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

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

Icon Index Symbol • 17

Questions Concerning Certain Faculties Claimed For Signs Re: Peirce List Discussion • Helmut Raulien Our object being to clarify the relationships among icons, indices, and symbols, I believe the maximum benefit possible at this point is to be gained from … Continue reading

Posted in Abduction, Algorithms, Artificial Intelligence, Automated Research Tools, C.S. Peirce, Cognitive Science, Computer Science, Data Structures, Deduction, Functional Logic, Icon Index Symbol, Induction, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretive Frameworks, Knowledge Representation, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Objective Frameworks, Peirce, Relation Theory, Relative Membership, Scientific Method, Semiotics, Set Theory, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Icon Index Symbol • 16

Questions Concerning Certain Faculties Claimed For Signs Re: Peirce List Discussion • JAS • HR Having lost my train of thought due to a week on the road, I would like to go back and pick up the thread at … Continue reading

Posted in Abduction, Algorithms, Artificial Intelligence, Automated Research Tools, C.S. Peirce, Cognitive Science, Computer Science, Data Structures, Deduction, Functional Logic, Icon Index Symbol, Induction, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretive Frameworks, Knowledge Representation, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Objective Frameworks, Peirce, Relation Theory, Relative Membership, Scientific Method, Semiotics, Set Theory, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Icon Index Symbol • 15

Questions Concerning Certain Faculties Claimed For Signs I put down the cup and turn to my mind.  It is up to my mind to find the truth.  But how?  What grave uncertainty, whenever the mind feels overtaken by itself;  when … Continue reading

Posted in Abduction, Algorithms, Artificial Intelligence, Automated Research Tools, C.S. Peirce, Cognitive Science, Computer Science, Data Structures, Deduction, Functional Logic, Icon Index Symbol, Induction, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretive Frameworks, Knowledge Representation, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Objective Frameworks, Peirce, Relation Theory, Relative Membership, Scientific Method, Semiotics, Set Theory, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Icon Index Symbol • 14

Questions Concerning Certain Faculties Claimed For Signs Re: Peirce List Discussion • Helmut Raulien Re: Icon Index Symbol • (10) • (11) • (12) • (13) Let me sum up the main points of the above exchange before moving on. … Continue reading

Posted in Abduction, Algorithms, Artificial Intelligence, Automated Research Tools, C.S. Peirce, Cognitive Science, Computer Science, Data Structures, Deduction, Functional Logic, Icon Index Symbol, Induction, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretive Frameworks, Knowledge Representation, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Objective Frameworks, Peirce, Relation Theory, Relative Membership, Scientific Method, Semiotics, Set Theory, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Icon Index Symbol • 13

Questions Concerning Certain Faculties Claimed For Signs Re: Peirce List Discussion • Helmut Raulien HR: I guess, that a difference between Peirce’s relation theory, and his semiotics and category theory, is, that the first is about all triadic relations, and … Continue reading

Posted in Abduction, Algorithms, Artificial Intelligence, Automated Research Tools, C.S. Peirce, Cognitive Science, Computer Science, Data Structures, Deduction, Functional Logic, Icon Index Symbol, Induction, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretive Frameworks, Knowledge Representation, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Objective Frameworks, Peirce, Relation Theory, Relative Membership, Scientific Method, Semiotics, Set Theory, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Icon Index Symbol • 12

Questions Concerning Certain Faculties Claimed For Signs Re: Peirce List Discussion • Helmut Raulien HR: Example:  The triadic function with the three sets not being classes of any kind, at least not of the special kind (whatever that is), that … Continue reading

Posted in Abduction, Algorithms, Artificial Intelligence, Automated Research Tools, C.S. Peirce, Cognitive Science, Computer Science, Data Structures, Deduction, Functional Logic, Icon Index Symbol, Induction, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretive Frameworks, Knowledge Representation, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Objective Frameworks, Peirce, Relation Theory, Relative Membership, Scientific Method, Semiotics, Set Theory, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments