Category Archives: Category Theory

Relation Theory • 4

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 , , , , , , , , , , , , , , , | 6 Comments

Relation Theory • 3

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 , , , , , , , , , , , , , , , | 6 Comments

Relation Theory • 2

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 , , , , , , , , , , , , , , , | 6 Comments

Relation Theory • 1

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 , , , , , , , , , , , , , , , | 6 Comments

Semiotics, Semiosis, Sign Relations • Discussion 19

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 , , , , , , , | 2 Comments

Semiotics, Semiosis, Sign Relations • Discussion 18

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 , , , , , , , | 2 Comments

Relations & Their Relatives • Discussion 23

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 , , , , , , , , , , , , , , , , | 3 Comments

Differential Logic • Discussion 15

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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Relations & Their Relatives • Discussion 22

Re: Ontolog Forum • Roberto Rovetto (1) (2) RR: What’s your view on: When to create a greater-than-binary relation rather than a binary relation? Consider:  You want to represent some information, statement, or knowledge, without necessarily being forced to limit … 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 , , , , , , , , , , , , , , , , | 4 Comments

Relations & Their Relatives • Discussion 21

Re: Ontolog Forum • Alex Shkotin AS: Let me underline an important point:  first of all, we have found in nature and society one or another relation and ask how many members each example of this relation can have?  i.e. … 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 , , , , , , , , , , , , , , , , | 4 Comments