Category Archives: Peirce

Precursors Of Category Theory • 5

Posted on May 29, 2024 by Jon Awbrey

A demonstration rests in a finite number of steps. G. Spencer Brown • Laws of Form David Hilbert • “On the Infinite” (1925) Finally, let us recall our real subject and, so far as the infinite is concerned, draw the … 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

Precursors Of Category Theory • 4

Posted on May 28, 2024 by Jon Awbrey

C.S. Peirce • “Prolegomena to an Apology for Pragmaticism” (1906) I will now say a few words about what you have called Categories, but for which I prefer the designation Predicaments, and which you have explained as predicates of predicates. … 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

Precursors Of Category Theory • 3

Posted on May 27, 2024 by Jon Awbrey

Act only according to that maxim by which you can at the same time will that it should become a universal law. Immanuel Kant (1785) C.S. Peirce • “On a New List of Categories” (1867) §1.  This paper is based … 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

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

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

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 5 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

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 , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments