Category Archives: Category Theory

Relations & Their Relatives • Discussion 25

Posted on July 30, 2024 by Jon Awbrey

Re: Daniel Everett • Polyunsaturated Predicates Re: Relations & Their Relatives • Discussion 24 Dear Daniel, I’ve been meaning to get back to this as it keeps coming up and it’s kind of important but it took me a while … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Rheme, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • Discussion 24

Posted on July 28, 2024 by Jon Awbrey

Re: Daniel Everett • Polyunsaturated Predicates DE: Among the several ideas Peirce and Frege came up with was the idea of a predicate before and after it is linked to its arguments.  Frege called the unlinked predicate unsaturated.  But Peirce … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Rheme, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 5 Comments

Precursors Of Category Theory • 6

Posted on May 30, 2024 by Jon Awbrey

Hilbert and Ackermann • Principles of Mathematical Logic (1928) For the intuitive interpretation on which we have hitherto based the predicate calculus, it was essential that the sentences and predicates should be sharply differentiated from the individuals, which occur as … 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 • 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

Survey of Relation Theory • 8

Posted on March 23, 2024 by Jon Awbrey

In the present Survey of blog and wiki resources for Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set‑theoretic constructions, many … Continue reading →

Posted in Algebra, Algebra of Logic, C.S. Peirce, Category Theory, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Graph Theory, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , | 9 Comments