## Triadic Relation Irreducibility • 1

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.

### 11 Responses to Triadic Relation Irreducibility • 1

1. Say why.

• Jon Awbrey says:

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 …

• Jon Awbrey says:

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.

• Joseph Harry says:

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.

2. robert marty says:

Approved …

• Jon Awbrey says:

Hi Robert, long time no see …

• robert marty says:

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!

• Jon Awbrey says:

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.

3. 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).

• Jon Awbrey says:

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.

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