[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

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PLOI.  Note 22

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It's a small world indeed that has just three Red things, 'A', 'B', 'C',
and so long as we occupy ourselves with a finite cosmos like the one in
this story, there is once again a way to warp "zeroth order logic" (ZOL)
to the task.  To wit, we declare the "qualities of being" 'A', 'B', 'C',
respectively, to be named by their names, and in order to say that they
number three distinct things we state three distinctions or inequations:

   A =/= B

   B =/= C

   C =/= A

This much we can do in any logical calculus, grammar, language, or syntax
that is adequate to express the expressions of ZOL, but there are certain
pragmatic benefits that accrue to a more efficient form of representation.

Let's draw the sub-universe (subverse?) of Red things in euler-venn style,
the heavier shading (^) for being's rule, the lighter (`) for its absence:

o-----------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` `o-------------o` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` / ^ ^ ^ ^ ^ ^ ^ \ ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` `/^ ^ ^ ^ ^ ^ ^ ^ ^\` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` / ^ ^ ^ ^ ^ ^ ^ ^ ^ \ ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `/^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^\` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` / ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ \ ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `o^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^o` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `|^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^|` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `|^ ^ ^ ^ ^ ^ A ^ ^ ^ ^ ^ ^|` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `|^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^|` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `|^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^|` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` `|^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^|` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` o--o----------o ^ o----------o--o ` ` ` ` ` ` |
| ` ` ` ` ` `/^ ^ \ ` ` ` ` `\^/` ` ` ` ` / ^ ^\` ` ` ` ` ` |
| ` ` ` ` ` / ^ ^ ^\` ` ` ` ` o ` ` ` ` `/^ ^ ^ \ ` ` ` ` ` |
| ` ` ` ` `/^ ^ ^ ^ \ ` ` ` `/`\` ` ` ` / ^ ^ ^ ^\` ` ` ` ` |
| ` ` ` ` / ^ ^ ^ ^ ^\` ` ` / ` \ ` ` `/^ ^ ^ ^ ^ \ ` ` ` ` |
| ` ` ` `/^ ^ ^ ^ ^ ^ \ ` `/` ` `\` ` / ^ ^ ^ ^ ^ ^\` ` ` ` |
| ` ` ` o ^ ^ ^ ^ ^ ^ ^o--o-------o--o^ ^ ^ ^ ^ ^ ^ o ` ` ` |
| ` ` ` | ^ ^ ^ ^ ^ ^ ^ ^ | ` ` ` | ^ ^ ^ ^ ^ ^ ^ ^ | ` ` ` |
| ` ` ` | ^ ^ ^ ^ ^ ^ ^ ^ | ` ` ` | ^ ^ ^ ^ ^ ^ ^ ^ | ` ` ` |
| ` ` ` | ^ ^ ^ ^ ^ ^ ^ ^ | ` ` ` | ^ ^ ^ ^ ^ ^ ^ ^ | ` ` ` |
| ` ` ` | ^ ^ ^ B ^ ^ ^ ^ | ` ` ` | ^ ^ ^ ^ C ^ ^ ^ | ` ` ` |
| ` ` ` | ^ ^ ^ ^ ^ ^ ^ ^ | ` ` ` | ^ ^ ^ ^ ^ ^ ^ ^ | ` ` ` |
| ` ` ` o ^ ^ ^ ^ ^ ^ ^ ^ o ` ` ` o ^ ^ ^ ^ ^ ^ ^ ^ o ` ` ` |
| ` ` ` `\^ ^ ^ ^ ^ ^ ^ ^ ^\` ` `/^ ^ ^ ^ ^ ^ ^ ^ ^/` ` ` ` |
| ` ` ` ` \ ^ ^ ^ ^ ^ ^ ^ ^ \ ` / ^ ^ ^ ^ ^ ^ ^ ^ / ` ` ` ` |
| ` ` ` ` `\^ ^ ^ ^ ^ ^ ^ ^ ^\`/^ ^ ^ ^ ^ ^ ^ ^ ^/` ` ` ` ` |
| ` ` ` ` ` \ ^ ^ ^ ^ ^ ^ ^ ^ o ^ ^ ^ ^ ^ ^ ^ ^ / ` ` ` ` ` |
| ` ` ` ` ` `\^ ^ ^ ^ ^ ^ ^ ^/`\^ ^ ^ ^ ^ ^ ^ ^/` ` ` ` ` ` |
| ` ` ` ` ` ` o-------------o ` o-------------o ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-----------------------------------------------------------o

In their imports for this sub-universe, the three propositional inequalities
A =/= B, B =/= C, C =/= A, so constrain the qualities of being 'A', 'B', 'C',
respectively, that only one of the corresponding propositions can be true of
any given thing.  The whole region marked by circumflecks is the rule of Red.

Jon Awbrey

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