other sciences without exception depend upon the principles of mathematics;  and mathematics borrows nothing from them but hints. C.S. Peirce • “Logic of Number” A principal intention of this essay is to separate what are known as algebras of … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 20 Comments

Pragmatic Semiotic Information • Discussion 21

Posted on February 8, 2021 by Jon Awbrey

Re: FB | Medieval Logic • Kollbjorn Oldtheyn • Edward Buckner On the question of which later developments in logic Peirce anticipated, I’ve been more focused on the points where he saw through to features we would not see again … Continue reading →

Posted in Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Intention, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments