Category Archives: C.S. Peirce

Relation Theory • Discussion 5

Posted on April 22, 2023 by Jon Awbrey

Re: Survey of Relation Theory Re: Ontolog Forum • Ravi Sharma RS: Is there also an attempt at integrating these relation concepts?  Like a meta‑model of relations? Dear Ravi, I haven’t run across the concept of a meta‑model before so … 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, Triadic Relations, Type Theory, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Relation Theory • Discussion 4

Posted on April 19, 2023 by Jon Awbrey

Re: Survey of Relation Theory Re: Ontolog Forum • Ravi Sharma RS: Is there also an attempt at integrating these relation concepts?  Like a meta‑model of relations? Dear Ravi, Thanks for the question.  I believe I’d say yes to the … 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, Triadic Relations, Type Theory, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Theme One Program • Discussion 10

Posted on April 17, 2023 by Jon Awbrey

Re: Mathstodon • Seamus Bradley SB: I thought of a programming language where every function can only return one type:  the return type.  The return type is just a wrapper around a struct that contains the actual return value, but … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Definition and Determination • 2

Posted on April 6, 2023 by Jon Awbrey

In the early 1990s, “in the middle of life’s journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from … Continue reading →

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Indication, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Peirce, Semiotics, Structure | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Survey of Semiotics, Semiosis, Sign Relations • 4

Posted on April 5, 2023 by Jon Awbrey

C.S. Peirce defines logic as “formal semiotic”, using formal to highlight the place of logic as a normative science, over and above the descriptive study of signs and their role in wider fields of play.  Understanding logic as Peirce understands … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadicity | Tagged , , , , , , , , | Leave a comment

Survey of Pragmatic Semiotic Information • 6

Posted on April 4, 2023 by Jon Awbrey

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, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Survey of Precursors Of Category Theory • 3

Posted on April 3, 2023 by Jon Awbrey

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

Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 3

Posted on April 2, 2023 by Jon Awbrey

This is a Survey of blog and wiki posts on three elementary forms of inference, as recognized by a logical tradition extending from Aristotle through Charles S. Peirce.  Particular attention is paid to the way these inferential rudiments combine to … Continue reading →

Posted in Abduction, Aristotle, C.S. Peirce, Deduction, Dewey, Discovery, Doubt, Fixation of Belief, Functional Logic, Icon Index Symbol, Induction, Inference, Information, Inquiry, Invention, Logic, Logic of Science, Mathematics, Morphism, Paradigmata, Paradigms, Pattern Recognition, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Scientific Inquiry, Scientific Method, Semiotics, Sign Relations, Surveys, Syllogism, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Survey of Relation Theory • 6

Posted on April 1, 2023 by Jon Awbrey

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 , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Theme One Program • 5

Posted on March 30, 2023 by Jon Awbrey

This is a Survey of blog and wiki posts relating to the Theme One Program I worked on all through the 1980s.  The aim was to develop fundamental algorithms and data structures for integrating empirical learning with logical reasoning.  I … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, Constraint Satisfaction Problems, Data Structures, Differential Logic, Equational Inference, Formal Languages, Graph Theory, Inquiry Driven Systems, Laws of Form, Learning Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments