Category Archives: Logic

Survey of Animated Logical Graphs • 3

Posted on August 23, 2020 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 Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Differential Logic, 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 , , , , , , , , , , , , , , , , , , , , , , , , | 26 Comments

Animated Logical Graphs • 37

Posted on August 22, 2020 by Jon Awbrey

Re: Richard J. Lipton • Logical Complexity Of Proofs Another dimension of proof style has to do with how much information is kept or lost as the argument develops.  For the moment let’s focus on classical deductive reasoning at 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 13 Comments

Animated Logical Graphs • 36

Posted on August 21, 2020 by Jon Awbrey

Re: Richard J. Lipton • Logical Complexity Of Proofs Dear Dick, You asked, “Is this measure, the logical flow of a proof, of any interest?” I was not sure how you define the measure of flow in a proof — … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 13 Comments

Animated Logical Graphs • 35

Posted on August 19, 2020 by Jon Awbrey

Re: Richard J. Lipton • Logical Complexity Of Proofs The smoothest way I know to do propositional calculus is by using minimal negation operators as primitives, parsing propositional formulas into (painted and rooted) cactus graphs, and using the appropriate extension … 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 13 Comments

Mathematical Method • Discussion 7

Posted on August 15, 2020 by Jon Awbrey

Re: Ontolog Forum • Alex Shkotin Dear Alex, You raised the following point: AS: One important usage of a sign is as an element of a language, especially a formal one, i.e. with a formal grammar. For context you cited … Continue reading →

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Mathematical Method • Discussion 6

Posted on August 13, 2020 by Jon Awbrey

Re: Ontolog Forum • Alex Shkotin Dear Alex, Thanks for the very apt segue from Jon Barwise — Modern mathematics might be described as the science of abstract objects, be they real numbers, functions, surfaces, algebraic structures or whatever.  Mathematical … Continue reading →

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Animated Logical Graphs • 34

Posted on August 11, 2020 by Jon Awbrey

Re: Ontolog Forum • John Sowa Re: Peirce List • John Sowa Dear John, I can’t imagine why anyone would bother with Peirce’s logic if it’s just Frege and Russell in a different syntax, which has been the opinion I … 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

Mathematical Method • Discussion 5

Posted on August 10, 2020 by Jon Awbrey

Re: Ontolog Forum • Paul Tyson Dear Paul, “How We Think” is a topic for the descriptive science of psychology, and its ways are legion beyond definitive or exhaustive description. “How We Ought To Think” if we wish to succeed … Continue reading →

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Mathematical Method • Discussion 4

Posted on August 8, 2020 by Jon Awbrey

Re: Peirce List • Helmut Raulien Dear Helmut, It’s one of the occupational hazards of the classifying mind that one can start out consciously characterizing aspects of real situations and end up unwittingly thinking one’s gotten everything under the sun sorted … Continue reading →

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Mathematical Method • Discussion 3

Posted on August 7, 2020 by Jon Awbrey

Re: Peirce List • John Sowa • Auke van Breemen • Jon Awbrey • Gary Fuhrman Dear Gary, Auke van Breemen wrote: AvB: It seems to come down to:  never consider the textual production of a scientist only in itself, … Continue reading →

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged , , , , , , , , , , , , , , , , | Leave a comment