ONT Re: Information = Comprehension x Extension -- Discussion

[Jon Awbrey <jawbrey@att.net>]

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ICE.  Discussion Note 18

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We have this picture:

   q_1  q_2  q_3
    o    o    o
     \   |   /
      \  |  /
       \ | /
        \|/
         x
        /|\
       / | \
      /  |  \
     /   |   \
    o    o    o
   u_1  u_2  u_3

I drew this picture to represent the "state of information" (SOI)
where the object x has the comprehension Q = {q_1, q_2, q_3} and
the extension U = {u_1, u_2, u_3}, and thus by my interpretation
of Peirce's formula an "information content" of Info(x) = Q x U.

There are a number of nagging doubts that I have about this picture,
both with regard to its cogency as an interpretation of reality and
as an interpretation of Peirce's thinking about information in its
sundry aspects of comprehension and extension.  Still, I can think
of no better way to proceed at present than to continue with this
line of interpretation and see what develops.

Just by way of marking a backtrack point against the possibility
of adverse future contingencies, however, let me record as best
I can presently express them, a few of these residual worries:

   1.  I have gone ahead and drawn, or made as if to draw, the conventional
       distinction between "dividuals" like q_i and "individuals" like u_j.
       If we convene this convention in a critically reflective way, then
       it will be possible to go back and redraw it or withdraw it as the
       occasion demands or as the picture develops.  That is the theory.
       As a practical matter, and as the history of ideas amply shows,
       it tends to become almost impossible to see the contingency,
       much less review the cogency, of such founding conventions
       once we have taken the first few steps along their planks.

   2.  I have also gone ahead, if it be ahead, and introduced the object x
       as a hypostatic abstraction from the many signs that may refer to x.
       Any step that involves "reifying syntax" in this way is very chancy,
       has to be carried out with the utmost care, and has to be revisited
       on a periodic or a recurring basis to see if its warrant is genuine.

With all that in mind, we may now put it to the back thereof, and continue.

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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