[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

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PLOI.  Note 12

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Let's see if we have enough tackle to
haul our first example into the light:

| Thus suppose a blind man to be told that no red things are blue.
| 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'.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 463

Supposing for the moment that we begin with the minimal model, to wit,
the "complete muddle" that has the form of the complete bigraph K_2,3,
it's tantamount to preposing prior to the place where Peirce comes in
a primal experience that is even more inchoate than the one where our
hero takes the term "red" as denoting a class or an object of thought:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` A ` ` B ` ` C ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` o-------------------o ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` Color | ` 1 ` ` 1 ` ` 1 ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` Red ` | ` 1 ` ` 1 ` ` 1 ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` o-------------------o ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

Initiated into this predicament of buzzing booming confusion,
the most that we have is three moments of experience, A, B, C,
each of which has the same two marks of quality, Color and Red.
It doesn't make any real difference if we call them "Exemplars"
and "Qualities", respectively, so for brevity we might as well.

The odd thing about the maximal muddle, in so far as it's constrained
to fill out the given frame, is that it's actually one of the easiest
to bring to order through the simple act of introducing a middle term:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` Color ` ` ` `Red` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` `\` ` ` ` `/` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` \ ` ` ` / ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` `\` ` `/` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` \ ` / ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` `\`/` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` Intermediate Object ` o<<<<<<<<<<<o ` Middle Term ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` `/|\` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` / | \ ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` `/` | `\` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` / ` | ` \ ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` `/` ` | ` `\` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` o ` ` o ` ` o ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` A ` ` B ` ` C ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

Except for the chevroned relation of denotation from the middle term
to the intermediate object, this is cast as a lattice diagram, where
transitive closure of lattice relations is understood to be in force.
Accordingly, there is an implicit line between each point at the top
and each node at the bottom, inducing the same K_2,3 on these points
that we had before.  With regard to the middling object that we used
to factor the initial muddle, it has a breadth of 3 and a depth of 2.
At least that's 1 way to look at it.  I'm not saying it's the only 1.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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