ONT Re: Information = Comprehension x Extension -- Discussion
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ICE. Discussion Note 28
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Your faithful scribe continues with his efforts
to illuminate Peirce's parable of the blind man.
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'.
I have in my plotting way just now gotten as far as illuminating the bare
beginnings of the story in two different styles of illustrations, to wit,
the probability density picture, of which the venn diagram epitomizes
the naivest form of primitivism, and the quotient lattice picture.
The logic of inquiry, especially when pursued in a computational setting,
has a tendency to be recursive, which is to say that it recreates itself
in the image of mathematical induction. For this reason I do not think
that we squander energy to spend so much time with these base cases,
since I know that a due form of recourse to them can pay handsome
dividends on the investment, in due course, in due time.
So let's persist in our effort to get as clear as we can about
the relationship between information, comprehension, extension,
not to mention possibility and probability, as illustrated here
in the two different styles of diagram.
Since we are presently concerned only with the relationship
between Color and Red, we may safely revert to the universe
W% = [c, r], whose LOC has 2^2 = 4 coordinates or cells and
whose LOP has 2^4 = 16 predicates or propositions. Here is
the corresponding venn diagram:
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|```````````````````````````````````````````````````````````|
|``W````````````````````````````````````````````````````````|
|```````````````````````````````````````````````````````````|
|``````````````````````o-------------o``````````````````````|
|`````````````````````/`````Color`````\`````````````````````|
|````````````````````/`````````````````\````````````````````|
|```````````````````/```````````````````\```````````````````|
|``````````````````/`````````````````````\``````````````````|
|`````````````````/```````````````````````\`````````````````|
|````````````````o`````````````````````````o````````````````|
|````````````````|`````````````````````````|````````````````|
|````````````````|`````````````````````````|````````````````|
|````````````````|``````````c`(r)``````````|````````````````|
|````````````````|`````````````````````````|````````````````|
|````````````````|`````````````````````````|````````````````|
|````````````````o``````````````o----------o--o`````````````|
|`````````````````\````````````/``````````/ \````````````|
|``````````````````\``````````/``````````/ \```````````|
|```````````````````\````````/```c``r```/ \``````````|
|````````````````````\``````/``````````/ \`````````|
|`````````````````````\````/``````````/ \````````|
|``````````````````````o--o----------o o```````|
|`````````````````````````| |```````|
|`````````````````````````| |```````|
|`````````(c)(r)``````````| (c) r |```````|
|`````````````````````````| |```````|
|`````````````````````````| |```````|
|`````````````````````````o o```````|
|``````````````````````````\ /````````|
|```````````````````````````\ /`````````|
|````````````````````````````\ /``````````|
|`````````````````````````````\ /```````````|
|``````````````````````````````\ Red /````````````|
|```````````````````````````````o-------------o`````````````|
|```````````````````````````````````````````````````````````|
|```````````````````````````````````````````````````````````|
|```````````````````````````````````````````````````````````|
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Figure 6. Imposition of the Constraint ( Red ( Color ))
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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