Category Archives: Surveys

Survey of Relation Theory • 3

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 , , , , , , , , , , , , , , , , , , , , , , , , | Leave a 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 , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Theme One Program • 1

This is a Survey of previous blog and wiki posts on the Theme One Program that I worked on all through the 1980s. The aim of the project was to develop fundamental algorithms and data structures to support an integrated … Continue reading

Posted in Algorithms, Animata, Artificial Intelligence, Automated Research Tools, Boolean Algebra, Boolean Functions, Cactus Graphs, Cognitive Science, Computation, Computational Complexity, Computer Science, Computing, Constraint Satisfaction Problems, Cybernetics, Data Structures, Diagrammatic Reasoning, Diagrams, Differential Analytic Turing Automata, Education, Educational Systems Design, Educational Technology, Equational Inference, Functional Logic, Graph Theory, Indicator Functions, Inquiry, Inquiry Driven Education, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Knowledge, Learning, Learning Theory, Logic, Logical Graphs, Machine Learning, Mathematics, Mental Models, Minimal Negation Operators, Painted Cacti, Peirce, Programming, Programming Languages, Propositional Calculus, Propositional Equation Reasoning Systems, Propositions, Research Technology, Semeiosis, Semiosis, Semiotics, Sign Relations, Surveys, Teaching, Theorem Proving, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Semiotic Theory Of Information • 1

This is a Survey of previous blog and wiki posts on the Semiotic Theory Of Information.  All my projects are exploratory in essence but this line of inquiry is more open-ended than most.  The question is: What is information and how … Continue reading

Posted in Abduction, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Entropy, Epistemology, Fixation of Belief, Ignorance, Illusion, Induction, Information, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Mental Models, Objective Frameworks, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Thirdness, Triadic Relations, Triadicity, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Relation Theory • 1

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

Survey of Precursors Of Category Theory • 1

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. This post is … Continue reading

Posted in Abstraction, Ackermann, Analogy, Aristotle, Carnap, Category Theory, Diagrammatic Reasoning, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Iconicity, Kant, Logic, Mathematics, Mental Models, Peirce, Propositions As Types Analogy, Saunders Mac Lane, Surveys, Triadic Relations, Type Theory, Universals, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Inquiry Driven Systems • 1

This is a Survey of previous blog and wiki posts on Inquiry Driven Systems, material that I plan to refine toward a more compact and systematic treatment of the subject. An inquiry driven system is a system that has among … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment