Category Archives: Triadic Relations

Interpreter and Interpretant • Selection 4

Posted on January 9, 2025 by Jon Awbrey

Interpretation and Inquiry To illustrate the role of sign relations in inquiry we begin with Dewey’s elegant and simple example of reflective thinking in everyday life. A man is walking on a warm day.  The sky was clear the last … Continue reading →

Posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Interpreter and Interpretant • Selection 3

Posted on January 8, 2025 by Jon Awbrey

The following selection from Peirce’s “Lowell Lectures on the Logic of Science” (1866) lays out in detail his “metaphorical argument” for the relationship between interpreters and interpretant signs. I think we need to reflect upon the circumstance that every word implies … Continue reading →

Posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Interpreter and Interpretant • Selection 2

Posted on January 7, 2025 by Jon Awbrey

A idea of what Peirce means by an Interpretant and the part it plays in a triadic sign relation is given by the following passage. It is clearly indispensable to start with an accurate and broad analysis of the nature … Continue reading →

Posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Interpreter and Interpretant • Selection 1

Posted on January 6, 2025 by Jon Awbrey

Questions about the relationship between “interpreters” and “interpretants” in Peircean semiotics have broken out again.  To put the matter as pointedly as possible — because I know someone or other is bound to — “In a theory of three‑place relations … Continue reading →

Posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Relations & Their Relatives • 4

Posted on August 3, 2024 by Jon Awbrey

From Dyadic to Triadic to Sign Relations Peirce’s notation for elementary relatives was illustrated earlier by a dyadic relation from number theory, namely, the relation written for Table 1 shows the first few ordered pairs of the relation on positive … 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 , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • 3

Posted on August 2, 2024 by Jon Awbrey

Here are two ways of looking at the divisibility relation, a dyadic relation of fundamental importance in number theory. Table 1 shows the first few ordered pairs of the relation on positive integers corresponding to the relative term, “divisor of”.  Thus, … 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 , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • 2

Posted on August 1, 2024 by Jon Awbrey

What is the relationship between “logical relatives” and “mathematical relations”?  The word relative used as a noun in logic is short for relative term — as such it refers to an item of language used to denote a formal object. … 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 , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • 1

Posted on July 31, 2024 by Jon Awbrey

Sign relations are special cases of triadic relations in much the same way binary operations in mathematics are special cases of triadic relations.  It amounts to a minor complication that we participate in sign relations whenever we talk or think … 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 , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • Discussion 25

Posted on July 30, 2024 by Jon Awbrey

Re: Daniel Everett • Polyunsaturated Predicates Re: Relations & Their Relatives • Discussion 24 Dear Daniel, I’ve been meaning to get back to this as it keeps coming up and it’s kind of important but it took me a while … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Rheme, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • Discussion 24

Posted on July 28, 2024 by Jon Awbrey

Re: Daniel Everett • Polyunsaturated Predicates DE: Among the several ideas Peirce and Frege came up with was the idea of a predicate before and after it is linked to its arguments.  Frege called the unlinked predicate unsaturated.  But Peirce … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Rheme, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 5 Comments