[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

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PLOI.  Note 8

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We come to the first example of an information process:

| 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

I can think of two distinct ways that we might interpret what Peirce
is saying about the relationship between the terms "color" and "red".
The harder path is the intransitive interpretation, which is what we
do when we say that an apple is red and red is a color but object to
anyone getting the notion that an apple is a color.  The easier path,
which I'll naturally take in the absence of any evidence that Peirce
intends otherwise, is the transitive interpretation, as if to intend
that "color" means "colored thing" or "having any color", whereby it
follows from anything being red that it necessarily has color.  This
puts the terms "color" and "red" on an equal par with each other, in
distinction to having "color" be a higher order predicate than "red".

It had at first sight seemed to me that our protagonist's
initial state of information could be represented like so:

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

But on further reflection it seems to me that, in the absence of information
to the contrary, our hero doesn't really know yet which of the terms "color"
or "red", if either, to place above the other.  In other words, as far as he
can know at this stage of the game, red could just as well be the only color
in town, making "being red" and "having color" into indiscernible predicates.

On this account, the agent's initial state of knowledge
is more accurately represented by the following bigraph:

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

I have no idea if this is the proper way to see things.
But we can always backtrack to this point if necessary.

Jon Awbrey

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