Category Archives: Set Theory

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

Relation Theory • Discussion 1

Re: Cybernetics • Arthur Phillips Responding to what I’ll abductively interpret as a plea for relevance from the cybernetic galley, let me give a quick review of where we are in this many-oared expedition. Our reading of Ashby (see Survey … 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 , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Relation Theory • 4

In this Survey of blog and wiki posts on 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 of … 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 , , , , , , , , , , , , , , , , , , , , , , | 7 Comments

Indicator Functions • Discussion 1

Peter Smith, on his Logic Matters blog, asks the question, “What Is A Predicate?”, and considers a number of answers. There are of course other possible answers, and one I learned quite early on, arising very naturally in applying mathematical … Continue reading

Posted in Boole, Boolean Functions, C.S. Peirce, Category Theory, Indication, Indicator Functions, Logic, Mathematics, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Set Theory, Venn Diagrams | Tagged , , , , , , , , , , , , | 1 Comment

Survey of Relation Theory • 3

In this Survey of blog and wiki posts on 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 of … 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 , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Relation Theory • 2

In this Survey of previous blog and wiki posts on 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, C.S. Peirce, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Logic, Logic of Relatives, Mathematics, Model Theory, Peirce, Proof Theory, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Teridentity, Thirdness, Triadic Relations, Triadicity, Type Theory, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Signs Of Signs • 4

Re: Michael Harris • Language About Language But then inevitably I find myself wondering whether a proof assistant, or even a formal system, can make the distinction between “technical” and “fundamental” questions.  There seems to be no logical distinction.  The … Continue reading

Posted in Aesthetics, C.S. Peirce, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Music, Objective Frameworks, Objectivism, Peirce, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Riffs and Rotes, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Signs Of Signs • 3

Re: Michael Harris • Language About Language And if we don’t, who puts us away? One’s answer, or at least one’s initial response to that question will turn on how one feels about formal realities.  As I understand it, reality … Continue reading

Posted in Aesthetics, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Objective Frameworks, Objectivism, Peirce, Philosophy, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Signs Of Signs • 2

Re: Michael Harris • Language About Language I compared mathematics to a “consensual hallucination,” like virtual reality, and I continue to believe that the aim is to get (consensually) to the point where that hallucination is a second nature. I … Continue reading

Posted in Aesthetics, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Objective Frameworks, Objectivism, Peirce, Philosophy, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Signs Of Signs • 1

Re: Michael Harris • Language About Language There is a language and a corresponding literature that approaches logic and mathematics as related species of communication and information gathering, namely, the pragmatic-semiotic tradition passed on to us through the lifelong efforts … Continue reading

Posted in Aesthetics, Category Theory, Coherentism, Communication, Connotation, Form, Formal Languages, Foundations of Mathematics, Higher Order Propositions, Illusion, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Intuition, Language, Logic, Mathematics, Objective Frameworks, Objectivism, Peirce, Philosophy, Philosophy of Mathematics, Pragmata, Pragmatics, Pragmatism, Recursion, Reflection, Semantics, Semiotics, Set Theory, Sign Relations, Syntax, Translation, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment