Tag Archives: Relation Theory

Inquiry, Signs, Relations • 1

Posted on July 5, 2015 by Jon Awbrey

Re: Michael Harris • A Non-Logical Cognitive Phenomenon Human spontaneous non-demonstrative inference is not, overall, a logical process.  Hypothesis formation involves the use of deductive rules, but is not totally governed by them;  hypothesis confirmation is a non-logical cognitive phenomenon:  … Continue reading →

Posted in Abduction, Action, Analogy, C.S. Peirce, Cognition, Cognitive Science, Communication, Deduction, Foundations of Mathematics, Induction, Information, Information Theory, Inquiry, Inquiry Into Inquiry, Interpretation, Logic, Logic of Relatives, Logic of Science, Mathematics, Michael Harris, Peirce, Philosophy, Philosophy of Mathematics, Philosophy of Science, Pragmatism, Relation Theory, Relevance, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Relations & Their Relatives • Discussion 10

Posted on July 2, 2015 by Jon Awbrey

Re: Peirce List Discussion • Helmut Raulien The facts about relational reducibility are relatively easy to understand and I included links to relevant discussions in my earlier survey of relation theory. The following article discusses relational reducibility and irreducibility in … Continue reading →

Posted in C.S. Peirce, Combinatorics, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • Discussion 9

Posted on July 2, 2015 by Jon Awbrey

Re: Peirce List Discussion • Jeffrey Brian Downard In viewing the structures of relation spaces, even the smallest dyadic cases we’ve been exploring so far, no one need feel nonplussed at the lack of obviousness in this domain.  Anyone who … Continue reading →

Posted in C.S. Peirce, Combinatorics, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • Discussion 8

Posted on June 30, 2015 by Jon Awbrey

Re: Peirce List Discussion • Jeffrey Brian Downard In discussing the “combinatorial explosion” of dyadic relations that takes off in passing from a universe of two elements to a universe of three elements, I made the following observation: Looking back … Continue reading →

Posted in Combinatorics, Graph Theory, Group Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 13 Comments

Relations & Their Relatives • Discussion 7

Posted on June 28, 2015 by Jon Awbrey

Re: Peirce List Discussion • Jim Willgoose Here is the series of blog posts on Chapter 3 (The Logic of Relatives) from Peirce’s 1880 “Algebra of Logic” up to the point where I left off on May Day. Preliminaries Selections … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , | 13 Comments

Relations & Their Relatives • Discussion 6

Posted on June 19, 2015 by Jon Awbrey

Re: Peirce List Discussion • Helmut Raulien In discussing Peirce’s concept of a triadic sign relation as existing among objects, signs, and interpretant signs the question arises whether any of the classes so related are classes by themselves, that is, … Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , | 11 Comments

Survey of Semiotic Theory Of Information • 1

Posted on May 17, 2015 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

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

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