Tag Archives: Dyadic Relations

Survey of Relation Theory • 9

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 , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Relations & Their Relatives • 4

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

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

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

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

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

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

Survey of Relation Theory • 8

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, 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 , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

The object of reasoning is to find out …

No longer wondered what I would do in life but defined my object. — C.S. Peirce (1861), “My Life, written for the Class-Book”, (CE 1, 3) The object of reasoning is to find out, from the consideration of what we already … Continue reading

Posted in C.S. Peirce, Determination, Dyadic Relations, Fixation of Belief, Inference, Inquiry, Intention, Intentional Contexts, Intentional Objects, Logic, Objects Objectives Objectivity, Pragmata, Pragmatism, Reasoning, Scientific Inquiry, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , , , | 6 Comments

Survey of Relation Theory • 7

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, 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 , , , , , , , , , , , , , , , , , , , , , , | Leave a comment