{ Information = Comprehension × Extension } • Comment 7

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Jon Awbrey

Oct 5, 2018, 5:50:28 PM10/5/18
to Ontolog Forum @ GG, SysSciWG, Structural Modeling
Ontologists and Kindred Spirits,

One of the most tantalizing puzzles in Peirce's work is the relation between
his theory of inquiry and his theory of signs. From the outset I found it
useful to return to his early ventures where the two theories work most
closely in tandem, indeed as offshoots of a single conception, namely,

Peirce's discussion of what he called “the laws of information”,
going back to his lectures of 1865 and 1866, marks one of those
places where he leapt far ahead of his time, anticipating ideas
we'd not see again until much later in the Twentieth Century.

So I've long found it well worth the effort to tease out the
hints of information theory he sketched in those early days.
In that spirit I'm going to make another try at returning
to a line of inquiry I started two years ago. Here is
where I last left off —

• { Information = Comprehension × Extension } • Comment 6



PS. My blog pre-hash:

cf: { Information = Comprehension × Extension } • Comment 7


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Jon Awbrey

Oct 8, 2018, 3:56:22 PM10/8/18
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So what is all this fuss about the relation between inquiry and signs,
as analyzed in Peirce's theories of their structure and function and
synthesized in his theory of information?

The best way I've found to see where the problem lies is to run through
a series of concrete examples Peirce used to illustrate the main ideas,
examples just complex enough to show their interactions with each other.

There is a small but very enlightening set of such examples in Peirce's
early lectures on the Logic of Science. Here is the blog post I wrote
by way of setting up their discussion:


• { Information = Comprehension × Extension }

Another angle from which to approach the incidence of signs and inquiry
is by way of C.S. Peirce’s “laws of information” and the corresponding
theory of information he developed from the time of his lectures on the
“Logic of Science” at Harvard University (1865) and the Lowell Institute (1866).

When it comes to the supposed reciprocity between extensions and intensions,
Peirce, of course, has another idea, and I would say a better idea, partly
because it forms the occasion for him to bring in his new-fangled notion of
“information” to mediate the otherwise static dualism between the other two.
The development of this novel idea brings Peirce to enunciate the formula:

• Information = Comprehension × Extension


• C.S. Peirce • Upon Logical Comprehension and Extension

• My Notes • Information = Comprehension × Extension




Jon Awbrey

Oct 10, 2018, 11:00:44 AM10/10/18
to SysSciWG, "Ontolog Forum"@GG, Structural Modeling
Aleksandar & Teams,

All life's branches and tangents are interesting ... but I'm deep in
the middle of a residential transformation that is eating up far more
time and concentration than I ever could have anticipated ... and I'm
trying to jump start a bit of work that seemed like a breakthrough in
my understanding of a root and branch issue in Peirce's work but got
waylaid by some annoying business a couple years ago ... so I'll be
trying to keep my eyes on that prize for the time being ...

Just by way of reminder, here's my blog rehashes of the thread so far:

On 10/10/2018 4:48 AM, Aleksandar Malečić wrote:
> The Tree of Porphyry is mentioned in that Peirce's article.
> https://en.wikipedia.org/wiki/Porphyrian_tree#Example - Each branch in this
> example makes sense, but how about the whole tree? In other words, does
> Nature use it? Is their any relationship between thinking substance and
> Plato as a particular individual?
> Aleksandar

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