Monthly Archives: May 2025

Cactus Language • Discussion 1

Posted on May 7, 2025 by Jon Awbrey

Re: Cactus Language • Preliminaries 9 Re: Cybernetics • Joe Bury JB: What does subcatenation and surcatenation mean?  Their definitions are not found in a dictionary.  I get the formulas you wrote but I don’t understand the meaning. Thanks for … Continue reading →

Posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Survey of Theme One Program • 7

Posted on May 6, 2025 by Jon Awbrey

This is a Survey of resources 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 had earlier developed … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Automated Research Tools, Boolean Functions, C.S. Peirce, Cactus Graphs, 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, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 80 Comments

Survey of Semiotics, Semiosis, Sign Relations • 6

Posted on May 6, 2025 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, Icon Index Symbol, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity, Visualization | Tagged , , , , , , , , , , , , | 13 Comments

Survey of Relation Theory • 9

Posted on May 5, 2025 by Jon Awbrey

In the present Survey of blog and wiki resources for 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, Algebra of Logic, C.S. Peirce, Category Theory, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Formal Languages, Foundations of Mathematics, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Model Theory, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Survey of Precursors Of Category Theory • 6

Posted on May 5, 2025 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, Foundations of Mathematics, Hilbert, Hypostatic Abstraction, Kant, Logic, Mathematics, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Pragmatic Semiotic Information • 9

Posted on May 4, 2025 by Jon Awbrey

This is a Survey of blog and wiki posts on a theory of information which grows out of pragmatic semiotic ideas.  All my projects are exploratory in character but this line of inquiry is more open‑ended than most.  The question … 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, 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, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Survey of Inquiry Driven Systems • 7

Posted on May 4, 2025 by Jon Awbrey

This is a Survey of work in progress 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 variables some … Continue reading →

Posted in Abduction, Adaptive Systems, Analogy, Animata, Artificial Intelligence, Automated Research Tools, C.S. Peirce, Cognitive Science, Cybernetics, Deduction, Educational Systems Design, Educational Technology, Fixation of Belief, Induction, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretation, Logic, Logic of Science, Mathematics, Mental Models, Pragmatic Maxim, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Survey of Differential Logic • 8

Posted on May 3, 2025 by Jon Awbrey

This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment. Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Definition and Determination • 4

Posted on May 3, 2025 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, Information = Comprehension × Extension, Inquiry Driven Systems, Logic, Mathematics, Scientific Method, Semiotics, Sign Relations, Structure, Systems Theory, Visualization | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Cybernetics • 5

Posted on May 2, 2025 by Jon Awbrey

Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors? — Plato … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment