Relation Theory • Discussion 2

Re: Relation Theory • (1)(2)(3)(4)
Re: FB | Charles S. Peirce SocietyJoseph Harry

JH:
These are iconic representations dealing with logical symbolic relations, and so of course are semiotic in Peirce’s sense, since logic is semiotic.  But couldn’t a logician do all of this meticulous formalization and understand all of the discrete logical consequences of it without having any inkling of semiotics or of Peirce?

Dear Joseph,

As I noted at the top of the article and blog series —

This article treats relations from the perspective of combinatorics, in other words, as a subject matter in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many of which arise quite naturally in applications.  This approach to relation theory, or the theory of relations, is distinguished from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other.

Of course one can always pull a logical formalism out of thin air, with no inkling of its historical sources, and proceed in a blithely syntactic and deductive fashion.  But if we hew more closely to applications, original or potential, and even regard logic and math as springing from practice, we must take care for the semantic and pragmatic grounds of their use.  From that perspective, models come first, well before the deductive theories whose consistency they establish.

Regards,

Jon

cc: Category Theory • Cybernetics (1) (2) • Ontolog Forum (1) (2)
cc: Structural Modeling (1) (2) • Systems Science (1) (2)
cc: FB | Relation TheoryLaws of FormPeirce List

This entry was 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, Triadic Relations, Type Theory, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

4 Responses to Relation Theory • Discussion 2

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

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

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

  4. Pingback: Survey of Relation Theory • 3 | 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.