Questions Concerning Certain Faculties Claimed For Signs

Re: Peirce List (1) (2) (3) • Helmut Raulien
Re: Icon Index Symbol • (10) (11) (12) (13)

Let me sum up the main points of the above exchange before moving on.

Mathematics is useful in our present endeavor because it treats relations in general.  In addition — and multiplication, too — mathematics is chock full of well-studied examples of triadic relations.  When it comes to the job of analyzing sign relations and teasing out their structures we can save ourselves a lot of trouble and trial and error by examining this record of prior art and adapting its methods to handle sign relations.

On the other hand, there are hints in Peirce’s work of how triadic relations extend across a threshold of complexity in such a way that relations of all higher adicities can be analyzed in terms of 1-adic, 2-adic, and 3-adic relations.  This is where the analogy between Peirce’s category theory and mathematical category theory both forms and breaks.  The utility of categories in mathematical theory derives from the ubiquity of functions in mathematical practice, and functions are dyadic relations.  Still, triadic relations pervade the background of mathematical category theory, being visible in the triadic composition relation and in the concept of “natural transformations”, the clarification of which is one of the original motivations for the subject.  Bringing the triadic roots of category theory into higher relief is one of my motives for bringing about an encounter with Peirce’s categories, an effort to which I have given not a few years of thought.

That brings us to the case of sign relations proper.  These types of triadic relations form our first stepping stones and also our first stumbling blocks in the inquiry into inquiry and I gave some indications why that might be true.  I don’t know if I can do better than that at this time, but I’ll think on it further after that all-essential secondness of caffeination.

Resources

• Sign Relations
• Triadic Relations
• Relation Theory
• Peirce’s Logic Of Information
• Precursors Of Category Theory
• Information = Comprehension × Extension
• Peirce’s 1870 Logic Of Relatives : The Wiki Article
• Peirce’s 1870 Logic Of Relatives : The Series Pilot

cc: Peirce List (1) (2) (3)