Directory:Jon Awbrey/Projects/Notes And Queries

Peircean Pragmata

Several recent blog and discussion list postings have brought to mind a congeries of perennial themes out of Peirce. I am prompted to collect what old notes of mine I can glean off the Web, and — The Horror! The Horror! — maybe even plumb the verdimmerung depths of that old box of papyrus under the desk …

Peirce's Law : Tertia Datur And Non

• Shawn Standefer @ Words and Other Things
  • Classical Howard–Curry

Peirce's Law and the Pragmatic Maxim

Jacob Longshore conjectures a link between Peirce's Law and the Pragmatic Maxim.

• Jacob Longshore @ Wordverter

1. Peirce Lays Down The Law!
2. Peirce's Pragmatic Law : A Conjecture
3. Extensions on Peirce's Pragmatic Law
4. Further Extensions : Out on the Leafy Edge
5. Peirce's Pragmatic Law : The Point of It All

Jon Awbrey freely associates to Post N°3.

Pieces of the Puzzle

For the Time Being, a Sleightly Random Recap of Notes …

Pragmatic Maxim as Closure Principle

Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object.

Consider the following attempts at interpretation:

Your concept of \(x\!\) is your concept of the practical effects of \(x.\!\)

Not exactly. It seems a bit more like:

Your concept of \(x\!\) is your concept of your-conceived-practical-effects of \(x.\!\)

Converting to a third person point of view:

\[j\!\]'s concept of \(x\!\) is \(j\!\)'s concept of \(j\!\)'s-conceived-practical-effects of \(x.\!\)

An ordinary closure principle looks like this:

\[C(x) = C(C(x))\!\]

It is tempting to try and read the pragmatic maxim as if it had the following form, where \(C\!\) and \(E\!\) are supposed to be a 1-adic functions for "concept of" and "effects of", respectively.

1-adic functional case:

\[C(x) = C(E(x))\!\]

But it is really more like:

2-adic functional case:

\[C(y, x) = C(y, E(y, x))\!\]

where:

\[y\!\] = you.

\[C(y, x)\!\] = the concept that you have of \(x.\!\)

\[E(y, x)\!\] = the effects that you know of \(x.\!\)

      x           C(y, x)
      o------------>o 
     /|\            ^  
    / | \           =
   /  |  \          =
  /   |   \         =
e_1  e_2  e_3       =
  \   |   /         =
   \  |  /          =
    \ | /           =
     \|/            =
      o------------>o
    E(y, x)       C(y, E(y, x))

The concept that you have of \(x\!\) is the concept that you have of the effects that you know of \(x.\!\)

It is also very likely that the functional interpretations will not do the trick, and that 3-adic relations will need to be used instead.

Source. Jon Awbrey (08 Aug 2002), "Inquiry Driven Systems : Note 23", Ontology List, Peirce List.