ONT Re: Differential Logic
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DLOG. Note D47
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Analytic Expansion of Conjunction
| In her sufferings she read a great deal and discovered
| that she had lost something, the possession of which
| she had previously not been much aware of: a soul.
|
| What is that? It is easily defined negatively:
| it is simply what curls up and hides when there
| is any mention of algebraic series.
|
| Robert Musil, 'The Man Without Qualities', [Mus, 118]
Figure 35 pictures the form of conjunction J : B^2 -> B as a transformation
from the 2-dimensional universe [u, v] to the 1-dimensional universe [x].
This is a subtle but significant change of viewpoint on the proposition,
attaching an arbitrary but concrete quality to its functional value.
Using the language introduced earlier, we can express this change by
saying that the proposition J : <|u, v|> -> B is being recast into
the thematized role of a transformation J : [u, v] -> [x], where
the new variable "x" takes the part of a thematic variable ¢(J).
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| |
| |
| o---------o o---------o |
| / \ / \ |
| / o \ |
| / /`\ \ |
| / /```\ \ |
| o o`````o o |
| | |`````| | |
| | u |`````| v | |
| | |`````| | |
| o o`````o o |
| \ \```/ / |
| \ \`/ / |
| \ o / |
| \ / \ / |
| o---------o o---------o |
| |
| |
o---------------------------------------o
\ /
\ /
\ /
\ J /
\ /
\ /
\ /
o--------------\---------/--------------o
| \ / |
| \ / |
| o------@------o |
| /```````````````\ |
| /`````````````````\ |
| /```````````````````\ |
| /`````````````````````\ |
| o```````````````````````o |
| |```````````````````````| |
| |`````````` x ``````````| |
| |```````````````````````| |
| o```````````````````````o |
| \`````````````````````/ |
| \```````````````````/ |
| \`````````````````/ |
| \```````````````/ |
| o-------------o |
| |
| |
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Figure 35. Conjunction as Transformation
Jon Awbrey
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