Semiotics, Semiosis, Sign Relations • Comment 3

Posted on August 12, 2021 by Jon Awbrey

It helps me to compare sign relations with my other favorite class of triadic relations, namely, groups.  Applications of mathematical groups came up just recently in the Laws of Form discussion group, so it will save a little formatting time to adapt the definition used there.

Cf: Animated Logical Graphs • 60

Definition 1.  A group (G, *) is a set G together with a binary operation * : G \times G \to G satisfying the following three conditions.

  1. Associativity.  For any x, y, z \in G,
    we have (x * y) * z = x * (y * z).
  2. Identity.  There is an identity element 1 \in G such that \forall g \in G,
    we have 1 * g = g * 1 = g.
  3. Inverses.  Each element has an inverse, that is, for each g \in G,
    there is some h \in G such that g * h = h * g = 1.

cc: Category Theory • Cybernetics (1) (2)
cc: Ontolog Forum • Structural Modeling • Systems Science
cc: FB | Semeiotics • Laws of Form • Peirce List (1) (2) (3) (4) (5) (6)

This entry was posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations and tagged , , , , , , , . Bookmark the permalink.