Project : Notes And Queries

Peircean Pragmata

Several recent blog 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

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Inquiry Driven Systems : Note 23

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

| 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:

1.  Your concept of x is your concept of the practical effects of x.

Not exactly.  It seems a bit more like:

2.  Your concept of x is your concept of your-conceived-practical-effects of x.

Converting to a third person point of view:

3.  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:

1.  y = you.

2.  C(y, x) = the concept that you have of x.

3.  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.

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Source. Jon Awbrey (08 Aug 2002), Ontology List, Peirce List.