{ Information = Comprehension × Extension } • Revisited

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Jon Awbrey

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Jan 23, 2019, 3:14:37 PM1/23/19
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Ontolog Forum, Systems Science, Structural Modeling —

Three summers ago I hit on what struck me as a new insight into one of the most recalcitrant problems
in Peirce's semiotics and logic of science, namely, the relation between “the manner in which different
representations stand for their objects” and the way in which different inferences transform states of
information. I roughed out a sketch of my epiphany in a series of blog posts then set it aside for the
cool of later reflection. Now looks to be that later and looking out my window it is certainly cooler.

A first pass through the variations of representation and reasoning distinguishes
the axes of iconic, indexical, and symbolic manners of representation on the one hand
and the axes of abductive, inductive, and deductive modes of inference on the other.
Early and often Peirce will argue for a natural correspondence between these modes of
inference and these manners of representation but Peirce's early arguments differ from
his later accounts in ways deserving a second look. This is partly for the extra points
in his line of reasoning and partly for his explanation of indices as signs constituted
by convening the variant conceptions of sundry interpreters.

To be continued ...

Jon

joseph simpson

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Jan 23, 2019, 4:10:24 PM1/23/19
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Jon:

You wrote:
" I roughed out a sketch of my epiphany in a series of blog posts then set it aside for the
cool of later reflection. "

Are you able to provide pointers to the existing blog posts?

Thanks for the additional information.

Take care, be good to yourself and stay warm,

Joe

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Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw
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Jon Awbrey

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Jan 24, 2019, 6:30:42 AM1/24/19
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Re: { Information = Comprehension × Extension } • Revisited
https://inquiryintoinquiry.com/2019/01/23/information-comprehension-x-extension-%e2%80%a2-revisited/

Here's a few resource links I meant to add:

• Survey of Pragmatic Semiotic Information • 4 (See especially the section on I = C × E)
https://inquiryintoinquiry.com/2019/01/08/survey-of-pragmatic-semiotic-information-%e2%80%a2-4/

• My Notes • Information = Comprehension × Extension
http://intersci.ss.uci.edu/wiki/index.php/Information_%3D_Comprehension_%C3%97_Extension

• C.S. Peirce • Upon Logical Comprehension and Extension
http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm

Regards,

Jon

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Jon Awbrey

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Jan 24, 2019, 8:16:27 AM1/24/19
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Joe:

I collected links to previous Selections, Comments, and Discussions on this topic at the following Survey page:


But my plan for the next month or so will be to review all this material in a careful if somewhat plodding manner.  I’ve been studying Peirce for just over 50 years now and I’m still seeing new facets of the gem 💎 each time I return to what I imagined was familiar texts, so I’ll be taking time to nose 👃 the roses 🌹 this time around. 

Regards,

joseph simpson

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Jan 24, 2019, 1:10:05 PM1/24/19
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Jon:

Thanks for the additional information.

In the context of the current discussion it is interesting to consider the following formula:

Implication = Extension x Intension

In addition, it is interesting to further consider a point by John Sowa:

"One sense is the process of informing, and the other sense
     is the direct object of the verb, i.e., that meaning which
     is conveyed by the process."

In the context of the process of informing (receiving a message), the information receiver performs a state change when receiving new information.

If the information receiver acquires that same message again, then the information 
receiver does not respond with a state change (the receiver already knows this information).

The meaning of the message is the same in each case.

The information content of the message is high when it is first received (the message contains information).

The information content of the message is zero when the message is received again (the message contains no information).

Take care, be good to yourself and have fun,

Joe

Jon Awbrey

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Jan 25, 2019, 9:20:30 AM1/25/19
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Dear Mihai,

I remember us having some previous discussions on the Peirce List, or maybe it was
some other list, quite a few years ago, but just by way of becoming re-acquainted
here's an article of mine bearing on the present topic, namely, the relationship
between Peirce's theory of triadic sign relations and his theory of inquiry.
It also gives a smattering of historical context, bracketing Peirce between
Aristotle and Dewey.

Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”,
''Inquiry : Critical Thinking Across the Disciplines'' 15(1), pp. 40–52.

https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry
On 1/23/2019 5:07 PM, Nadin, Mihai wrote:
> Dear Jon Awbrey,
>
> Dear everyone,
>
> If you do not consider all the elements constitutive
> of a sign together, you are not working with a Peirce
> understanding of the sign. I kept out of the discussion
> because I feel no need to correct anyone.
>
> In this case I will only submit to all of you a diagram that
> describes the sign in its unity. There is no semantics that
> can be defined without acknowledging the sign in its UNITY —
> between the object represented, the representation, the
> process (open ended) of interpretation:
>
> [cid:image0...@01D4B335.D15CDE70]
>
> I wish you all well. And will step back again.
>
> Mihai Nadin
>

Jon Awbrey

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Jan 26, 2019, 11:26:27 AM1/26/19
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Cf: { Information = Comprehension × Extension } Revisited • Selection 1
At: http://inquiryintoinquiry.com/2019/01/26/information-comprehension-x-extension-revisited-%e2%80%a2-selection-1/

Ontolog Forum, Systems Science, Structural Modeling —

Our first text comes from Peirce's Lowell Lectures of 1866,
titled “The Logic of Science, or, Induction and Hypothesis”.
I still remember the first time I read these words and the
light that lit up the page and my mind.

<QUOTE>

Let us now return to the information. The information of a term is
the measure of its superfluous comprehension. That is to say that the
proper office of the comprehension is to determine the extension of the
term. For instance, you and I are men because we possess those attributes —
having two legs, being rational, &c. — which make up the comprehension of man.
Every addition to the comprehension of a term lessens its extension up to a
certain point, after that further additions increase the information instead.

Thus, let us commence with the term colour; add to the comprehension
of this term, that of red. Red colour has considerably less extension
than colour; add to this the comprehension of dark; dark red colour
has still less [extension]. Add to this the comprehension of non-blue —
non-blue dark red colour has the same extension as dark red colour, so
that the non-blue here performs a work of supererogation; it tells us
that no dark red colour is blue, but does none of the proper business of
connotation, that of diminishing the extension at all. Thus information
measures the superfluous comprehension. And, hence, whenever we make a
symbol to express any thing or any attribute we cannot make it so empty
that it shall have no superfluous comprehension.

I am going, next, to show that inference is symbolization and that
the puzzle of the validity of scientific inference lies merely in
this superfluous comprehension and is therefore entirely removed
by a consideration of the laws of information.

(Peirce 1866, p. 467)

</QUOTE>

Reference
=========

• Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”,
Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce :
A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project,
Indiana University Press, Bloomington, IN, 1982.

joseph simpson

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Jan 27, 2019, 1:12:48 AM1/27/19
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Mihai:

Interesting work, just a few short comments.

Shannon and Weaver focused on "The Mathematical Theory of Communication."

In their work, communication was used "in a very broad sense to include all of the procedures by which one mind may affect another."

Their work defined three levels of communication problems:
  Level A: The technical problem
  Level B: The semantic problem
  Level C: The effectiveness problem.

These three levels provide a basic discussion framework.

Two primary questions are:
  -- What amount of information is encoded in any communication?
  -- What is the value of the information encoded in any communication?

Answering these two primary questions in terms of the basic discussion framework may be an approach that helps illuminate the information and semiotic processes involved in any specific communication.

Take care, b good to yourself and have fun,

Joe

On Sat, Jan 26, 2019 at 5:35 PM Nadin, Mihai <na...@utdallas.edu> wrote:
Dear and respected colleagues,
The discussion in information is too important is you deal with ontology aspects. May I suggest a reading to the group?
ftp://ftp.inf.puc-rio.br/pub/docs/FomularioSolicitacoes/nsmail.pdf

Willing to entertain questions. Peirce is more than meets the eye.

Mihai Nadin
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joseph simpson

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Jan 27, 2019, 7:48:58 PM1/27/19
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---------- Forwarded message ---------
From: joseph simpson <jjs...@gmail.com>
Date: Sun, Jan 27, 2019 at 4:45 PM
Subject: Re: [ontolog-forum] Re: { Information = Comprehension × Extension } • Revisited
To: Ontolog Forum @ GG <ontolo...@googlegroups.com>


Mihai:

Interesting response.

My text:

'In their work, communication was used "in a very broad sense to include all of the procedures by which one mind may affect another." '

The portion in double quotes was taken directly from page 3, of "The Mathematical Theory of Communication," Claude E. Shannon and Warren Weaver, 1963.

My text:

"Level A: The technical problem
  Level B: The semantic problem
  Level C: The effectiveness problem."

Was adapted from page 4, of "The Mathematical Theory of Communication," Claude E. Shannon and Warren Weaver, 1963.  I did not use double quotes in my original message because I did not quote that section word for word.

In addition, the book, "Operations Research and Systems Engineering," Charles D. Flagle, William H. Huggins and Robert H. Roy, 1960, Johns Hopkins Press, has a nice section on Information Theory.  It is my plan to adapt the examples from the Johns Hopkins work as practical scenarios to provide a basis for message and communication analysis.

I will try to be more careful when I do not use a complete quote, and just indicate that it is adapted from a specific source.

Take care, be good to yourself and have fun,

Joe



On Sun, Jan 27, 2019 at 2:55 PM Nadin, Mihai <na...@utdallas.edu> wrote:

Dear Joseph Simpson,

Thank you. What you call Level B was not addressed. Shannon made it clear that there is no semantics in the model.

No, they did not deal with information. They dealt with data. More precisely:  how do we transmit data in the most effective way. No semantics, no meaning. Only data associated with meaning becomes in formation.

 

The value of the data encoded (at the emitter side) was never a subject. Shannon wrote often about the fact that his model was strictly syntactic. That was their assignment (from the military and from the Lab where Shannon worked).

If you ever want to learn more about it, please let me know.

 

May I quote you: Take care, be good to yourself and have fun

 

Mihai Nadin


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kall...@gmail.com

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Jan 27, 2019, 8:00:14 PM1/27/19
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I expanded on Shannon et al’s concept of communication in a broader sense – the exchange of matter, energy, information or entropy between two bound objects. What is common to both Shannon and Clausius entropy are structures that allowed communication now missing that once existed.

 

Ken

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joseph simpson

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Jan 27, 2019, 10:57:07 PM1/27/19
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Mihai:

A final comment on this subject.

Please see the quote below, from : 

Reprinted with corrections from The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, July, October, 1948.

A Mathematical Theory of Communication 


"Two extremes of redundancy in English prose are represented by Basic English and by James Joyce’s book “Finnegans Wake”. The Basic English vocabulary is limited to 850 words and the redundancy is very high. This is reflected in the expansion that occurs when a passage is translated into Basic English. Joyce on the other hand enlarges the vocabulary and is alleged to achieve a compression of semantic content.
The redundancy of a language is related to the existence of crossword puzzles. If the redundancy is zero any sequence of letters is a reasonable text in the language and any two-dimensional array of letters forms a crossword puzzle. If the redundancy is too high the language imposes too many constraints for large crossword puzzles to be possible. A more detailed analysis shows that if we assume the constraints imposed by the language are of a rather chaotic and random nature, large crossword puzzles are just possible when the redundancy is 50%. If the redundancy is 33%, three-dimensional crossword puzzles should be possible, etc.  "

Communication may be enhanced using semantic correction.  While the noise in some communication channels may be addressed using correction codes and other error correcting approaches, there are some communication channels that do not have these types of capabilities.

A simple example of a semantic correction communication system is the "Talking Drums of Africa." 
For a brief background see:  


The talking drum technology did not have the tonal range of the human voice.  Therefore the spoken tonal languages could not be reproduced 100 percent on the drums.  A good drummer would craft words that fit the drum tonal range and then create a semantic story that eliminated any uncertainty in the message information.  Note, the message sender and receiver would have to share a common semantic context.

Information uncertainty can be eliminated using semantic compression or decompression. 

Further, messages may be encrypted in a similar manner.  The Navajo code talkers are an example.

That is enough for now.

Take care, be good to yourself and have fun,

Joe





On Sun, Jan 27, 2019 at 5:28 PM Nadin, Mihai <na...@utdallas.edu> wrote:

Dear Joseph Simpson,

Your integrity was never questioned.

Just a quote:

Roughly speaking, Shannon entropy is concerned with the statistical

properties of a given system and the correlations between the states of two systems,

independently of the meaning and any semantic content of those states.

Cf. What is Shannon information? Lomardi, Holik, Vanni

 

Shannon himself (A Mathematical Theory of Communication, Reprinted with corrections from

The Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, July, October, 1948):

The fundamental problem of communication is that of reproducing at one point either exactly or ap-

proximately a message selected at another point. Frequently the messages have meaning ; that is they refer

to or are correlated according to some system with certain physical or conceptual entities. These semantic

aspects of communication are irrelevant to the engineering problem.

 

Well, he was solving an engineering problem. Please note also that his initial paper was a theory of communication. Later he regretted to have named it (with Weaver) a theory of information.

 

Take care, be good to yourself and have fun,

 

Mihai Nadin

 

 

 

From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> On Behalf Of joseph simpson
Sent: Sunday, January 27, 2019 6:46 PM
To: Ontolog Forum @ GG <ontolo...@googlegroups.com>
Subject: Re: [ontolog-forum] Re: { Information = Comprehension × Extension } • Revisited

 

Mihai:

 

Interesting response.

 

My text:

 

'In their work, communication was used "in a very broad sense to include all of the procedures by which one mind may affect another." '

 

The portion in double quotes was taken directly from page 3, of "The Mathematical Theory of Communication," Claude E. Shannon and Warren Weaver, 1963.

 

My text:

 

"Level A: The technical problem

  Level B: The semantic problem

  Level C: The effectiveness problem."

 

Was adapted from page 4, of "The Mathematical Theory of Communication," Claude E. Shannon and Warren Weaver, 1963.  I did not use double quotes in my original message because I did not quote that section word for word.

 

In addition, the book, "Operations Research and Systems Engineering," Charles D. Flagle, William H. Huggins and Robert H. Roy, 1960, Johns Hopkins Press, has a nice section on Information Theory.  It is my plan to adapt the examples from the Johns Hopkins work as practical scenarios to provide a basis for message and communication analysis.

 

I will try to be more careful when I do not use a complete quote, and just indicate that it is adapted from a specific source.

 

Take care, be good to yourself and have fun,

 

Joe

 

 

 

On Sun, Jan 27, 2019 at 2:55 PM Nadin, Mihai <na...@utdallas.edu> wrote:

Dear Joseph Simpson,

Thank you. What you call Level B was not addressed. Shannon made it clear that there is no semantics in the model.

No, they did not deal with information. They dealt with data. More precisely:  how do we transmit data in the most effective way. No semantics, no meaning. Only data associated with meaning becomes in formation.

 

The value of the data encoded (at the emitter side) was never a subject. Shannon wrote often about the fact that his model was strictly syntactic. That was their assignment (from the military and from the Lab where Shannon worked).

If you ever want to learn more about it, please let me know.

 

May I quote you: Take care, be good to yourself and have fun

 

Mihai Nadin

 

From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> On Behalf Of joseph simpson


Sent: Sunday, January 27, 2019 12:13 AM
To: Ontolog Forum @ GG <ontolo...@googlegroups.com>; mjs...@gmail.com


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Joe Simpson

“Reasonable people adapt themselves to the world. 

Unreasonable people attempt to adapt the world to themselves. 

All progress, therefore, depends on unreasonable people.”

George Bernard Shaw

Git Hub link:

Research Gate link:

YouTube Channel

Web Site:

 

 

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Jon Awbrey

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Jan 28, 2019, 4:04:19 PM1/28/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Selection 2
At: http://inquiryintoinquiry.com/2019/01/28/information-comprehension-x-extension-revisited-%e2%80%a2-selection-2/

Ontolog Forum, Systems Science, Structural Modeling —

Over the course of Selection 1 Peirce introduces the ideas he needs
to answer stubborn questions about the validity of scientific inference.
Briefly put, the validity of scientific inference depends on the ability
of symbols to express “superfluous comprehension”, the measure of which
Peirce calls “information”.

Selection 2 sharpens our picture of symbols as “general representations”,
contrasting them with two species of representation whose characters
fall short of genuine symbols.

<QUOTE>

For this purpose, I must call your attention to the differences there are
in the manner in which different representations stand for their objects.

In the first place there are likenesses or copies — such as statues,
pictures, emblems, hieroglyphics, and the like. Such representations
stand for their objects only so far as they have an actual resemblance
to them — that is agree with them in some characters. The peculiarity
of such representations is that they do not determine their objects —
they stand for anything more or less; for they stand for whatever
they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by a convention of men
or a decree of God. Such are tallies, proper names, &c. The peculiarity of these
conventional signs is that they represent no character of their objects.

Likenesses denote nothing in particular;
conventional signs connote nothing in particular.

The third and last kind of representations are symbols or general representations.
They connote attributes and so connote them as to determine what they denote.
To this class belong all words and all conceptions. Most combinations of words
are also symbols. A proposition, an argument, even a whole book may be, and
should be, a single symbol.

(Peirce 1866, pp. 467–468)

</QUOTE>

Reference
=========

• Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”,
Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce :
A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project,
Indiana University Press, Bloomington, IN, 1982.

Resources
=========

• Survey of Pragmatic Semiotic Information
https://inquiryintoinquiry.com/2019/01/08/survey-of-pragmatic-semiotic-information-%e2%80%a2-4/

Jon Awbrey

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Jan 30, 2019, 10:50:30 PM1/30/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Selection 3
At: http://inquiryintoinquiry.com/2019/01/30/information-comprehension-x-extension-revisited-%e2%80%a2-selection-3/

Ontolog Forum, Systems Science, Structural Modeling —

Selection 3 opens with Peirce remarking a critical property of genuine symbols —
the class of symbols is not closed under combinations. In particular, there are
logical conjunctions of symbols and logical disjunctions of symbols which are not
themselves genuine symbols.

Applying this paradigm to terms, Peirce introduces two sets of examples under the
headings of “conjunctive terms” and “disjunctive terms” designed to illustrate the
correspondence between manners of representation and modes of inference.

<QUOTE>

Yet there are combinations of words and combinations of conceptions
which are not strictly speaking symbols. These are of two kinds
of which I will give you instances. We have first cases like:

• man and horse and kangaroo and whale,

and secondly, cases like:

• spherical bright fragrant juicy tropical fruit.

The first of these terms has no comprehension which is adequate to the
limitation of the extension. In fact, men, horses, kangaroos, and whales
have no attributes in common which are not possessed by the entire class
of mammals. For this reason, this disjunctive term, man and horse and
kangaroo and whale, is of no use whatever. For suppose it is the subject
of a sentence; suppose we know that men and horses and kangaroos and whales
have some common character. Since they have no common character which does
not belong to the whole class of mammals, it is plain that mammals may be
substituted for this term. Suppose it is the predicate of a sentence, and
that we know that something is either a man or a horse or a kangaroo or a whale;
then, the person who has found out this, knows more about this thing than that
it is a mammal; he therefore knows which of these four it is for these four
have nothing in common except what belongs to all other mammals. Hence in
this case the particular one may be substituted for the disjunctive term.
A disjunctive term, then, — one which aggregates the extension of several
symbols, — may always be replaced by a simple term.

Hence if we find out that neat are herbivorous, swine are herbivorous,
sheep are herbivorous, and deer are herbivorous; we may be sure that
there is some class of animals which covers all these, all the members
of which are herbivorous. Now a disjunctive term — such as neat swine
sheep and deer, or man, horse, kangaroo, and whale — is not a true symbol.
It does not denote what it does in consequence of its connotation, as a
symbol does; on the contrary, no part of its connotation goes at all to
determine what it denotes — it is in that respect a mere accident if it
denote anything. Its sphere is determined by the concurrence of the four
members, man, horse, kangaroo, and whale, or neat swine sheep and deer
as the case may be.

Now those who are not accustomed to the homologies of the conceptions of
men and words, will think it very fanciful if I say that this concurrence
of four terms to determine the sphere of a disjunctive term resembles the
arbitrary convention by which men agree that a certain sign shall stand for
a certain thing. And yet how is such a convention made? The men all look
upon or think of the thing and each gets a certain conception and then they
agree that whatever calls up or becomes an object of that conception in either
of them shall be denoted by the sign. In the one case, then, we have several
different words and the disjunctive term denotes whatever is the object of
either of them. In the other case, we have several different conceptions —
the conceptions of different men — and the conventional sign stands for
whatever is an object of either of them. It is plain the two cases are
essentially the same, and that a disjunctive term is to be regarded as
a conventional sign or index. And we find both agree in having a
determinate extension but an inadequate comprehension.

(Peirce 1866, pp. 468–469)

Jon Awbrey

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Feb 1, 2019, 2:40:27 PM2/1/19
to Ontolog Forum, SysSciWG, Structural Modeling
Azamat, All —

By my lights, the semiotics or theory of signs handed down to us
by Aristotle, Augustine, Medieval Scholastics, Locke, and others
took a significant leap forward toward a truly scientific theory
with the work of C.S. Peirce. This became possible, I believe,
not so much driven by any mutations in the taxonomy of signs as
due to his concurrent development of the logic of relative terms
and the mathematics of relations, especially triadic relations.

The task I've set for myself under this heading is threefold:

1. There is the scholarly task of figuring out what Peirce meant
by his formula: “Information = Comprehension × Extension”.

2. There is the scientific task of finding out whether Peirce's theory
of information tells us anything useful about empirical realities.

3. There is the theory-engineering task that bridges tasks 1 and 2.
It looks for ways to repair incomplete or inconsistent theories
in order to give them a better grasp of the empirical realities.

So I'll be maintaining a focus on that for the time being.

Regards,

Jon

On 1/29/2019 9:52 AM, Azamat Abdoullaev wrote:
>
> It looks no life-critical things so corrupted as the
> critical matter of signs and symbols, regardless that
> the best minds attended to it. We are lost in signs,
> indications, manifestations, marks, notes, omens, patterns,
> prognostics, signals, symbols, symptoms, tokens and types.
> A sign signifies, or points to and points out something.
> A symbol stands for, represents or takes place of some thing,
> because of likeness or resemblance in nature, qualities, etc.
>
> So, any sign is signifying.
>
> Any symbol is functioning as a substitute or surrogate.
> Traditionally, we are free to mix signs and symbols,
> so we call notations of language, science or the arts,
> as music, while there is a distinction, paper money
> substitutes the gold, and road signs points out some
> location or direction.
>
> In all, there are three kinds of signs:
> natural signs;
> conventional signs;
> hybrid signs, as digital things.
>
> As to Augustine, there are also 3 types of things in the world:
> things per se, some things are simply things, and any signs at all;
> some things are also signs of other things;
> some things are always used as signs, as words or ideas or images,
> meanings or intentions.
>
> Natural signs are subject to causation, as the fire and its smoke,
> ideas/images and actions, or animal cries communicating pain or
> pleasure, fear or anger.
>
> Natural signs are the cause of meaning in conventional signs;
> as mental entities are the means of through which words signify things.
> Thus, the kinds of things functioning as signs and the the kinds of things
> the signify define the nature of meaning or the modes of signification.
>
> Bottom line
> Humans are better defined as Homo Symbolicus.
> Symbolism is now everywhere, in maths, science, language, psychology,
> poetry, philosophy, religion, and, of course, computing, its best product,
> real AI technology.
>
> Then it is important to know 3 simple truths:
>
> Sings and symbols differ in nature
> Signification = Denotation x Connotation
> Meaning = Extension x Intension
> Information = Data + Signification (Meaning)
>
> As an information signal is a sign of communication
> to convey some meaningful information; a radio wave
> or e-current transmitting intelligence in code.
>
> In more details, signs and symbols discussed in
> Reality and Universal Ontology ...
>
> https://www.igi-global.com/book/reality-universal-ontology-knowledge-systems/859

Jon Awbrey

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Feb 3, 2019, 11:05:22 AM2/3/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Selection 4
At: http://inquiryintoinquiry.com/2019/02/03/information-comprehension-x-extension-revisited-%e2%80%a2-selection-4/

Ontolog Forum, Systems Science, Structural Modeling —

Selection 3 showed how it was possible to combine symbols in such a way as
to end up with species of representation outside the class of genuine symbols
and introduced the concepts of “conjunctive terms” and “disjunctive terms” to
describe two ways of doing this. The essence of wit being quickly grasping the
middle term, Peirce's wit fastens on these terms to highlight the links between
manners of representation and modes of inference.

Selection 4 finds Peirce in the middle of articulating the connection between
indexical reference and inductive inference, using examples of disjunctive terms
as pivotal cases.

<QUOTE>

Accordingly, if we are engaged in symbolizing and we come to such
a proposition as “Neat, swine, sheep, and deer are herbivorous”, we
know firstly that the disjunctive term may be replaced by a true symbol.
But suppose we know of no symbol for neat, swine, sheep, and deer except
cloven-hoofed animals. There is but one objection to substituting this
for the disjunctive term; it is that we should, then, say more than we
have observed. In short, it has a superfluous information. But we have
already seen that this is an objection which must always stand in the way
of taking symbols. If therefore we are to use symbols at all we must use
them notwithstanding that. Now all thinking is a process of symbolization,
for the conceptions of the understanding are symbols in the strict sense.
Unless, therefore, we are to give up thinking altogeher we must admit the
validity of induction. But even to doubt is to think. So we cannot
give up thinking and the validity of induction must be admitted.

(Peirce 1866, p. 469)

Jon Awbrey

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Feb 4, 2019, 10:30:11 AM2/4/19
to Ontolog Forum, SysSciWG, Structural Modeling
Bruce, All —

When I was first learning information theory, one of my favorite tag lines was:

☞ Redundancy is the Essence of Information

It's a bit tongue-in-cheek but none-the-less apt.

Although I had already happened on hints of Peirce's information theory in the
microfilm edition of his Nachlass, it was only when the Chronological Edition
of his Writings started coming out that I began to grasp the full scope of
what he was setting forth in his early Lectures on the Logic of Science.

And when I lit on Peirce's otherwise enigmatic “superfluous comprehension”
I could hardly help but flash back to my earlier kenning of redundancy and
sense the two phrases must be pointing to the same property of information.
However things may turn out, I think it gives us a clue worth following up.

Regards,

Jon

On 1/29/2019 2:56 PM, bruces...@cox.net wrote:
>> AA = Azamat Abdoullaev
>> AA: It looks no life-critical things so corrupted as the critical matter of signs and symbols, regardless that the best
>> minds attended to it.
>>
>> AA: We are lost in signs, indications, manifestations, marks, notes, omens, patterns, prognostics, signals, symbols,
>> symptoms, tokens and types.
>
> I had to laugh. I fully sympathize. How confused and swamp-trapped are we? 😊 (actually, trying to figure out
> Peirce’s definitions make me feel this way. How can “scientists” build a working analytical model designed to solve
> real-world problems on a foundation of sheer vagueness and ambiguity? What for heaven’s sake is “superfluous
> comprehension” https://goo.gl/LKHRHV ?)
>
>> AA: A sign signifies, or points to and points out something.
>>
>> AA: A symbol stands for, represents or takes place of some thing, because of likeness or resemblance in nature,
>> qualities, etc
>
> What I want to see emerge is a universal/general-purpose single method for building information structures that
> accomplishes this. We need a single method to “describe anything” (any abstract symbolic structure) in terms of
> qualities (properties, characteristics, attributes, dimensions, facets – all of which become measurable to a known
> error tolerance through this method)
>
> For me, the great core mystery of semantic ontology is the principle of “a cut on a cut” – a distinction on a
> distinction – the way a species is a distinction on a genus. That’s the generic form of hierarchical categorization
> across descending levels. https://en.wikipedia.org/wiki/Taxon
>
> I want to see all of this defined in terms of an isomorphism linking dimension and ordered class (“a dimension is an
> ordered class”). It seems that this method is “absolutely recursive” – it defines any level of abstraction – and
> because measurement is grounded in dimensionality, creates an unbroken algebraic definition chain to ground any
> abstraction in empirical measurement.
>
> But what is the bottom of this cascade (“it’s turtles all the way down” --
> https://en.wikipedia.org/wiki/Turtles_all_the_way_down )?
>
> The chain looks like this: “a cut on a cut on a cut on a cut on a cut…” “A taxon cuts a taxon cuts a taxon…” -- and
> a taxon – an ordered class – is isomorphic to a dimension. And every facets in the description or representation is
> also a dimension.
>
> This is potentially infinite recursion. But the mystery seems to be – this thing hits a limit. How do we define
> this? This is the deep mystery, I think.
>
> My suspicion is – this is an innately closed space – like the center-point of the Big Bang – from which every
> possibility of abstract representation springs forth. But how does it close and become a sealed space? What is the
> limit of this process? How can it be described in a finite way?
>
> Maybe complementarity is a clue – sort a yang/yin active/passive – “that which cuts” (“the cutter”) versus “that
> which is cut” (“the cuttee”) – both taking the same algebraic form, but somehow perceived in a different polarity
> (active/passive, black/white, full/empty. Perhaps ee have to view the process from an angle to see it this way (?)
>
> So – in this vision, every symbolic object in this list is constructed the same way:
>
>> AA: Symbolism is now everywhere, in maths, science, language, psychology, poetry, philosophy, religion, and, of course,
>> computing, its best product, real AI technology.
>
> I’d say construct every facet of ontological thinking mentioned in this paragraph in the same way:
>
> https://goo.gl/w8Gxdz
>
> All kinds of science, basic or applied, hard or soft, theoretical or empirical, fundamental or
> descriptive, natural or humane, to some degree partake in the general theory of entities and
> relationships as special sciences, or domain specific ontologies. All types of knowledge,
> theoretical, formal, experimental or practical, presuppose essential, ontological knowledge
> of things. Implicitly or explicitly, ontological principles can be found among mostly general
> theories, mostly universal axioms and laws, and in mostly interesting scientific problems. As
> underlying ideas, ontological categories, classes, concepts, notions, and terms lead the list
> of the great ideas making the very substance of the grand elemental conceptions. For they
> are the abstractions by which thought knows the world and minds think things, the terms
> in which we formulate major principles and facts of reality, the notions in which we make
> definitions, put fundamental questions, and solve decisive problems. Ontological ideas constitute
> the very framework of mental contents and cognitive processes as the heart of mental life. They
> reside in languages, natural or artificial, as the mind in the body, as pungency in
> pepper; since the syntactic and grammatical categories and semantic classes are inherently
> tied to world things. Our human language is pervaded with ontological categories, in terms
> of which we describe the fundamental constituents and properties of reality and explain the
> complex dynamics of the nonlinear world of things. All great human actions and intellectual
> achievements, all our rational practice of choice and moral codes are intrinsically guided by
> ontological rules and principles as primary and unvarying truths of reality.
>
> The large order and broad goal of ontology is to produce the explanatory schemas of all
> being and reality, giving the guiding principles and rules for a wide variety of special truths
> and particular facts. The ontological verities come up as the basic laws of reality occupying
> the highest level in the hierarchy of truths and meanings: mental, logical, mathematical,
> semantic, verbal, scientific, empirical as well as moral, ethical, esthetic, and religious. So the
> quest of underlying truths, universal and necessary, is the ultimate goal of the fundamental
> ontology and ontological theories, aimed to uncover the general knowledge and universal
> laws applicable to all existence in its basic levels, parts, and domains. These are not all
> the substantial implications of the general knowledge of reality. Never-foreseen before
> technological artifacts and engineering systems are lining up beyond the current horizons
> of knowledge and technology.
>
> Bruce Schuman
> Santa Barbara CA USA, 805-705-9174
>

Jon Awbrey

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Feb 6, 2019, 12:00:28 PM2/6/19
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Cf: { Information = Comprehension × Extension } Revisited • Selection 5
At: http://inquiryintoinquiry.com/2019/02/06/information-comprehension-x-extension-revisited-%e2%80%a2-selection-5/

Ontolog Forum, Systems Science, Structural Modeling —

Peirce now turns to his example of a conjunctive term, which he uses
to show the connection between iconic reference and abductive inference.

<QUOTE>

A similar line of thought may be gone through in reference to hypothesis.
In this case we must start with the consideration of the term:

• spherical, bright, fragrant, juicy, tropical fruit.

Such a term, formed by the sum of the comprehensions of several terms,
is called a conjunctive term. A conjunctive term has no extension adequate
to its comprehension. Thus the only spherical bright fragrant juicy tropical
fruit we know is the orange and that has many other characters besides these.
Hence, such a term is of no use whatever. If it occurs in the predicate and
something is said to be a spherical bright fragrant juicy tropical fruit,
since there is nothing which is all this which is not an orange, we may say
that this is an orange at once. On the other hand, if the conjunctive term
is subject and we know that every spherical bright fragrant juicy tropical
fruit necessarily has certain properties, it must be that we know more than
that and can simplify the subject. Thus a conjunctive term may always be
replaced by a simple one.

So if we find that light is capable of producing certain phenomena which
could only be enumerated by a long conjunction of terms, we may be sure
that this compound predicate may be replaced by a simple one. And if
only one simple one is known in which the conjunctive term is contained,
this must be provisionally adopted.

(Peirce 1866, p. 470)

Jon Awbrey

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Feb 8, 2019, 6:08:19 PM2/8/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Selection 6
At: https://inquiryintoinquiry.com/2019/02/08/information-comprehension-x-extension-revisited-%e2%80%a2-selection-6/

Ontolog Forum, Systems Science, Structural Modeling —

Selection 1 opens with Peirce proposing,

“The information of a term is the measure of its superfluous comprehension”,

and it closes with his offering the following promise:

“I am going, next, to show that inference is symbolization
and that the puzzle of the validity of scientific inference
lies merely in this superfluous comprehension and is therefore
entirely removed by a consideration of the laws of information.”

Summing up his account to this point, Peirce appears confident
he's kept his promise. Promising on our own account to give it
another pass, we'll let him have the last word — for now:

<QUOTE>

We have now seen how the mind is forced by the very nature
of inference itself to make use of induction and hypothesis.

But the question arises how these conclusions come to receive
their justification by the event. Why are most inductions and
hypotheses true? I reply that they are not true. On the contrary,
experience shows that of the most rigid and careful inductions and
hypotheses only an infinitesimal proportion are never found to be
in any respect false.

And yet it is a fact that all careful inductions are nearly true
and all well-grounded hypotheses resemble the truth; why is that?
If we put our hand in a bag of beans the sample we take out has
perhaps not quite but about the same proportion of the different
colours as the whole bag. Why is that?

The answer is that which I gave a week ago. Namely, that there is a
certain vague tendency for the whole to be like any of its parts taken
at random because it is composed of its parts. And, therefore, there
must be some slight preponderance of true over false scientific inferences.
Now the falsity in conclusions is eliminated and neutralized by opposing
falsity while the slight tendency to the truth is always one way and is
accumulated by experience. The same principle of balancing of errors
holds alike in observation and in reasoning.

(Peirce 1866, pp. 470–471)

Jon Awbrey

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Feb 9, 2019, 9:00:50 PM2/9/19
to Ontolog Forum, SysSciWG, Structural Modeling
Re: { Information = Comprehension × Extension } • Discussion 10
At: https://inquiryintoinquiry.com/2019/02/01/information-comprehension-x-extension-%e2%80%a2-discussion-10/

Azamat, All —

As I suggested in my second sentence, the difference that makes a difference
in Peirce's contribution to our understanding of inference and reference is
“due to his concurrent development of the logic of relative terms and the
mathematics of relations, especially triadic relations.” It is only with
the addition of these tools to our toolbox that we begin to form models
adequate to the complexity of the object phenomena, namely, the whole
panoply of activities involved in observation, conceptualization,
communication, and inquiry.

As a matter of course I'll be bringing these tools to bear as needed
in the current engagement with Peirce's incipient information theory,
but only as they become needed. For a more general grounding in the
brand of relational logic and math Peirce was developing in parallel,
my notes, still in progress, on his 1870 Logic of Relatives may help:

Cf: Peirce's 1870 Logic Of Relatives
At: http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives

Regards,

Jon

On 2/9/2019 7:21 AM, Azamat Abdoullaev wrote:
> Jon wrote:
> “By my lights, the semiotics or theory of signs handed down to us
> by Aristotle, Augustine, Medieval Scholastics, Locke, and others
> took a significant leap forward toward a truly scientific theory
> with the work of C.S. Peirce.”
>
> I have a big doubt if a "leap forward" consists in
> “Information = Comprehension × Extension”
>
> The real semantics is in the assumptions that
> “Meaning = Comprehension × Extension”
> “Significance = Connotation × Denotation”

Jon Awbrey

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Feb 11, 2019, 10:24:16 AM2/11/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Comment 1
At: http://inquiryintoinquiry.com/2019/02/11/information-comprehension-x-extension-revisited-%e2%80%a2-comment-1/
NB: The blog version linked above is much better formatted.

Ontolog Forum, Systems Science, Structural Modeling —

At this point in his inventory of scientific reasoning, Peirce
is relating the nature of inference, information, and inquiry
to the character of the signs mediating the process in question,
a process he is presently describing as “symbolization”.

In the interest of clarity let's draw from Peirce's account
a couple of quick sketches, designed to show how the examples
he gives of conjunctive terms and disjunctive terms might look
if they were cast within a lattice-theoretic frame.

Let's examine Peirce's example of a conjunctive term —
“spherical, bright, fragrant, juicy, tropical fruit” —
within a lattice framework. We have these six terms:

t₁ = spherical
t₂ = bright
t₃ = fragrant
t₄ = juicy
t₅ = tropical
t₆ = fruit

Suppose z is the logical conjunction of the above six terms:

z = t₁ ∙ t₂ ∙ t₃ ∙ t₄ ∙ t₅ ∙ t₆

What on earth could Peirce mean by saying that such a term
is “not a true symbol” or that it is “of no use whatever”?

In particular, consider the following statement:

“If it occurs in the predicate and something is said to be
a spherical bright fragrant juicy tropical fruit, since
there is nothing which is all this which is not an orange,
we may say that this is an orange at once.”

In other words, if something x is said to be z, then we may guess
fairly surely that x is really an orange, in other words, that x has
all the additional features that would be summed up quite succinctly
in the much more constrained term y, where y means “an orange”.

Figure 1 shows the implication ordering of logical terms
in the form of a lattice diagram.

[See Figure 1. Conjunctive Term z, Taken as Predicate (attached)]
https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-1.jpg

What Peirce is saying about z not being a genuinely useful symbol
can be explained in terms of the gap between the logical conjunction z,
in lattice terms, the greatest lower bound (glb) of the conjoined terms,
z = glb{t₁, t₂, t₃, t₄, t₅, t₆}, and what we might regard as the natural
conjunction or natural glb of these terms, namely, y, “an orange”.

That is to say, there is an extra measure of constraint that goes into
forming the natural kinds lattice from the free lattice that logic and
set theory would otherwise impose. The local manifestations of this
global information are meted out over the structure of the natural
lattice by just such abductive gaps as the one between z and y.
ICE Figure 1.jpg

Jon Awbrey

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Feb 12, 2019, 5:00:20 PM2/12/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Comment 2
At: http://inquiryintoinquiry.com/2019/02/12/information-comprehension-x-extension-revisited-%e2%80%a2-comment-2/
NB: The blog version linked above is formatted better.

Ontolog Forum, Systems Science, Structural Modeling —

Let's examine Peirce's second example of a disjunctive term —
“neat, swine, sheep, deer” — within the style of lattice
framework we used before.

“Hence if we find out that neat are herbivorous, swine are herbivorous,
sheep are herbivorous, and deer are herbivorous; we may be sure that
there is some class of animals which covers all these, all the members
of which are herbivorous.” (pp. 468–469).

“Accordingly, if we are engaged in symbolizing and we come to such
a proposition as ‘Neat, swine, sheep, and deer are herbivorous’,
we know firstly that the disjunctive term may be replaced by a
true symbol. But suppose we know of no symbol for neat, swine,
sheep, and deer except cloven-hoofed animals.” (p. 469).

This is apparently a stock example of inductive reasoning which
Peirce is borrowing from traditional discussions, so let us pass
over the circumstance that modern taxonomies may classify swine
as omnivores.

In view of the analogical symmetries the disjunctive term shares
with the conjunctive case, we can run through this example in
fairly short order. We have an aggregate of four terms:

s₁ = neat
s₂ = swine
s₃ = sheep
s₄ = deer

Suppose u is the logical disjunction of the above four terms:

u = ((s₁)(s₂)(s₃)(s₄))

Figure 2 diagrams the situation before us.

[See Figure 2. Disjunctive Term u, Taken as Subject (attached)]
https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-2.jpg

Here we have a situation that is dual to the structure of the conjunctive example.
There is a gap between the logical disjunction u, in lattice terminology, the
least upper bound (lub) of the disjoined terms, u = lub{s₁, s₂, s₃, s₄}, and
what we might regard as the natural disjunction or natural lub of these terms,
namely, v, “cloven-hoofed”.

Once again, the sheer implausibility of imagining the disjunctive term u
would ever be embedded exactly as such in a lattice of natural kinds leads
to the evident naturalness of the induction to v ⇒ w, namely, the rule that
cloven-hoofed animals are herbivorous.
ICE Figure 2.jpg

Jon Awbrey

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Feb 13, 2019, 3:48:47 PM2/13/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Comment 3
At: http://inquiryintoinquiry.com/2019/02/13/information-comprehension-x-extension-revisited-%e2%80%a2-comment-3/
NB: The blog version linked above is formatted better.

Ontolog Forum, Systems Science, Structural Modeling —

Peirce identifies inference with a process he describes as “symbolization”.
Let us consider what that might imply.

<QUOTE>

I am going, next, to show that inference is symbolization
and that the puzzle of the validity of scientific inference
lies merely in this superfluous comprehension and is therefore
entirely removed by a consideration of the laws of “information”.

(Peirce 1866, p. 467)

</QUOTE>

Even if it were only a rough analogy between inference and symbolization, a
principle of logical continuity, what is known in physics as a “correspondence
principle”, would suggest parallels between steps of reasoning in the neighborhood
of exact inferences and signs in the vicinity of genuine symbols. This would lead us
to expect a correspondence between degrees of inference and degrees of symbolization
extending from exact to approximate (“non-demonstrative”) inferences and from genuine
to approximate (“degenerate”) symbols.

<QUOTE>

For this purpose, I must call your attention to the differences there are
in the manner in which different representations stand for their objects.

In the first place there are likenesses or copies — such as statues,
pictures, emblems, hieroglyphics, and the like. Such representations
stand for their objects only so far as they have an actual resemblance
to them — that is agree with them in some characters. The peculiarity
of such representations is that they do not determine their objects —
they stand for anything more or less; for they stand for whatever
they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by a convention of men
or a decree of God. Such are tallies, proper names, &c. The peculiarity of these
conventional signs is that they represent no character of their objects.

Likenesses denote nothing in particular;
conventional signs connote nothing in particular.

The third and last kind of representations are symbols or general representations.
They connote attributes and so connote them as to determine what they denote.
To this class belong all words and all conceptions. Most combinations of words
are also symbols. A proposition, an argument, even a whole book may be, and
should be, a single symbol.

(Peirce 1866, pp. 467–468)

</QUOTE>

In addition to Aristotle, the influence of Kant on Peirce is very
strongly marked in these earliest expositions. The invocations of
“conceptions of the understanding”, the “use of concepts” and thus of
symbols in reducing the manifold of extension, and the not so subtle
hint of the synthetic à priori in Peirce's discussion, not only of
natural kinds but also of the kinds of signs leading up to genuine
symbols, can all be recognized as pervasive Kantian themes.

In order to draw out these themes and see how Peirce was led to
develop their leading ideas, let us bring together our previous
Figures, abstracting from their concrete details, and see if we
can figure out what is going on.

Figure 3 shows an abductive step of inquiry, as taken on the cue of an iconic sign.

[See Figure 3. Conjunctive Predicate z, Abduction of Case x ⇒ y (attached)]

https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-3.jpg

Figure 4 shows an inductive step of inquiry, as taken on the cue of an indicial sign.

[See Figure 4. Disjunctive Subject u, Induction of Rule v ⇒ w (attached)]

https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-4.jpg

To be continued …
ICE Figure 3.jpg
ICE Figure 4.jpg

Jon Awbrey

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Feb 14, 2019, 9:28:50 AM2/14/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Comment 4
At: http://inquiryintoinquiry.com/2019/02/14/information-comprehension-x-extension-revisited-%e2%80%a2-comment-4/

Ontolog Forum, Systems Science, Structural Modeling —

Many things still puzzle me about Peirce's account at this point.
I indicated a few of them by means of question marks at several
places in the last two Figures:

https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-3.jpg
https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-4.jpg

There is nothing for it but returning to the text and trying once more
to follow the reasoning.

Let's go back to Peirce's example of abductive inference and try to
get a clearer picture of why he connects it with conjunctive terms
and iconic signs.

Figure 1 shows the implication ordering of logical terms in the form of
a lattice diagram.

See Figure 1. Conjunctive Term z, Taken as Predicate (attached)
https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-1.jpg

The relationship between conjunctive terms and iconic signs may be understood
as follows. If there is anything with all the properties described by the
conjunctive term — “spherical bright fragrant juicy tropical fruit” — then
sign users may use that thing as an icon of an orange, precisely by virtue
of the fact it shares those properties with an orange. But the only natural
examples of things with all those properties are oranges themselves, so the
only thing qualified to serve as a natural icon of an orange by virtue of
those very properties is that orange itself or another orange.
ICE Figure 1.jpg

Jon Awbrey

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Feb 15, 2019, 2:40:13 PM2/15/19
to Ontolog Forum, SysSciWG, Structural Modeling
Cf: { Information = Comprehension × Extension } Revisited • Comment 5
At: http://inquiryintoinquiry.com/2019/02/15/information-comprehension-x-extension-revisited-%e2%80%a2-comment-5/

Ontolog Forum, Systems Science, Structural Modeling —

Let's stay with Peirce's example of abductive inference a little longer
and try to clear up the more troublesome confusions that tend to arise.

Figure 1 shows the implication ordering of logical terms in the form of a lattice diagram.

[Attached] Figure 1. Conjunctive Term z, Taken as Predicate
https://inquiryintoinquiry.files.wordpress.com/2016/10/ice-figure-1.jpg

One thing needs to be stressed at this point. It is important to recognize the
conjunctive term itself — namely, the syntactic string “spherical bright fragrant
juicy tropical fruit” — is not an icon but a symbol. It has its place in a formal
system of symbols, for example, a propositional calculus, where it would normally
be interpreted as a logical conjunction of six elementary propositions, denoting
anything in the universe of discourse with all six of the corresponding properties.
The symbol denotes objects which may be taken as icons of oranges by virtue of
their bearing those six properties in common with oranges. But there are no
objects denoted by the symbol which aren't already oranges themselves. Thus
we observe a natural reduction in the denotation of the symbol, consisting in
the absence of cases outside of oranges that have all the properties indicated.

The above analysis provides another way to understand the abductive inference
from the Fact x ⇒ z and the Rule y ⇒ z to the Case x ⇒ y. The lack of any
cases which are z and not y is expressed by the implication z ⇒ y. Taking
this together with the Rule y ⇒ z gives the logical equivalence y = z. But
this reduces the Case x ⇒ y to the Fact x ⇒ z and so the Case is justified.

Viewed in the light of the above analysis, Peirce's example of abductive reasoning
exhibits an especially strong form of inference, almost deductive in character.
Do all abductive arguments take this form, or may there be weaker styles of
abductive reasoning which enjoy their own levels of plausibility?
That must remain an open question at this point.
ICE Figure 1.jpg

Jon Awbrey

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Mar 1, 2019, 6:24:10 PM3/1/19
to Ontolog Forum, SysSciWG, Structural Modeling
Re: { Information = Comprehension × Extension } • Discussion 14
At: https://inquiryintoinquiry.com/2019/02/21/information-comprehension-x-extension-%e2%80%a2-discussion-14/
Cf: { Information = Comprehension × Extension } • Discussion 15
At: https://inquiryintoinquiry.com/2019/02/28/information-comprehension-x-extension-%e2%80%a2-discussion-15/

Ontolog Forum, Systems Science, Structural Modeling —

I am roughly at the halfway point of my comments on Peirce's information formula,
having just finished up the link between abductive inference and iconic reference.
The discussion of induction and indexicals will follow pretty much the same pattern,
though there are a few wrinkles having to do with a number of interesting differences
between Peirce's early and later accounts of indices.

The rest of this post is slightly tangent to the topic at hand,
but I couldn't resist saying a few more words about the duality
of information and control once other discussions brought the
issue to mind.

----

Viewing systems topics like change, control, dynamics, goals, objectives,
optimization, process, purpose and so on in the light of the information
dimension opens up a wide field of investigation. It's been my custom to
cultivate that field layer by layer, working my way up from the most basic
layer with much utility, namely, propositional calculus. This is the layer
of qualitative description underlying every layer of quantitative description.

Propositional calculus is the level of logic we've been using in our present
discussion to describe various classes of entities populating a given universe of
discourse. Whether we call the corresponding descriptors predicates, propositions,
or terms is of no importance for present purposes so long as we are using them solely
as symbols in a symbolic calculus following a specific set of rules.

Extending the layer of propositional calculus from its coverage of static situations
to the description of time-evolving states can be done fairly easily. One follows the
model of physics, where dealing with change made little progress until the development
of differential calculus. The analogous medium at the logical level is the differential
extension of propositional calculus, or “differential propositional calculus”, for short.
See the following resource for a gentle introduction.

• Differential Propositional Calculus
http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus

joseph simpson

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Mar 1, 2019, 9:45:34 PM3/1/19
to structura...@googlegroups.com, Ontolog Forum, SysSciWG
Jon:

This is an interesting section:

"“If it occurs in the predicate and something is said to be
  a spherical bright fragrant juicy tropical fruit, since
  there is nothing which is all this which is not an orange,
  we may say that this is an orange at once.”"

The phrase, 

  "since there is nothing which is all this which is not an orange"

indicates that there is no uncertainty associated with the identification of the fruit.

Lets say that there are at least three fruits that have all the listed properties:

Passion fruit -- larger than an orange; a tangerine -- smaller than an orange and the orange.

Now an additional property, size,  is needed to determine the exact fruit.

If we were given the size of the fruit, then the size property would provide information.

If we already know the information, before the information is transferred.

Then information content of the message is zero.

In the stated case, it is difficult to determine what part is the message.

That is all for now...

Take care, be good to yourself and have fun,

Joe


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joseph simpson

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Mar 6, 2019, 3:55:34 PM3/6/19
to structura...@googlegroups.com, Ontolog Forum, SysSciWG
Jon:

Viewing the section copied below:

"“If it occurs in the predicate and something is said to be
  a spherical bright fragrant juicy tropical fruit, since
  there is nothing which is all this which is not an orange,
  we may say that this is an orange at once.”"

In terms of:

“the manner in which different representations stand for their objects”

It is clear that the listed properties associated with the object of interest must be used to specifically identify the object.

The process of object identification takes place in a given context.

The context of the identification process could be one of:

1) No existing data or information about the object of interest

2) Existing data and information about the object of interest indicate only one object (an orange).

3) Existing data and information about the object of interest indicate two or more candidate objects.

In context 1, the statements about the properties of an orange could be accepted as fact or as an indication that the statements need to be further verified. The level of acceptable uncertainty would determine if the statement was evaluated as true or not.

In context 2, the statements would be evaluated as true statements.

In context 3, the statements would need to be modified to address the existence of the other objects.

Take care and have fun,

Joe 



joseph simpson

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Mar 7, 2019, 9:57:46 PM3/7/19
to structura...@googlegroups.com, Ontolog Forum, SysSciWG
Jon:

The previous descriptions of the statement context appear to be too constrained.

How can someone make a statement about an object in a context that has:

" No existing data or information about the object of interest." ?

For the situation to make sense there needs to be at least two entities capable of communicating.

One entity, in context 1, could have a complete set of data and/or information about the object of interest.

Another entity, in context 1, could have no data or information about the object of interest.

Given at least two communicating entities and a graded range of data and knowledge about the object of interest, then it may be possible to view the situation as a message passing example.

Given this expanded description of context 1, then the entity with no information about the object of interest has the opportunity to gain data and information about the object of interest.  This new information decreases the uncertainty about the nature of the world at large (new information about objects that exist).  Therefore, the message contained information that reduced uncertainty about the world at large.

Jon Awbrey

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Mar 8, 2019, 3:56:54 PM3/8/19
to Ontolog Forum, joseph simpson, Structural Modeling, SysSciWG
Cf: { Information = Comprehension × Extension } • Discussion 16
At: https://inquiryintoinquiry.com/2019/03/08/information-comprehension-x-extension-%e2%80%a2-discussion-16/

Joe, All —

The following little preamble was prompted by Joe's comments but it really
has to do with a very old issue that has come up from time to time on this
list, not to mention its predecessors, so I made another try at getting it
clear in my own mind. There's more to say about what it means for present
business, but I've been struggling all week through worldly distractions —
this is as far as I got ...

⁂ ⁂ ⁂

To understand the purpose of Peirce’s lecture hall illustrations I think
we need to consider how these sorts of expository examples come into being.
Having crafted a few myself the technique is much like the Art of the Story
Problem I remember from my days teaching math. We have a universe of discourse
circumscribed by a particular subject matter, say linear algebra, plane geometry,
the quadratic formula, or the like, and we have a set of methods that work well
enough in that context to recommend their use to others. The methods themselves
have been abstracted and formalized over the years, if not millennia, to the point
of being detached from everyday life and potential practice, so we flesh them out
with names and local habitations and narrative figures designed to tutor nature — ⁂
or at least the students thereof.

The main thing we want from our stock examples and story problems is
to show how it’s possible to bring a body of abstract ideas to bear on
ordinary practical affairs. We are thus reversing to a degree the process
by which a formalized subject matter is abstracted from a host of concrete
situations, but only to a degree, as dredging up the mass of adventitious
and conflicting details would be too distracting. Instead we stipulate
a hypothetical state of affairs whose concrete structure falls under
the class of ideal structures studied in our formal subject matter.

Regards,

Jon

joseph simpson

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Mar 9, 2019, 10:06:56 PM3/9/19
to Jon Awbrey, Ontolog Forum, Structural Modeling, SysSciWG
Jon:

You wrote:

"The main thing we want from our stock examples and story problems is
to show how it’s possible to bring a body of abstract ideas to bear on
ordinary practical affairs. "

This response appears to cast the "stock examples" as a message from one individual to one or more individuals.

In this case it appears that the information associated with the message only depends on the state of the individual receiving and interpreting the message.

That all works from my point of view.

Take care, be good to yourself and have fun,

Joe


Jon Awbrey

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Mar 15, 2019, 7:28:28 PM3/15/19
to Ontolog Forum, Structural Modeling, SysSciWG
Cf: { Information = Comprehension × Extension } • Discussion 17
At: https://inquiryintoinquiry.com/2019/03/15/information-comprehension-x-extension-%e2%80%a2-discussion-17/

We are in the middle of trying to work out what Peirce had in mind with his
concept of information. He appears to have developed it from purely logical
considerations, if logic can remain pure in applying itself to experience, and
he thinks it solves “the puzzle of the validity of scientific inference”.

<QUOTE>

I am going, next, to show that inference is symbolization and that
the puzzle of the validity of scientific inference lies merely in
this superfluous comprehension and is therefore entirely removed
by a consideration of the laws of information.

(Peirce 1866, p. 467)
https://inquiryintoinquiry.com/2019/01/26/information-comprehension-x-extension-revisited-%e2%80%a2-selection-1/

</QUOTE>

We will eventually come to the task of seeing how a theory of information born in
that environment relates to concepts of information in common use today, sprouted
as they were from the needs of telegraph operators to detect and correct errors
of transmission through noisy channels of communication. As I see it, Peirce's
concept of information is potentially deeper and more general than concepts of
information based on quantitative measures of probability and quantifiable
statistics of messages. This is possible because the qualitative properties
of spaces studied in topology are deeper and more general than the quantitative
properties of spaces bearing real-valued measures.

All in good time, though. We have a ways to go understanding
Peirce's idea before we can say how the two paradigms compare.

Regards,

Jon

Reference
=========

• Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”,
Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce :
A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project,
Indiana University Press, Bloomington, IN, 1982.

Resources
=========

• Survey of Pragmatic Semiotic Information
https://inquiryintoinquiry.com/2019/01/08/survey-of-pragmatic-semiotic-information-%e2%80%a2-4/

• Information = Comprehension × Extension
http://intersci.ss.uci.edu/wiki/index.php/Information_%3D_Comprehension_%C3%97_Extension

• C.S. Peirce • “Upon Logical Comprehension and Extension”
http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm

On 3/9/2019 10:06 PM, joseph simpson wrote:
> Jon:
>

joseph simpson

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Mar 17, 2019, 2:19:20 PM3/17/19
to structura...@googlegroups.com, Ontolog Forum, SysSciWG
Jon:

Great idea..

I have started to read...

Upon Logical Comprehension and Extension


We will see how things go..

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