Changes

I will start with some loose threads that were left hanging the last time that I tangled with this topic, but here are some bits of background reading for those who would like to thread the maze on their own:

I will start with some loose threads that were left hanging the last time that I tangled with this topic, but here are some bits of background reading for those who would like to thread the maze on their own:

* ICE. Information = Comprehension x Extension

* Information = Comprehension × Extension • [http://web.archive.org/web/20150302042625/http://stderr.org/pipermail/inquiry/2004-November/thread.html#1913 Inquiry List] • [http://web.archive.org/web/20140330191602/http://forum.wolframscience.com/showthread.php?threadid=609 NKS Forum]

* ICE. http://web.archive.org/web/20140330191602/http://forum.wolframscience.com/showthread.php?threadid=609

* ICE. http://web.archive.org/web/20150302042625/http://stderr.org/pipermail/inquiry/2004-November/thread.html#1913

In my current state of information I'm aware of Peirce having investigated at least two different measures of information, one that we may call ''multiplicative'' and the other that we may call ''exponential''.  Though I'll take up with the multiplicative measure first, it will be one of my interests here to understand the possible relation between these two measures of information and also their relation to current concepts of information.

In my current state of information I'm aware of Peirce having investigated at least two different measures of information, one that we may call ''multiplicative'' and the other that we may call ''exponential''.  Though I'll take up with the multiplicative measure first, it will be one of my interests here to understand the possible relation between these two measures of information and also their relation to current concepts of information.

|

|

| C.S. Peirce, 'Chronological Edition', CE 1, 276

| C.S. Peirce, 'Chronological Edition', CE 1, 276

</pre>

</pre>

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:

 

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

{| align="center" border="0" cellpadding="10"

{| align="center" border="0" cellpadding="10"

|

|

| C.S. Peirce, 'Chronological Edition', CE 1, 463

| C.S. Peirce, 'Chronological Edition', CE 1, 463

</pre>

</pre>

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.

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.

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

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

* Cf: ICE 2.  http://stderr.org/pipermail/inquiry/2004-November/001914.html

* Cf: [http://stderr.org/pipermail/inquiry/2004-November/001914.html ICE 2]

* In: ICE.    http://stderr.org/pipermail/inquiry/2004-November/thread.html#1913

* In: [http://stderr.org/pipermail/inquiry/2004-November/thread.html#1913 ICE]

* Cf: PLOI-DIS 1.  http://stderr.org/pipermail/inquiry/2005-December/003280.html

* Cf: [http://stderr.org/pipermail/inquiry/2005-December/003280.html PLOI-DIS 1]

* In: PLOI-DIS.    http://stderr.org/pipermail/inquiry/2005-December/thread.html#3280

* In: [http://stderr.org/pipermail/inquiry/2005-December/thread.html#3280 PLOI-DIS]

As mentioned in the above Discussion Note, one of the difficulties that we encounter in trying to model Peirce's blind man story is the problem of how to handle ''improper implications'' or ''trivial intensions'' of the form ''X'' &rArr; ''X''.  On the one hand, any concept or term will significantly alter the informational situation when it first arises, for example, on the prompting of an abductive hypothesis or other creative intervention.  On the other hand, Peirce appears to discount these types of intensions by accounting for the information as the "superfluous comprehension" of a symbol, in effect, as the intension that a symbol has "over and above what is necessary for limiting its extension" (CE 1, 276).  I sought to finesse this issue in my retelling of the story by interjecting a prior episode where the abductive factorization is more explicitly considered.  Only time will tell whether this is a sensible direction to take or not.

As mentioned in the above Discussion Note, one of the difficulties that we encounter in trying to model Peirce's blind man story is the problem of how to handle ''improper implications'' or ''trivial intensions'' of the form ''X'' &rArr; ''X''.  On the one hand, any concept or term will significantly alter the informational situation when it first arises, for example, on the prompting of an abductive hypothesis or other creative intervention.  On the other hand, Peirce appears to discount these types of intensions by accounting for the information as the "superfluous comprehension" of a symbol, in effect, as the intension that a symbol has "over and above what is necessary for limiting its extension" (CE 1, 276).  I sought to finesse this issue in my retelling of the story by interjecting a prior episode where the abductive factorization is more explicitly considered.  Only time will tell whether this is a sensible direction to take or not.