ONT Re: Information = Comprehension x Extension -- Discussion
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ICE. Discussion Note 17
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Suppose a person resides in a "state of information" (SOI) where an object x
has the comprehension that is given by the set of intensions {q_1, q_2, q_3}
and the extension that is determined by the set of entities {u_1, u_2, u_3}.
Here I am treating the object x as an abstract formal object, for instance,
an element in a "partially ordered set" (poset), in particular, a lattice.
q_1 q_2 q_3
o o o
\ | /
\ | /
\ | /
\|/
x
/|\
/ | \
/ | \
/ | \
o o o
u_1 u_2 u_3
The object x will typically be denoted by many different signs from
a suitable sign domain, and it seems okay, at least, for the moment,
to say that each of these signs has the comprehension and extension
of x itself.
Adapted to this modestly transformed symbolic environment, Peirce's formula for
the information content of a symbol (term, proposition, argumentation) says that
the information content of the object x is given by the cartesian product Q x U
of its comprehension Q = {q_1, q_2, q_3} and its extension U = {u_1, u_2, u_3}.
The natural measure of information among discrete constellations like these is
the number of elements in each set, and so we have |Info(x)| = |Q x U| = |Q||U|.
I will need to think about that a while
to see if there are any hidden problems.
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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