ONT Re: Information = Comprehension x Extension -- Discussion
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ICE. Discussion Note 23
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Peirce's treatment of the relation between information and comprehension
is perhaps a bit more challenging at first sight than his account of the
relation between information and extension. It might be good, therefore,
to take a more gradual approach, to back up and start from more familiar
grounds. I will bring together a number of different ways that are used
to understand the relation between logic and information theory, attempt
to build up an integrated picture of how they articulate with each other,
and attempt to use the perspective thus gained to tackle Peirce's theory.
That is the plan.
More specifically, it would be good if we could get a sense of how
the lattice quotient picture and the probability density picture of
information relate to common sense ideas about logical constraints,
for instance, as exhibited at the level of propositional calculus.
Back to the beginning of the universe of discourse, then, at any rate,
the one that we get if we ignore for the moment the more particulate
elements of extension A, B, C, D, ..., and consider nothing but the
3-fold of abstract qualities {Blue, Color, Red}. The lot of these
qualities have no especially colorful meaning as of yet, but are
born rather basely into the equipotential, undifferentiated, or
primordial ylematic state of information that I may attempt to
portray in the form shown here:
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Figure 1. Three-Dimensional Universe Of Discourse
At this primal stage of the game we have imposed no constraints
on the relations among any of the three qualities, as indicated
by the circumstance that each circle bisects each of the others
and all of the cells have the same shade of logical possibility.
For future reference, the next Figure shows the scheme of color
"coordinates" that I will use to indicate the cells of the venn
diagram, adopting the lower case letters "b", "c", "r" to refer
to the properties Blue, Color, Red, respectively, and enclosing
a label in parentheses to indicate its negation.
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Figure 2. Three-Dimensional Universe with Cell Coordinates
To be continued ...
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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