ONT Re: Information = Comprehension x Extension -- Discussion
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
ICE. Discussion Note 32
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Re: ICE 19. http://suo.ieee.org/ontology/msg03780.html
Hx: ICE. http://suo.ieee.org/ontology/thrd28.html#03746
Hx: ICE. http://suo.ieee.org/ontology/thrd28.html#04746
| But when he learns that no red thing is blue,
| 'non-blue' is added to the comprehension of red,
| without the least diminution of its extension.
|
| Its comprehension becomes 'non-blue color'.
| Its extension remains 'A', 'B', 'C'.
|
| Peirce, CE 1, 463-464 (1866).
Our hero next has it, for the sake of the argument let's assume on good
information, that the predicate Red and the predicate Blue are mutually
exclusive in their application to objects in the universe of discourse.
It is easy enough to register the intensional effects of this new
parcel of information on the probability density picture, that we
chart at its simplest plateaunic levels in the topographic map of
a venn diagram, so let's take the tack of doing what's easy first.
Figure 9 depicts the state of information on being informed by the
two propositions ( Red ( Color )) and ( Red Blue ), that is to say,
"not Red without Color" and "not both Red and Blue". I didn't see
Peirce say anything about Blue being a Color, so I did not take it
for granted at this point.
o-----------------------------------------------------------o
|```````````````````````````````````````````````````````````|
|``X````````````````````````````````````````````````````````|
|```````````````````````````````````````````````````````````|
|``````````````````````o-------------o``````````````````````|
|`````````````````````/`````Color`````\`````````````````````|
|````````````````````/`````````````````\````````````````````|
|```````````````````/```````````````````\```````````````````|
|``````````````````/`````````````````````\``````````````````|
|`````````````````/```````````````````````\`````````````````|
|````````````````o`````````````````````````o````````````````|
|````````````````|`````````````````````````|````````````````|
|````````````````|`````````````````````````|````````````````|
|````````````````|`````````(b)c(r)`````````|````````````````|
|````````````````|`````````````````````````|````````````````|
|````````````````|`````````````````````````|````````````````|
|`````````````o--o----------o```o----------o--o`````````````|
|````````````/````\``````````\`/``````````/ \````````````|
|```````````/``````\``b`c(r)``o``(b)c`r``/ \```````````|
|``````````/````````\````````/ \````````/ \``````````|
|`````````/``````````\``````/ \``````/ \`````````|
|````````/````````````\````/b c r\````/ \````````|
|```````o``````````````o--o-------o--o o```````|
|```````|`````````````````| | |```````|
|```````|`````````````````| | |```````|
|```````|`````b`(c)(r)````| b(c)r | (b)(c) r |```````|
|```````|`````````````````| | |```````|
|```````|`````````````````| | |```````|
|```````o`````````````````o o o```````|
|````````\`````````````````\ / /````````|
|`````````\`````````````````\ / /`````````|
|``````````\`````````````````\ / /``````````|
|```````````\`````````````````o /```````````|
|````````````\`````Blue``````/`\ Red /````````````|
|`````````````o-------------o```o-------------o`````````````|
|```````````````````````````````````````````````````````````|
|`````````````````````````(b)(c)(r)`````````````````````````|
|```````````````````````````````````````````````````````````|
o-----------------------------------------------------------o
Figure 9. State of Information ( Red ( Color )) ( Red Blue )
Jon Awbrey
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
http://www.cs.bsu.edu/homepages/mighty/history.html
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o