Tag Archives: Relation Theory

Precursors Of Category Theory • Discussion 2

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 , , , , , , , , , , , , , , , , | 1 Comment

Survey of Precursors Of Category Theory • 2

A few years ago I began a sketch on the “Precursors of Category Theory”, aiming to trace the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of … 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 , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Precursors Of Category Theory • Discussion 1

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 , , , , , , , , , , , , , , , , | 1 Comment

Sign Relations • Discussion 10

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 , , , , , , , , , , , , , , | Leave a comment

Sign Relations • Discussion 9

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 , , , , , , , , , , , , , , | Leave a comment

Sign Relations • Semiotic Equivalence Relations 2

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 , , , , , , , , , , , , , , | 1 Comment

Sign Relations • Discussion 8

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 , , , , , , , , , , , , , , | 1 Comment

Sign Relations • Semiotic Equivalence Relations 1

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 , , , , , , , , , , , , , , | 1 Comment

Sign Relations • Ennotation

A third aspect of a sign’s complete meaning concerns the reference its objects have to its interpretants, which has no standard name in semiotics.  It would be called an induced relation in graph theory or the result of relational composition … 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 7

Re: Sign Relations • Definition Re: Ontolog Forum • Alex Shkotin Dear Alex, Please forgive the long and winding dissertation.  I’ve been through many discussions of Peirce’s definition of “logic as formal semiotic” but I keep discovering new ways of … 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 , , , , , , , , , , , , , , | Leave a comment