Tag Archives: Proof Theory

Charles Sanders Peirce, George Spencer Brown, and Me • 11

There’s a new Laws of Form group in town.  James Bowery et al. have just revived the earlier group on a new platform and everything looks pretty handy so far.  There’s an honest-to-goodness 60s vibe about it for me since … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Animated Logical Graphs • 52

Re: Richard J. Lipton • The Future Of Mathematics? • Is The End Near? Re: Peirce List • Jon Alan Schmidt Peirce’s explorations in logic and the theory of signs opened several directions of generalization from logics of complete information … 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 • 51

Re: Richard J. Lipton • The Future Of Mathematics? • Is The End Near? Synchronicity being what it is, a long-running discussion on the Peirce List just gave me a handy bridge to a topic I’ve been meaning to take … 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 • 50

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) (46) (47) (48) (49) In the last of our six ways of looking at the Peirce duality between entitative and existential interpretations, we consider … 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 • 49

Re: Richard J. Lipton • The Art Of Math Re: Animated Logical Graphs • (30) (45) (46) (47) (48) Dualities are symmetries of order two and symmetries bear on complexity by reducing its measure in proportion to their order.  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 , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

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

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 • 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 7 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Problems In Philosophy • 12

Re: R.J. Lipton and K.W. Regan • The Night Of The Ethical Algorithm Re: K.W. Regan • The Election Night Time Warp Re: Ontolog Forum • John Sowa JFS: C.S. Peirce made a very clear and sharp distinction between formal … 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 , , , , , , , , , , , , , , , , , , , | 1 Comment