Author Archives: Jon Awbrey

Precursors Of Category Theory • 2

Posted on May 26, 2024 by Jon Awbrey

Thanks to art, instead of seeing one world only, our own, we see that world multiply itself and we have at our disposal as many worlds as there are original artists … ☙ Marcel Proust When it comes to looking … Continue reading →

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Precursors Of Category Theory • 1

Posted on May 25, 2024 by Jon Awbrey

A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  My notes on the project … Continue reading →

Posted in Abstraction, Ackermann, Aristotle, C.S. Peirce, Carnap, Category Theory, Hilbert, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Relation Theory, Saunders Mac Lane, Sign Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Survey of Precursors Of Category Theory • 5

Posted on May 24, 2024 by Jon Awbrey

A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of resources on … Continue reading →

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Transformations of Logical Graphs • Discussion 1

Posted on May 22, 2024 by Jon Awbrey

Re: Laws of Form • Mauro Bertani Dear Mauro, The couple of pages linked below give the clearest and quickest introduction I’ve been able to manage so far when it comes to the elements of logical graphs, at least, in … 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 , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Transformations of Logical Graphs • 14

Posted on May 21, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) • (12) • (13) Completing our scan of the Table in Episode 8, the last orbit up for consideration contains the logical graphs for the boolean … 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 , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Transformations of Logical Graphs • 13

Posted on May 18, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) • (12) Continuing our scan of the Table in Episode 8, the next orbit contains the logical graphs for the boolean functions and The boolean … 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 , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Transformations of Logical Graphs • 12

Posted on May 16, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) Re: Interpretive Duality as Sign Relation • Orbit Order Taking from our wallets an old schedule of orbits, let’s review the classes of logical graphs … 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 , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Transformations of Logical Graphs • 11

Posted on May 15, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) Continuing our scan of the Table in Episode 8, the next two orbits contain the logical graphs for the boolean functions in that order.  A first glance … 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 , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Transformations of Logical Graphs • 10

Posted on May 14, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (4) • (5) • (6) • (7) • (8) • (9) After the four orbits of self‑dual logical graphs we come to six orbits of dual pairs.  In no particular order of importance, we … 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 , , , , , , , , , , , , , , , , , , , , , , , , | 7 Comments

Transformations of Logical Graphs • 9

Posted on May 13, 2024 by Jon Awbrey

Semiotic Transformations Re: Transformations of Logical Graphs • (4) • (5) • (6) • (7) • (8) Last time we took up the four singleton orbits in the action of on and saw each consists of a single logical graph … 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 , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments