Category Archives: Logic

Survey of Relation Theory • 1

Posted on May 16, 2015 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 , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Precursors Of Category Theory • 1

Posted on May 15, 2015 by Jon Awbrey

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.  A Survey of … Continue reading →

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Sign Relations, Surveys, Triadic Relations, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments

Survey of Inquiry Driven Systems • 1

Posted on May 14, 2015 by Jon Awbrey

This is a Survey of blog and wiki posts 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 … 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

Survey of Differential Logic • 1

Posted on May 11, 2015 by Jon Awbrey

This is a Survey of blog and wiki posts on Differential Logic, material I plan to develop toward a more compact and systematic account. Elements Differential Logic • Introduction Differential Propositional Calculus • Part 1 • Part 2 Differential Logic … 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, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Animated Logical Graphs • 1

Posted on May 10, 2015 by Jon Awbrey

This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years.  After that I’ll look to organizing … Continue reading →

Posted in Abstraction, Amphecks, Animata, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Surveys, Theorem Proving, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.5

Posted on May 1, 2015 by Jon Awbrey

Suppose we add another individual to our initial universe of discourse, arriving at a three-point universe It might be thought that adding one more element to the universe of discourse would allow slightly more complicated relations to be compounded from … Continue reading →

Posted in Dyadic Relations, Graph Theory, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 10 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.4

Posted on April 24, 2015 by Jon Awbrey

Dyadic relations enjoy yet another form of graph-theoretic representation as labeled bipartite graphs or labeled bigraphs.  I’ll just call them bigraphs here, letting the labels be understood in this logical context. The figure below shows the bigraphs of the 16 … Continue reading →

Posted in Dyadic Relations, Graph Theory, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 9 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.3

Posted on April 23, 2015 by Jon Awbrey

Dyadic relations have graph-theoretic representations as labeled directed graphs with loops, also known as labeled pseudo-digraphs in some schools of graph theory.  I’ll just call them digraphs here, letting the labels and loops be understood in this logical context. The … Continue reading →

Posted in Dyadic Relations, Graph Theory, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 10 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2

Posted on April 19, 2015 by Jon Awbrey

Because it can sometimes be difficult to reconnect abstractions with their concrete instances, especially after the abstract types have become autonomous and taken on a life of their own, let us resort to a simple concrete case and examine the … Continue reading →

Posted in Dyadic Relations, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , | 11 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.1

Posted on April 13, 2015 by Jon Awbrey

I wanted to call attention to a very important statement from Selection 7 (CP 3.225–226).  Peirce enumerates the fundamental forms of individual dual relatives in the following terms: 225.   Individual relatives are of one or other of the two forms … Continue reading →

Posted in Dyadic Relations, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , | 9 Comments