[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

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PLOI.  Note 16

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For ease of reference, let's give our hero a name, say "Homer",
and let's now try to imagine how it might have transpired that
he arrived at yet another state of information that we know he
must have reached some time before we came in, namely, when he
learned that not all colors are red.  This could have happened
by "acquaintance" or by "being told", but Peirce has ruled out
the former route to knowledge, it seems, by making Homer blind.

The minimal elements of knowledge involved in taking this step
seem to be that Red => Color, but that Color =/= Red, possibly
along with the fact that there is at least one thing, say 'D',
that has Color but is not Red.

We have at this point stepped outside the bounds of what can be
represented in a "zeroth order model" (ZOM), as we can tell from
the use of the existential quantifier "there exists at least one"
in the above statement, and also, less conspicuously, from the fact
that the condition "Color =/= Red" is not being invoked in a purely
propositional sense, but refers to the inequality of two propositions
regarded as whole functions, that is, Color =/= Red : X -> B, where X
is a suitable universe of discourse and B is the boolean domain {0, 1}.

The following Figure will give us some hint of the situation:

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

This seems to suggest that the term "Red" has increased in depth
while remaining the same in breadth, but that the term "Color"
has increased in breadth while remaining the same in depth.

Jon Awbrey

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