[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

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PLOI.  Note 13

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Once again, it looks like we need to back away from our current pictures
of the problem, take in a wider view, and think a bit more broadly about
what's really going on here.  One of the big ideas in the background, so
pervasive that we frequently overlook it, can be emblazoned in the theme:
"The Information's The Thing".  In other words, the total information is
at all times the principal reality to be taken into consideration, while
comprehension and extension are but projected aspects of the information.

This can be made clearer if we recall the places where Peirce
characterizes the information borne by a sign as the totality
of synthetic facts that are implicit in its use.  For example:

| We see then that all symbols besides their denotative and
| connotative objects have another;  their informative object.
| The denotative object is the total of possible things denoted.
| The connotative object is the total of symbols translated or implied.
| The informative object is the total of forms manifested and is measured
| by the amount of intension the term has, over and above what is necessary
| for limiting its extension.
|
| For example the denotative object of 'man' is such collections of
| matter the word knows while it knows them, i.e., while they are organized.
| The connotative object of 'man' is the total form which the word expresses.
| The informative object of 'man' is the total fact which it embodies;  or the
| value of the conception which is its equivalent symbol.
|
| C.S. Peirce, 'Chronological Edition', CE 1, 276
| Cf: ICE 28.  http://stderr.org/pipermail/inquiry/2004-November/001945.html
| In: ICE.     http://stderr.org/pipermail/inquiry/2004-November/thread.html#1913

The use of the phrase "total fact" recalls the classical articulations of
the three kinds of inference -- abduction, deduction, induction -- by way
of Cases, Facts, and Rules, as prefigured in the following generic sketch:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` |\` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | \ ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | `\` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` \ Rule` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` `\` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` \ ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` `\` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` Fact` | ` ` ` o ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` `/` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` / ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` `/` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` / Case` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

In trying to form a minimal model of Peirce's story, which we must be
able to do if his story is the least bit consistent, we find ourselves
engaged in two different types of reasoning in parallel with each other.
At one level, we are thinking out the constitution of a particular model,
also known as a "situation", a "structure", or a "universe of discourse".
At another level, we are thinking about the structures of many alternative
models, many different imaginary scenarios that might flesh out the script.
The former is actually a "zeroth order model" (ZOM), and can be constructed
within the bounds of propositional logic or partial orderings of propositions.
Getting to the next level will take a few "higher order propositions" (HOP's),
that is, propositions about propositions, or propositions about the structures
of whole different universes of discourse.  That is more or less tantamount to
the "first order predicate calculus", or the "logic of quantified propositions".
However, if we are really satisfied with finding a "minimal" model, any way that
we can arrange one, and don't really need a complete analysis of the story, then
it is possible to carry out almost all of the reasoning in and about a simple ZOM.

Jon Awbrey

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