Category Archives: C.S. Peirce

Interpretive Duality in Logical Graphs • 5

Posted on April 26, 2024 by Jon Awbrey

Re: Interpretive Duality in Logical Graphs • 1 Another way of looking at interpretive duality in logical graphs is given by the following Table, showing how logical graphs denote the sixteen boolean functions on two variables under entitative and existential … 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, Interpretive Duality, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Interpretive Duality, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | 1 Comment

Interpretive Duality in Logical Graphs • 4

Posted on April 25, 2024 by Jon Awbrey

Re: Interpretive Duality in Logical Graphs • (1) • (2) • (3) Last time we took up Peirce’s law, and saw how it might be expressed in two different ways, under the entitative and existential interpretations, respectively. The next thing … Continue reading →

Interpretive Duality in Logical Graphs • 3

Posted on April 24, 2024 by Jon Awbrey

Re: Interpretive Duality in Logical Graphs • (1) • (2) For a sense of how the choice of interpretation bears on cases beyond the bare minimum complexity let us start with the familiar example of Peirce’s law, commonly expressed in … Continue reading →

Interpretive Duality in Logical Graphs • 2

Posted on April 23, 2024 by Jon Awbrey

Re: Interpretive Duality in Logical Graphs • 1 A logical concept represented by a boolean variable has its extension, the cases it covers in a designated universe of discourse, and its comprehension (or intension), the properties it implies in a … Continue reading →

Interpretive Duality in Logical Graphs • 1

Posted on April 22, 2024 by Jon Awbrey

The duality between Entitative and Existential interpretations of logical graphs is a good example of a mathematical symmetry, in this case a symmetry of order two. Symmetries of this and higher orders give us conceptual handles on excess complexity in … Continue reading →

Operator Variables in Logical Graphs • 12

Posted on April 21, 2024 by Jon Awbrey

Re: Operator Variables in Logical Graphs • 11 The rules given in the previous post for evaluating cactus graphs were given in purely formal terms, that is, by referring to the mathematical forms of cacti without mentioning their potential for … 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 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 | 1 Comment

Operator Variables in Logical Graphs • 11

Posted on April 20, 2024 by Jon Awbrey

Re: Futures Of Logical Graphs • Themes and Variations This post and the next wrap up the Themes and Variations section of my speculation on Futures of Logical Graphs. I made an effort to “show my work”, reviewing the steps … 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 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 | 2 Comments

Operator Variables in Logical Graphs • 10

Posted on April 18, 2024 by Jon Awbrey

Re: Operator Variables in Logical Graphs • 9 Let’s examine the Formal Operation Table for the third in our series of reflective forms to see if we can elicit the general pattern. Alternatively, if we think in terms of the corresponding … 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 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 | 1 Comment

Operator Variables in Logical Graphs • 9

Posted on April 17, 2024 by Jon Awbrey

The following Table will suffice to show how the “streamer‑cross” forms C.S. Peirce used in his essay on “Qualitative Logic” and Spencer Brown used in his Laws of Form, as they are extended through successive steps of controlled reflection, translate into syntactic … 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 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 | 2 Comments

Operator Variables in Logical Graphs • 8

Posted on April 16, 2024 by Jon Awbrey

Re: Operator Variables in Logical Graphs • 7 A trick of discovery I learned by observing Peirce’s working methods, more than anything he wrote outright, might be put in the following words. Take what is constant, Treat it as variable, … 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 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 | 1 Comment

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Recent Posts
- Interpretive Duality in Logical Graphs • 5
- Interpretive Duality in Logical Graphs • 4
- Interpretive Duality in Logical Graphs • 3
- Interpretive Duality in Logical Graphs • 2
- Interpretive Duality in Logical Graphs • 1
- Operator Variables in Logical Graphs • 12
- Operator Variables in Logical Graphs • 11
- Operator Variables in Logical Graphs • 10
- Operator Variables in Logical Graphs • 9
- Operator Variables in Logical Graphs • 8
- Operator Variables in Logical Graphs • 7
- Operator Variables in Logical Graphs • 6
- Operator Variables in Logical Graphs • 5
- Operator Variables in Logical Graphs • 4
- Operator Variables in Logical Graphs • 3
- Operator Variables in Logical Graphs • Discussion 2
- Operator Variables in Logical Graphs • Discussion 1
- Operator Variables in Logical Graphs • 2
- Operator Variables in Logical Graphs • 1
- Peirce’s 1885 “Algebra of Logic” • Discussion 2
- Peirce’s 1885 “Algebra of Logic” • Discussion 1
- Peirce’s 1885 “Algebra of Logic” • Selection 4
- Peirce’s 1885 “Algebra of Logic” • Selection 3
- Peirce’s 1885 “Algebra of Logic” • Selection 2
- Peirce’s 1885 “Algebra of Logic” • Selection 1
- Survey of Relation Theory • 8
- Pragmatic Semiotic Information • Comment 3
- Pragmatic Semiotic Information • Comment 2
- Pragmatic Semiotic Information • Comment 1
- Survey of Animated Logical Graphs • 7
- Pragmatic Semiotic Information • 9
- Pragmatic Semiotic Information • 8
- Pragmatic Semiotic Information • 7
- Pragmatic Semiotic Information • 6
- Pragmatic Semiotic Information • 5
- Pragmatic Semiotic Information • 4
- Pragmatic Semiotic Information • 3
- Pragmatic Semiotic Information • 2
- Pragmatic Semiotic Information • 1
- Survey of Pragmatic Semiotic Information • 8
- Being In Time
- Survey of Inquiry Driven Systems • 6
- Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 4
- Survey of Theme One Program • 6
- Survey of Differential Logic • 7
- Sign Relations, Triadic Relations, Relation Theory • Discussion 12
- Sign Relations, Triadic Relations, Relation Theory • 4
- Sign Relations, Triadic Relations, Relation Theory • 3
- Sign Relations, Triadic Relations, Relation Theory • 2
- Sign Relations, Triadic Relations, Relation Theory • 1

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