Tag Archives: Relation Theory

Sign Relations, Triadic Relations, Relation Theory • 1

Posted on October 10, 2020 by Jon Awbrey

To understand how signs work in Peirce’s theory of triadic sign relations, or “semiotics”, we have to understand, in order of increasing generality, sign relations, triadic relations, and relations in general, each as conceived in Peirce’s logic of relative terms … Continue reading →

Posted in C.S. Peirce, Icon Index Symbol, Information, Inquiry Driven Systems, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity, Visualization | Tagged , , , , , , , , , , , , , , , | 12 Comments

Precursors Of Category Theory • Discussion 3

Posted on September 25, 2020 by Jon Awbrey

Take your place on The Great Mandala As it moves through your brief moment of time. Win or lose now you must choose now And if you lose you’re only losing your life. Peter Yarrow Re: Ontolog Forum • Alex … 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 , , , , , , , , , , , , , , , , | 6 Comments

Precursors Of Category Theory • Discussion 2

Posted on September 21, 2020 by Jon Awbrey

Re: Ontolog Forum • Alex Shkotin AS: Looking at “categories, or types” in Precursors Of Category Theory • Hilbert and Ackermann what do you think of to say “Precursors Of Type Theory” as Category Theory is a math discipline?   … 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 , , , , , , , , , , , , , , , , | 6 Comments

Survey of Precursors Of Category Theory • 2

Posted on September 20, 2020 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 , , , , , , , , , , , , , , , , , , , , , , | 7 Comments

Precursors Of Category Theory • Discussion 1

Posted on September 13, 2020 by Jon Awbrey

Re: FB | Medieval Logic • EB • JA • JA • EB • JA • EB • JA • JA • EB JA:  In the logic of Aristotle categories are adjuncts to reasoning designed to resolve ambiguities and thus … 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 , , , , , , , , , , , , , , , , | 6 Comments

Sign Relations • Discussion 10

Posted on July 9, 2020 by Jon Awbrey

Anthesis • Definition • Signs and Inquiry • Examples Dyadic Aspects • Denotation • Connotation • Ennotation Semiotic Equivalence Relations • (1) • (2) Re: Cybernetics • Klaus Krippendorff • Bernard Scott Re: Ontolog • Mihai Nadin • John Sowa … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 8 Comments

Sign Relations • Discussion 9

Posted on July 5, 2020 by Jon Awbrey

Re: Sign Relations • Ennotation Re: Peirce List • Helmut Raulien Dear Helmut, Thanks for your comments.  They prompt me to say a little more about the mathematical character of the sign relational models I’m using. Peirce without mathematics is … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 7 Comments

Sign Relations • Semiotic Equivalence Relations 2

Posted on July 3, 2020 by Jon Awbrey

A few items of notation are useful in discussing equivalence relations in general and semiotic equivalence relations in particular. In general, if is an equivalence relation on a set then every element of belongs to a unique equivalence class under … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 3 Comments

Sign Relations • Discussion 8

Posted on July 2, 2020 by Jon Awbrey

Re: Sign Relations • Ennotation Re: Peirce List • Helmut Raulien Dear Helmut, The important thing now is to extend our perspective beyond one sign at a time and one object, sign, interpretant at a time to comprehending a sign … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 8 Comments

Sign Relations • Semiotic Equivalence Relations 1

Posted on July 1, 2020 by Jon Awbrey

A semiotic equivalence relation (SER) is a special type of equivalence relation arising in the analysis of sign relations.  Generally speaking, any equivalence relation induces a partition of the underlying set of elements, known as the domain or space of the … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Philosophy, Pragmatic Semiotic Information, Pragmatism, Relation Theory, Semiotics, Sign Relations, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 3 Comments