Triadic Relation Irreducibility • 1

Posted on January 17, 2013 by Jon Awbrey

The core insight of Peirce’s conceptual system is the recognition that triadic relations are sui generis, constituting a class by themselves.  Understanding the properties of triadic relations and the consequences of their irreducibility is critical to understanding Peirce’s thought and work.  Every attempt to reconstruct Peirce’s system on a different basis must eventually fall like a house of cards.

This entry was posted in C.S. Peirce, Category Theory, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relational Manifolds, Sign Relations, Teridentity, Thirdness, Triadic Relations and tagged , , , , , , , , , , , , , , , . Bookmark the permalink.

11 Responses to Triadic Relation Irreducibility • 1

    • Jon Awbrey says:
      January 17, 2013 at 11:10 am

      Saying why would be a two-parter at least —

      1. Why triadic relations are irreducible.
      2. Why triadic relations are necessary to Peirce’s conceptual system.

      No doubt some party of the third part is lurking in there somewhere …

      Reply
    • Jon Awbrey says:
      January 18, 2013 at 2:00 pm

      After a day’s reflection, I guess the third part would have to be something like this —

      3. Why Peirce’s conceptual system is necessary to understand the world.

      That parses the question “Why” along the lines of a sign relation, where reality is part of an object domain O, Peirce’s conceptual system is part of a sign domain S, and our interpretation of his conceptual system is part of an interpretant domain I.

      Reply
      • Joseph Harry says:
        January 17, 2016 at 12:30 pm

        The argument from authority for the triad being irreducible is that Peirce says so, and given his proofs of same we should believe it.  A simpler quantitative argument (an argument being a third, by the way) in qualitative form is that 3 automatically requires a 2, and 2 by the same token (pardon the pun), a 1.

        Reply
    • Jon Awbrey says:
      January 17, 2013 at 11:18 am

      Hi Robert, long time no see …

      Reply
      • robert marty says:
        January 19, 2013 at 3:38 am

        Hello Jon,
        I am retired 10 years ago but I continue to follow the main subjects on which I worked in particular the thesis of reduction a proof of which I published within the framework of the category of the relational structures. However my English is always so bad!

        Reply
    • Jon Awbrey says:
      January 19, 2013 at 10:42 pm

      No problem if you write in French, since the online translators work well enough on the reading side these days to keep a conversation going. I only embarrass myself if I try to use them for writing though.

      Reply

  3. Pingback: ⚠ It’s A Trap ⚠ | Inquiry Into Inquiry

  4. Victor Porton says:
    May 19, 2013 at 8:30 am

    An n-ary relation can be composed with n binary relations. A generalization of this (I call it categories with star morphisms) naturally appear in the theory of funcoids:

    (see the chapter “Multifuncoids and Staroids” of the book located at this URL).

    Reply
    • Jon Awbrey says:
      May 19, 2013 at 10:48 pm

      A k-adic relation can be constructed from k dyadic relations, but only by means of a k-adic identity relation that connects k of their domains in a specific way. It is sufficient to use 3-adic identity relations for this purpose, which Peirce called teridentity relations.

      Reply

Leave a comment

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