ONT Re: Information = Comprehension x Extension -- Discussion
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
ICE. Discussion Note 21
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Re: ICE 19. http://stderr.org/pipermail/inquiry/2003-March/000212.html
In: ICE. http://stderr.org/pipermail/inquiry/2003-March/thread.html#194
Let us return to Peirce's example of a blind man who receives
various increments of information about the colors of objects.
The figure of a blind man takes the issue of relating sensory
data to conceptual information out of the picture. In effect,
it reduces the instigations of theory change to the medium of
"knowledge by being told", as separated from the complicating
data of "knowledge by acquaintance", and permits us to regard
all relevant information as represented in propositional form.
CSP: | He has previously known only that red is a color;
| and that certain things 'A', 'B', and 'C' are red.
|
| The comprehension of red then has been for him 'color'.
| Its extension has been 'A', 'B', 'C'.
Our hero, let's call him "Homer" and assign him the epithet "H",
starts out from a state of information where he is given to know
that Red => Color and that A, B, C are Red. For an agent in this
state of information, the comprehension of Red is {Color} and the
extension of Red is {A, B, C}.
Color
o
|
|
|
|
Red
/|\
/ | \
/ | \
/ | \
o o o
A B C
Introducing a few items of notation, we we may write the following:
Comp(Red) = {Color}
Exte(Red) = {A, B, C}
Info(Red) = Comp(Red) x Exte(Red)
= {Color} x {A, B, C}
= {<Color, A>, <Color, B>, <Color, C>}
Of course, all of this data ought to be parameterized
as belonging to Homer in a given state of information.
For example, Comp(Red, H, SOI_1) = {Color}, and so on.
And so it begins ...
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
http://www.cs.bsu.edu/homepages/mighty/history.html
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o