Tag Archives: Logic of Relatives

Relations & Their Relatives • 2

Posted on August 1, 2024 by Jon Awbrey

What is the relationship between “logical relatives” and “mathematical relations”?  The word relative used as a noun in logic is short for relative term — as such it refers to an item of language used to denote a formal object. … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • 1

Posted on July 31, 2024 by Jon Awbrey

Sign relations are special cases of triadic relations in much the same way binary operations in mathematics are special cases of triadic relations.  It amounts to a minor complication that we participate in sign relations whenever we talk or think … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 3 Comments

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