Relations & Their Relatives • Discussion 11

Re: Peirce ListHelmut Raulien
Cf: Relation ReductionExamples of Projectively Reducible Relations

I constructed the “Ann and Bob” examples of sign relations back at the beginning of my Systems Engineering program when I had to explain how triadic sign relations would naturally come up in building intelligent systems possessed of a capacity for inquiry.

My advisor asked me for a simple, concrete, but not too trivial example of a sign relation and after cudgeling my wits for a while this is what fell out.  Up till then I had never much considered finite examples of sign relation as the cases arising in logic almost always have formal languages with infinite numbers of elements as their syntactic domains if not also infinite numbers of elements in their object domains.

The illustration at hand involves two sign relations:

  • L_\text{A} is the sign relation that captures how Ann interprets the signs in the set S = I = \{ {}^{\backprime\backprime}\text{Ann}{}^{\prime\prime}, {}^{\backprime\backprime}\text{Bob}{}^{\prime\prime}, {}^{\backprime\backprime}\text{I}{}^{\prime\prime}, {}^{\backprime\backprime}\text{you}{}^{\prime\prime} \} to denote the objects in O = \{ \text{Ann}, \text{Bob} \}.
  • L_\text{B} is the sign relation that captures how Bob interprets the signs in the set S = I = \{ {}^{\backprime\backprime}\text{Ann}{}^{\prime\prime}, {}^{\backprime\backprime}\text{Bob}{}^{\prime\prime}, {}^{\backprime\backprime}\text{I}{}^{\prime\prime}, {}^{\backprime\backprime}\text{you}{}^{\prime\prime} \} to denote the objects in O = \{ \text{Ann}, \text{Bob} \}.

Each of the sign relations, L_\text{A} and L_\text{B}, contains eight triples of the form (o, s, i) where o is an object in the object domain O, s is a sign in the sign domain S, and i is an interpretant sign in the interpretant domain I.  These triples are called elementary or individual sign relations, as distinguished from the general sign relations that generally contain many sign relational triples.

If this much is clear we can move on next time to discuss the two types of reducibility and irreducibility that arise in semiotics.

To be continued …

This entry was posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations and tagged , , , , , , , , , , , , , , , , . Bookmark the permalink.

4 Responses to Relations & Their Relatives • Discussion 11

  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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.