ONT Information = Comprehension x Extension -- Discussion

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ICE.  Discussion Note 1

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antti,

random residuals ...

leibniz associated "intensions" (primitive qualities) with primes.
in scholastic terms, the "comprehension" of an object is all of
its qualities, or else the "comprehension" of a concept is all
of the qualities that it "contains", intensionally speaking,
or what we would probably call its collective implications.

for example:

HEC 2.  http://stderr.org/pipermail/inquiry/2003-April/000407.html

we have h = a r, or man = animal rational, or 6 = 2 * 3.

in numbers, 2|6 corresponds to 6 => 2,
in words, animal | man says man => rational,
no man we know, of course, just the prime ideal.

but positive integers imply powers of primes.
what should be the sense of 2^i 3^j 5^k ...?

here is where peirce comes in, defining a concept
of "information" and a measure |...| of information,
with |information| = |comprehension| x |extension|.

another slightly mysterious thing he says is:
"information is superfluous comprehension".

draw your own speculation ...

i am in the middle of redoing my very disorganized notes
on peirce's "theory of information", but will attach the
current working text just in case it might be of service.

ICE.  http://stderr.org/pipermail/inquiry/2003-March/thread.html#194
ICE.  http://stderr.org/pipermail/inquiry/2003-April/thread.html#356

jon awbrey

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