[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

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PLOI.  Note 14

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Back to the story:

| 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
| Cf: ICE 19.  http://stderr.org/pipermail/inquiry/2004-November/001933.html
| In: ICE.     http://stderr.org/pipermail/inquiry/2004-November/thread.html#1913

We have seen that there must be a state of information
that precedes the one where this story begins, a state
where being colored and being red are indistinct facts.

The information embodied in that state of knowledge,
regarded as a totality of synthetic facts, might be
represented in a propositional data base as follows:

   A => Color
   B => Color
   C => Color
   A => Red
   B => Red
   C => Red

The same raw data might be given in lattice form as follows:

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

Arbitrary congeries of empirical data or synthetic facts can be represented
in just these ways.  As such, the "total fact" embodied in them is perfectly
good information, as far as information goes.  But the particular collection
of empirical data or synthetic facts embodied in the above representations is
not arbitrary -- it has a special structure that permits it to be "factored"
through the medium of a hypothetical object M and a middle term as follows:

   A, B, C => M

   M => Color, Red

Or, to capture the total fact in a single picture:

` ` ` ` ` ` ` ` ` ` ` `Color,`Red ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` \ Rule` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` `\` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` Fact` | ` ` ` o M ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` `/` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` / Case` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` `A, B, C` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

Not every state of information allows the interpolation of a compact object
with its own comprehension and extension, but this epistemic situation does.

Jon Awbrey

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