Category Archives: Category Theory

Relation Theory • Discussion 2

Posted on November 1, 2021 by Jon Awbrey

Re: Relation Theory • (1) • (2) • (3) • (4) Re: FB | Charles S. Peirce Society • Joseph Harry JH: These are iconic representations dealing with logical symbolic relations, and so of course are semiotic in Peirce’s sense, … 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 , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Relation Theory • 5

Posted on October 31, 2021 by Jon Awbrey

Relation Theory Two further classes of incidence properties will prove to be of great utility. Regional Incidence Properties The definition of a local flag can be broadened from a point to a subset of a relational domain, arriving at the … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 10 Comments

Relation Theory • 4

Posted on October 30, 2021 by Jon Awbrey

Relation Theory • Local Incidence Properties The next few definitions of local incidence properties of relations are given at a moderate level of generality in order to show how they apply to -place relations.  In the sequel we’ll see what … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 11 Comments

Relation Theory • 3

Posted on October 29, 2021 by Jon Awbrey

Relation Theory • Definition It is convenient to begin with the definition of a -place relation, where is a positive integer. Definition.  A -place relation over the nonempty sets is a -tuple where is a subset of the cartesian product Several … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 11 Comments

Relation Theory • 2

Posted on October 28, 2021 by Jon Awbrey

Relation Theory • Preliminaries Two definitions of the relation concept are common in the literature.  Although it is usually clear in context which definition is being used at a given time, it tends to become less clear as contexts collide, … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 11 Comments

Relation Theory • 1

Posted on October 27, 2021 by Jon Awbrey

Here’s an introduction to Relation Theory geared to applications and taking a moderately general view at least as far as finite numbers of relational domains are concerned (-adic or -ary relations). Relation Theory This article treats relations from the perspective … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 11 Comments

Semiotics, Semiosis, Sign Relations • Discussion 19

Posted on October 5, 2021 by Jon Awbrey

Normative science rests largely on phenomenology and on mathematics; metaphysics on phenomenology and on normative science. ❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903) Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b) Re: Peirce List • John Sowa JS: … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 8 Comments

Semiotics, Semiosis, Sign Relations • Discussion 18

Posted on September 28, 2021 by Jon Awbrey

Re: FB | Medieval Logic • Edward Buckner (1) (2) Edward Buckner raised a few questions about the sign relations implicit in Aristotle’s treatise “On Interpretation”, prompting the following thoughts on my part. On Pragmata The object of a sign … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 8 Comments

Relations & Their Relatives • Discussion 23

Posted on September 21, 2021 by Jon Awbrey

Re: Ontolog Forum • Roberto Rovetto • Alex Shkotin Having lost my concentration to another round of home reconstruction disruption, let me loop back to the texts from Roberto and Alex which drew me into this discussion last week. RR: … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 8 Comments

Differential Logic • Discussion 15

Posted on September 18, 2021 by Jon Awbrey

Re: Differential Logic • Comment 7 Re: Laws of Form • Lyle Anderson LA: Differentials and partial differentials over the real numbers work because one can pick two real numbers that are arbitrarily close to one another.  The difference between … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments