Category Archives: Mathematics

Category Theory • Comment 1

I’m deep in the middle of upgrading my intro to sign relations and I am determined to stick to it this time but there will be a phase when it’s critical to bring category theory to bear on the development.  … Continue reading

Posted in Abstraction, C.S. Peirce, Category Theory, Differential Logic, Graph Theory, Group Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Categories, Research Technology, Scientific Method, Semiotics, Set Theory, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , | Leave a 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

Survey of Inquiry Driven Systems • 2

This is a Survey of previous blog and wiki posts on Inquiry Driven Systems, material I plan to refine toward a more compact and systematic treatment of the subject. An inquiry driven system is a system having among its state … Continue reading

Posted in Abduction, Action, Adaptive Systems, Aristotle, Artificial Intelligence, Automated Research Tools, Change, Cognitive Science, Communication, Cybernetics, Deduction, Descartes, Dewey, Discovery, Doubt, Education, Educational Systems Design, Educational Technology, Fixation of Belief, Induction, Information, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretation, Invention, Kant, Knowledge, Learning, Learning Theory, Logic, Logic of Science, Mathematics, Mental Models, Peirce, Pragmatic Maxim, Pragmatism, Process Thinking, Scientific Inquiry, Semiotics, Sign Relations, Surveys, Teaching, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Peirce’s Categories • 21

Re: Peirce List • Robert Marty Re: Peirce List • Robert Marty Dear Robert, Let’s go back to a point where paths diverged in the yarrow wood and a lot of synchronicity was lost … Variant understandings of words like … Continue reading

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | Leave a comment