Category Archives: Triadic Relations

Sign Relations • Dyadic Aspects

Posted on December 25, 2025 by Jon Awbrey

For an arbitrary triadic relation whether it happens to be a sign relation or not, there are six dyadic relations obtained by projecting on one of the planes of the ‑space   The six dyadic projections of a triadic relation … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 2 Comments

Sign Relations • Examples

Posted on December 18, 2025 by Jon Awbrey

Soon after I made my third foray into grad school, this time in Systems Engineering, I was trying to explain sign relations to my advisor and he, being the very model of a modern systems engineer, asked me to give … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 2 Comments

Sign Relations • Signs and Inquiry

Posted on December 16, 2025 by Jon Awbrey

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry.  In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 2 Comments

Sign Relations • Definition

Posted on December 14, 2025 by Jon Awbrey

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting. Logic will here be defined … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 5 Comments

Sign Relations • Anthesis

Posted on December 12, 2025 by Jon Awbrey

Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive … Continue reading →

Posted in C.S. Peirce, Connotation, Denotation, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotic Equivalence Relations, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , | 2 Comments

Survey of Semiotics, Semiosis, Sign Relations • 6

Posted on May 6, 2025 by Jon Awbrey

C.S. Peirce defines logic as “formal semiotic”, using formal to highlight the place of logic as a normative science, over and above the descriptive study of signs and their role in wider fields of play.  Understanding logic as Peirce understands … Continue reading →

Posted in C.S. Peirce, Icon Index Symbol, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity, Visualization | Tagged , , , , , , , , , , , , | 32 Comments

Survey of Relation Theory • 9

Posted on May 5, 2025 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, Formal Languages, Foundations of Mathematics, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Model Theory, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Survey of Pragmatic Semiotic Information • 9

Posted on May 4, 2025 by Jon Awbrey

This is a Survey of blog and wiki posts on a theory of information which grows out of pragmatic semiotic ideas.  All my projects are exploratory in character but this line of inquiry is more open‑ended than most.  The question … 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, 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, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Survey of Inquiry Driven Systems • 7

Posted on May 4, 2025 by Jon Awbrey

This is a Survey of work in progress 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 some … Continue reading →

Posted in Abduction, Adaptive Systems, Analogy, Animata, Artificial Intelligence, Automated Research Tools, C.S. Peirce, Cognitive Science, Cybernetics, Deduction, Educational Systems Design, Educational Technology, Fixation of Belief, Induction, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Interpretation, Logic, Logic of Science, Mathematics, Mental Models, Pragmatic Maxim, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Survey of Cybernetics • 5

Posted on May 2, 2025 by Jon Awbrey

Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors? — Plato … 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment