Tag Archives: Peirce

Animated Logical Graphs • 51

Posted on December 20, 2020 by Jon Awbrey

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 2

Posted on December 16, 2020 by Jon Awbrey

This is a Survey of blog and wiki posts on three elementary forms of inference, as recognized by a logical tradition extending from Aristotle through Charles S. Peirce.  Particular attention is paid to the way these inferential rudiments combine to … Continue reading →

Posted in Abduction, Aristotle, C.S. Peirce, Deduction, Dewey, Discovery, Doubt, Fixation of Belief, Functional Logic, Icon Index Symbol, Induction, Inference, Information, Inquiry, Invention, Logic, Logic of Science, Mathematics, Morphism, Paradigmata, Paradigms, Pattern Recognition, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Scientific Inquiry, Scientific Method, Semiotics, Sign Relations, Surveys, Syllogism, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Abduction, Deduction, Induction, Analogy, Inquiry • 30

Posted on December 15, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Future Of Mathematics? • Is The End Near? Re: “Proofs Are Not As Important As Discoveries” (PANAIAD). Conjecture and Discovery fall under the heading of Abductive Inference (AI’s missing grape). About which more when I pull … Continue reading →

Posted in Abduction, Analogy, Aristotle, Artificial Intelligence, C.S. Peirce, Deduction, Induction, Inquiry, Inquiry Driven Systems, Intelligent Systems Engineering, Logic, Mental Models, Peirce, Scientific Method, Semiotics, Systems | Tagged , , , , , , , , , , , , , , , | 5 Comments

Animated Logical Graphs • 50

Posted on December 5, 2020 by Jon Awbrey

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Animated Logical Graphs • 49

Posted on December 3, 2020 by Jon Awbrey

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Animated Logical Graphs • 48

Posted on November 30, 2020 by Jon Awbrey

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Animated Logical Graphs • 47

Posted on November 27, 2020 by Jon Awbrey

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Animated Logical Graphs • 46

Posted on November 15, 2020 by Jon Awbrey

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 14 Comments

Animated Logical Graphs • 45

Posted on November 12, 2020 by Jon Awbrey

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments

Problems In Philosophy • 12

Posted on November 10, 2020 by Jon Awbrey

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