Relations & Their Relatives • Discussion 1

Re: Peirce ListHelmut Raulien

The divisor of relation signified by x|y is a dyadic relation on the set of positive integers \mathbb{M} and thus may be understood as a subset of the cartesian product \mathbb{M} \times \mathbb{M}.  It is an example of a partial order, while the less than or equal to relation signified by x \le y is an example of a total order relation.

The mathematics of relations can be applied most felicitously to semiotics but there we must bump the adicity or arity up to three.  We take any sign relation L to be subset of a cartesian product O \times S \times I, where O is the set of objects under consideration in a given discussion, S is the set of signs, and I is the set of interpretant signs involved in the same discussion.

One thing we need to understand is the sign relation L \subseteq O \times S \times I relevant to a given level of discussion may be rather more abstract than what we would call a sign process proper, that is, a structure extended through a dimension of time.  Indeed, many of the most powerful sign relations generate sign processes through iteration or recursion or similar operations.  In that event, the most penetrating analysis of the sign process or semiosis in view is achieved through grasping the generative sign relation at its core.

Resources

cc: Category TheoryCyberneticsOntologStructural ModelingSystems Science
cc: FB | Relation TheoryLaws of FormPeirce List

This entry was 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 and tagged , , , , , , , , , , , , , , , . Bookmark the permalink.

6 Responses to Relations & Their Relatives • Discussion 1

  1. Pingback: Survey of Relation Theory • 1 | Inquiry Into Inquiry

  2. Pingback: Survey of Relation Theory • 2 | Inquiry Into Inquiry

  3. Pingback: Survey of Relation Theory • 3 | Inquiry Into Inquiry

  4. Pingback: Survey of Relation Theory • 4 | Inquiry Into Inquiry

  5. Pingback: Survey of Relation Theory • 4 | Inquiry Into Inquiry

  6. Pingback: Relations & Their Relatives • Review 1 | Inquiry Into Inquiry

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