Tag Archives: Semiotics

Theme One Program • Motivation 1

Posted on June 3, 2024 by Jon Awbrey

The main idea behind the Theme One program is the efficient use of graph-theoretic data structures for the tasks of “learning” and “reasoning”. I am thinking of learning in the sense of learning about an environment, in essence, gaining information about … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Survey of Precursors Of Category Theory • 5

Posted on May 24, 2024 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 , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Peirce’s 1885 “Algebra of Logic” • Discussion 2

Posted on April 3, 2024 by Jon Awbrey

Re: FB | Daniel Everett One thing I’ve been trying to understand for a very long time is the changes in Peirce’s writing about math and logic from 1865 to 1885.  If there’s anything I’ve learned from reading Peirce in … Continue reading →

Posted in Algebra of Logic, C.S. Peirce, Deduction, Diagrammatic Reasoning, Icon Index Symbol, Logic, Logic of Relatives, Mathematics, Philosophy of Notation, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , | 2 Comments

Peirce’s 1885 “Algebra of Logic” • Discussion 1

Posted on April 2, 2024 by Jon Awbrey

Re: FB | Daniel Everett DE: One of the most important papers in the history of logic.  “On the Algebra of Logic” was the first to introduce the term “quantifier”. Peirce, C.S. (1885), “On the Algebra of Logic : A … Continue reading →

Posted in Algebra of Logic, C.S. Peirce, Deduction, Diagrammatic Reasoning, Icon Index Symbol, Logic, Logic of Relatives, Mathematics, Philosophy of Notation, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , | 2 Comments

Peirce’s 1885 “Algebra of Logic” • Selection 4

Posted on April 1, 2024 by Jon Awbrey

Selection from C.S. Peirce, “On the Algebra of Logic : A Contribution to the Philosophy of Notation” (1885) §1.  Three Kinds Of Signs (concl.) In this paper, I purpose to develop an algebra adequate to the treatment of all problems … Continue reading →

Posted in Algebra of Logic, C.S. Peirce, Deduction, Diagrammatic Reasoning, Icon Index Symbol, Logic, Logic of Relatives, Mathematics, Philosophy of Notation, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

Peirce’s 1885 “Algebra of Logic” • Selection 3

Posted on March 30, 2024 by Jon Awbrey

Selection from C.S. Peirce, “On the Algebra of Logic : A Contribution to the Philosophy of Notation” (1885) §1.  Three Kinds Of Signs (cont.) For instance, take the syllogistic formula, This is really a diagram of the relations of and … Continue reading →

Posted in Algebra of Logic, C.S. Peirce, Deduction, Diagrammatic Reasoning, Icon Index Symbol, Logic, Logic of Relatives, Mathematics, Philosophy of Notation, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

Peirce’s 1885 “Algebra of Logic” • Selection 2

Posted on March 26, 2024 by Jon Awbrey

Selection from C.S. Peirce, “On the Algebra of Logic : A Contribution to the Philosophy of Notation” (1885) §1.  Three Kinds Of Signs (cont.) I have taken pains to make my distinction of icons, indices, and tokens clear, in order … Continue reading →

Posted in Algebra of Logic, C.S. Peirce, Deduction, Diagrammatic Reasoning, Icon Index Symbol, Logic, Logic of Relatives, Mathematics, Philosophy of Notation, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

Peirce’s 1885 “Algebra of Logic” • Selection 1

Posted on March 24, 2024 by Jon Awbrey

Selection from C.S. Peirce, “On the Algebra of Logic : A Contribution to the Philosophy of Notation” (1885) §1.  Three Kinds Of Signs Any character or proposition either concerns one subject, two subjects, or a plurality of subjects.  For example, … Continue reading →

Posted in Algebra of Logic, C.S. Peirce, Deduction, Diagrammatic Reasoning, Icon Index Symbol, Logic, Logic of Relatives, Mathematics, Philosophy of Notation, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

Survey of Relation Theory • 8

Posted on March 23, 2024 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, 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 , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Pragmatic Semiotic Information • Comment 3

Posted on March 22, 2024 by Jon Awbrey

Memories are coming back to me more through the association of ideas than ordered by time or place.  I can sense, almost touch a tangle of thoughts interlaced with each other — the “information first” approach to ontology, the “arrows … Continue reading →

Posted in C.S. Peirce, Definition, Determination, Information, Information = Comprehension × Extension, Inquiry, Logic, Pragmatic Semiotic Information, Scientific Method, Semiosis, Semiotics, Sign Relations, Triadic Relations, Uncertainty | Tagged , , , , , , , , , , , , , | 3 Comments