ONT Re: Extension x Comprehension = Information
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Seeing as how I have trouble understanding any thing at all of much
complexity without a picture to guide me -- and not to victimize me!
said Jon apotropaically -- whether it's that I can't get into it in
the first place, or that I can't hang onto it for very long if I do,
I cannot help but to keep trying to form a clearer picture of what
Peirce is saying about these relationships of the kinds of signs
and the aspects of the sign relation to the kinds of inference
that serve a function in the "logic of science", or inquiry.
It was not my intention to keep you in suspense quite so long about
the sorts of things that go into the "objective framework" (OF) of
my diploid arrangement, indeed, I have discussed this on numerous
prior occasions, but this time I wanted make the explanation of
the plan as clear as I possibly could, and that has obliged me
to do a bit of stalling before I attempted my next installment.
So it's back to the drawing board, and the half-wetted diptych,
to see if I can paint a congenial picture of icons and indices.
This time around I will temporarily set aside trying to fathom
all of the ins and outs of Peirce's relatively intricate cases
of conjunctive terms and disjunctive terms that fall short of
being genuine symbols, and just try to detail my own way of
seeing the forms of icons and indices in this dual frame.
How to begin? It is said that the usual vertebrate brain
begins with a pleroma of neural connections that has to be
trimmed as its creature grows and learns. Just by way of
analogy, then, nothing more literal than that, let me draw
a Figure that is meant to suggest a sign relation with all
possible 3-ads of some 3-ple product space !O!x!S!x!I!.
With the powers invested in me by my poet's license and the
full extent of pictographic conventionality that I may have
in my command, let me draw the following picture to suggest
a sign relation Q = !O!x!S!x!I!. Taken in its own right, Q
has the structure of a 3-partite hypergraph, but the Figure
below is intended merely to approximate selected aspects of
its plenipotential structure, suggesting a complete bigraph,
that is, a complete 2-partite graph, stretching between the
points of !O! and the points of !S! = !I!, finished up with
a complete graph on the points of a syntactic set !S! = !I!.
According to long-standing conventions, these graphs can be
written as K_m,n = K(!O!, !S!) and K_n = K(!S!), where m, n
are the number of points in !O! and !S! = !I!, respectively.
Among those in the know, the technical
gnomen for a pleromic sign relation of
this empty-full variety is a "muddle".
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| o s ) |
| o · · s )) |
| o · · · · s ))) |
| o · · · · s )))) |
| o · · · · s ))))) |
| o · · · · · · · · · · · · · · s )))))) |
| o · · · · s ))))) |
| o · · · · s )))) |
| o · · · · s ))) |
| o · · s )) |
| o s ) |
| |
| |
| Muddled Sign Relation Q = !O!x!S!x!I! |
o-----------------------------------------------------------o
To be continued ...
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤