Tag Archives: Diagrammatic Reasoning

Animated Logical Graphs • 48

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) (46) (47) A more graphic picture of Peirce duality is given by the next Table, which shows how logical graphs map to venn diagrams … Continue reading

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Animated Logical Graphs • 47

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) (46) A logical concept represented by a boolean variable has its extension, the cases it covers in a designated universe of discourse, and its … 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 • 46

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) Another way of looking at Peirce duality is given by the following Table, which shows how logical graphs denote boolean functions under entitative and … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Animated Logical Graphs • 45

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) There’s a nice interplay between geometric and logical dualities in C.S. Peirce’s graphical systems of logic, rooted in his discovery of the amphecks and and flowering … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Animated Logical Graphs • 44

Re: FB | Ecology Of Systems Thinking • Richard Saunders RS:  DNA and proteins might be good places to look for logical graphs in nature since our tech for mapping those structures has become fairly proficient lately.  Do you think … 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 • 43

Re: FB | Ecology Of Systems Thinking • Richard Saunders RS:  I wonder if we might find such graphs in the physical microstructures of brains, cells, proteins, etc. Dear Richard, You are reading my mind.  See the following post 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Animated Logical Graphs • 42

Re: Richard J. Lipton • Logical Complexity Of Proofs Re: Animated Logical Graphs • (35) (36) (37) (38) (39) (40) (41) Now that our propositional formula is cast in the form of a graph its evaluation proceeds as a sequence … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Animated Logical Graphs • 41

Re: Richard J. Lipton • Logical Complexity Of Proofs Re: Animated Logical Graphs • (35) (36) (37) (38) (39) (40) Last time we looked at a formula of propositional logic Leibniz called a Praeclarum Theorema (PT).  We don’t concur it’s … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Animated Logical Graphs • 40

Re: Richard J. Lipton • Logical Complexity Of Proofs Re: Animated Logical Graphs • (35) (36) (37) (38) (39) One way to see the difference between insight proofs and routine proofs is to pick a single example of a theorem … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Animated Logical Graphs • 39

Re: Richard J. Lipton • Logical Complexity Of Proofs Happy Peirce’s Birthday, Everyone ❢ We’ve been discussing aspects of proof style arising in connection with the complexity of proofs.  In previous posts we took up (1) the aspect of formal … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments