[PEIRCE-L] Re: { Information = Comprehension × Extension }

[Jon Awbrey]

John,

Why don't we put this on hold for later discussion?
What you say goes to the heart of a problem I saw in
Natural Propositions, whether it was Peirce's account
or Stjernfelt's analysis I did not have time to decide
as the schedule of the slow reading went too fast for me
to take it up on the List.  I marked the critical passages
and my copy of Natural Propositions is around here someplace
but I am trying to stay focused on the subject matter and the
set of problems that I introduced under the above subject line.

There are many issues here about cross-disciplinary communication,
the varieties of quasi-religious belief about the uses of words in
the whole proposition/sentence/statement complex, the various uses
Peirce and even sub-genius people use across contexts, disciplines,
historical time, and even within the same discussion.  But I think
it's best to hold the forte on that for now.

Regards,

Jon

On 6/28/2017 3:19 PM, John F Sowa wrote:> On 6/28/2017 1:44 PM, Jon Awbrey 
wrote:
>>
>> The short shrift for now is that neither Peirce nor I is talking about
>> propositions in the sense of dicisigns or dicent symbols at this juncture
>> but rather the simpler sorts of propositions that fall under the heading of
>> the Propositional Calculus in current usage, adequately and most felicitously
>> dealt with of course by means of Peirce's own Alpha Graphs.
>
> There is no difference.  A proposition (or dicisign or dicent symbol)
> is a proposition, no matter how it is used.  In propositional calculus
> or Peirce's Alpha, the letter p can represent any proposition or dicisign
> or dicent symbol of any kind.
>
>> The concept of information that comes up in this context is rather distinct.
>
> Yes.  Information is propositional content that is being communicated
> to someone in some way.  As an employee of AT&T, Claude Shannon focused
> on the transmission methods.  But he did not reject the fact that the
> people who use a telephone communicate propositional content.
>
> The terms 'comprehension' and 'extension' address the propositional content,
> not the method of communication.
>
> John
>

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Re: [PEIRCE-L] Re: { Information = Comprehension × Extension }

[Benjamin Udell]

Sorry, everybody. I admit I've been somewhat disengaged from peirce-l 
lately.
I mistakenly provided a link to a page of links to the slow read of 
Waal's _Peirce: A Guide for the Perplexed_, not to the slow read of 
Stjernfelt's _Natural Propositions_, for which we don't have a nicely 
organized page of links.


Best, Ben

On 6/28/2017 3:36 PM, Benjamin Udell wrote:


John, Jon, list,

We had a chapter-by-chapter slow read of Stjernfelt's _Natural 
Propositions_ here at peirce-l during January to June 2014. Arisbe has 
a page of links to the threads. (There are links to IUPUI archives, 
gmane archives, and mail archives. The gmane links mostly don't work 
but there still seems some effort to rebuild the gmane archive.)


http://www.iupui.edu/~arisbe/PEIRCE-L/seminar-waal.htm

Over the years, slow reads at Arisbe have covered, among other things, 
"Kaina Stoicheia" (twice, I think) and all of Joe Ransdell's papers 
posted at Arisbe.


Best, Ben

On 6/28/2017 11:53 AM, John F Sowa wrote:


Jon,

That's an important topic to explore:

JA

we can take up the issue of propositions in more detail
as it arises in the relevant context.


For a good analysis of the issues, I recommend the following book:
Stjernfelt, Frederik (2014) Natural Propositions: The Actuality
of Peirce’s Doctrine of Dicisigns, Boston: Docent Press.

I wrote a 5-page article on propositions from a Peircean perspective:
http://www.jfsowa.com/logic/proposit.pdf

That article is based on Peirce's notion of equivalence (CP 5.569):

A sign is only a sign in actu by virtue of its receiving an
interpretation, that is, by virtue of its determining another sign
of the same object. This is as true of mental judgments as it is of
external signs. To say that a proposition is true is to say that
every interpretation of it is true. Two propositions are equivalent
when either might have been an interpretant of the other. This
equivalence, like others, is by an act of abstraction (in the sense
in which forming an abstract noun is abstraction) conceived as 
identity.


And we speak of believing in a proposition, having in mind an entire
collection of equivalent propositions with their partial interpretants.
Thus, two persons are said to have the same proposition in mind. The
interpretant of a proposition is itself a proposition. Any necessary
inference from a proposition is an interpretant of it.

When we speak of truth and falsity, we refer to the possibility of the
proposition being refuted; and this refutation (roughly speaking) takes
place in but one way. Namely, an interpretant of the proposition would,
if believed, produce the expectation of a certain description of 
percept

on a certain occasion. The occasion arrives: the percept forced upon
us is different. This constitutes the falsity of every proposition of
which the disappointing prediction was the interpretant. Thus, a false
proposition is a proposition of which some interpretant represents
that, on an occasion which it indicates, a percept will have a certain
character, while the immediate perceptual judgment on that occasion is
that the percept has not that character.

A true proposition is a proposition belief in which would never lead
to such disappointment so long as the proposition is not understood
otherwise than it was intended.


In the article, I formalize Peirce's notion of equivalence in terms
of *meaning-preserving translations* (MPTs), which specify a class
of equivalent sentences in some language or languages.  It's easy to
define MPTs for formal logics, but much harder for natural languages.

John




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Re: [PEIRCE-L] Re: { Information = Comprehension × Extension }

[Benjamin Udell]

John, Jon, list,

We had a chapter-by-chapter slow read of Stjernfelt's _Natural 
Propositions_ here at peirce-l during January to June 2014. Arisbe has a 
page of links to the threads. (There are links to IUPUI archives, gmane 
archives, and mail archives. The gmane links mostly don't work but there 
still seems some effort to rebuild the gmane archive.)


http://www.iupui.edu/~arisbe/PEIRCE-L/seminar-waal.htm

Over the years, slow reads at Arisbe have covered, among other things, 
"Kaina Stoicheia" (twice, I think) and all of Joe Ransdell's papers 
posted at Arisbe.


Best, Ben

On 6/28/2017 11:53 AM, John F Sowa wrote:


Jon,

That's an important topic to explore:

JA

we can take up the issue of propositions in more detail
as it arises in the relevant context.


For a good analysis of the issues, I recommend the following book:
Stjernfelt, Frederik (2014) Natural Propositions: The Actuality
of Peirce’s Doctrine of Dicisigns, Boston: Docent Press.

I wrote a 5-page article on propositions from a Peircean perspective:
http://www.jfsowa.com/logic/proposit.pdf

That article is based on Peirce's notion of equivalence (CP 5.569):

A sign is only a sign in actu by virtue of its receiving an
interpretation, that is, by virtue of its determining another sign
of the same object. This is as true of mental judgments as it is of
external signs. To say that a proposition is true is to say that
every interpretation of it is true. Two propositions are equivalent
when either might have been an interpretant of the other. This
equivalence, like others, is by an act of abstraction (in the sense
in which forming an abstract noun is abstraction) conceived as identity.

And we speak of believing in a proposition, having in mind an entire
collection of equivalent propositions with their partial interpretants.
Thus, two persons are said to have the same proposition in mind. The
interpretant of a proposition is itself a proposition. Any necessary
inference from a proposition is an interpretant of it.

When we speak of truth and falsity, we refer to the possibility of the
proposition being refuted; and this refutation (roughly speaking) takes
place in but one way. Namely, an interpretant of the proposition would,
if believed, produce the expectation of a certain description of percept
on a certain occasion. The occasion arrives: the percept forced upon
us is different. This constitutes the falsity of every proposition of
which the disappointing prediction was the interpretant. Thus, a false
proposition is a proposition of which some interpretant represents
that, on an occasion which it indicates, a percept will have a certain
character, while the immediate perceptual judgment on that occasion is
that the percept has not that character.

A true proposition is a proposition belief in which would never lead
to such disappointment so long as the proposition is not understood
otherwise than it was intended.


In the article, I formalize Peirce's notion of equivalence in terms
of *meaning-preserving translations* (MPTs), which specify a class
of equivalent sentences in some language or languages.  It's easy to
define MPTs for formal logics, but much harder for natural languages.

John

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[PEIRCE-L] Re: { Information = Comprehension × Extension }

[John F Sowa]

On 6/28/2017 1:44 PM, Jon Awbrey wrote:

The short shrift for now is that neither Peirce nor I is talking about
propositions in the sense of dicisigns or dicent symbols at this juncture
but rather the simpler sorts of propositions that fall under the heading
of the Propositional Calculus in current usage, adequately and most 
felicitously dealt with of course by means of Peirce's own Alpha Graphs.


There is no difference.  A proposition (or dicisign or dicent symbol)
is a proposition, no matter how it is used.  In propositional calculus
or Peirce's Alpha, the letter p can represent any proposition or
dicisign or dicent symbol of any kind.


The concept of information that comes up in this context is rather distinct.


Yes.  Information is propositional content that is being communicated
to someone in some way.  As an employee of AT&T, Claude Shannon focused
on the transmission methods.  But he did not reject the fact that the
people who use a telephone communicate propositional content.

The terms 'comprehension' and 'extension' address the propositional
content, not the method of communication.

John

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[PEIRCE-L] Re: { Information = Comprehension × Extension }

[Jon Awbrey]

John,

Yes, I gave it a careful reading back when the List took it up:

http://web.archive.org/web/20150116150400/http://comments.gmane.org/gmane.science.philosophy.peirce/13825

I find some remnants of my comments here:

https://inquiryintoinquiry.com/2014/10/12/semiotic-theory-of-information-3/
https://inquiryintoinquiry.com/2014/10/13/semiotic-theory-of-information-4/

https://inquiryintoinquiry.com/2014/08/24/c-s-peirce-%e2%80%a2-syllabus-%e2%80%a2-selection-1/
https://inquiryintoinquiry.com/2014/10/04/c-s-peirce-%E2%80%A2-syllabus-%E2%80%A2-selection-2/

I have in mind getting back to the issues raised by that reading someday
but it would take me too far afield from my current focus to do that now.

The short shrift for now is that neither Peirce nor I is talking about
propositions in the sense of dicisigns or dicent symbols at this juncture
but rather the simpler sorts of propositions that fall under the heading of
the Propositional Calculus in current usage, adequately and most felicitously
dealt with of course by means of Peirce's own Alpha Graphs.

The concept of information that comes up in this context is rather distinct.
To my way of thinking the earlier notion of information, however roughly cut,
is superior in its basic principles, it being more realistic compared to the
residual nominalism in the later concept, at least, as interpreted by others.

Regards,

Jon

On 6/28/2017 11:53 AM, John F Sowa wrote:

Jon,

That's an important topic to explore:

JA

we can take up the issue of propositions in more detail
as it arises in the relevant context.


For a good analysis of the issues, I recommend the following book:
Stjernfelt, Frederik (2014) Natural Propositions: The Actuality
of Peirce’s Doctrine of Dicisigns, Boston: Docent Press.

I wrote a 5-page article on propositions from a Peircean perspective:
http://www.jfsowa.com/logic/proposit.pdf

That article is based on Peirce's notion of equivalence (CP 5.569):

A sign is only a sign in actu by virtue of its receiving an
interpretation, that is, by virtue of its determining another sign
of the same object. This is as true of mental judgments as it is of
external signs. To say that a proposition is true is to say that
every interpretation of it is true. Two propositions are equivalent
when either might have been an interpretant of the other. This
equivalence, like others, is by an act of abstraction (in the sense
in which forming an abstract noun is abstraction) conceived as identity.

And we speak of believing in a proposition, having in mind an entire
collection of equivalent propositions with their partial interpretants.
Thus, two persons are said to have the same proposition in mind. The
interpretant of a proposition is itself a proposition. Any necessary
inference from a proposition is an interpretant of it.

When we speak of truth and falsity, we refer to the possibility of the
proposition being refuted; and this refutation (roughly speaking) takes
place in but one way. Namely, an interpretant of the proposition would,
if believed, produce the expectation of a certain description of percept
on a certain occasion. The occasion arrives: the percept forced upon
us is different. This constitutes the falsity of every proposition of
which the disappointing prediction was the interpretant. Thus, a false
proposition is a proposition of which some interpretant represents
that, on an occasion which it indicates, a percept will have a certain
character, while the immediate perceptual judgment on that occasion is
that the percept has not that character.

A true proposition is a proposition belief in which would never lead
to such disappointment so long as the proposition is not understood
otherwise than it was intended.


In the article, I formalize Peirce's notion of equivalence in terms
of *meaning-preserving translations* (MPTs), which specify a class
of equivalent sentences in some language or languages.  It's easy to
define MPTs for formal logics, but much harder for natural languages.

John



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RE: [PEIRCE-L] Re: { Information = Comprehension × Extension }

[gnox]

John, speaking of Frederik Stjernfelt’s Natural Propositions, you may not be 
aware that peirce-l (and the biosemiotics list) hosted an intensive discussion 
of it that lasted through most of 2015. Frederik participated very generously 
in it, especially in the early months.

 

At Gary Richmond’s urging, I pitched the idea of this “slow read” to Frederik 
when I met him at the Peirce Centennial conference in Lowell, and he readily 
agreed to take part. (I had already read it, in fact proofread the text shortly 
before it went to the publisher, and had recommended it to the lists.) I then 
organized several discussion leaders who volunteered to take charge of various 
parts of the book, using the subject lines of posts to distinguish the various 
threads. In fact Jon was originally scheduled to be one of the leaders, but he 
withdrew before his turn came. So he may (or may not) be familiar with the book 
already; but many of us who’ve been on the list since 2014 are definitely 
familiar with it.

 

Some of what I considered the most crucial ideas in Natural Propositions also 
turn up in the late chapters of my book Turning Signs, for instance, notably 
here: http://www.gnusystems.ca/TS/scp.htm#nvlvn. (My book doesn’t deal much 
with formal logic, but it does with natural languages and their relations to 
biology, psychology and logic as semiotic.)

I think Ben Udell can probably dig out some useful links from the list 
archives, too.

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 28-Jun-17 11:54



Jon,

 

That's an important topic to explore:

 

JA

> we can take up the issue of propositions in more detail as it arises 

> in the relevant context.

 

For a good analysis of the issues, I recommend the following book:

Stjernfelt, Frederik (2014) Natural Propositions: The Actuality of Peirce’s 
Doctrine of Dicisigns, Boston: Docent Press.

 

I wrote a 5-page article on propositions from a Peircean perspective:

  
http://www.jfsowa.com/logic/proposit.pdf

 

That article is based on Peirce's notion of equivalence (CP 5.569):

> A sign is only a sign in actu by virtue of its receiving an 

> interpretation, that is, by virtue of its determining another sign of 

> the same object. This is as true of mental judgments as it is of 

> external signs. To say that a proposition is true is to say that every 

> interpretation of it is true. Two propositions are equivalent when 

> either might have been an interpretant of the other. This equivalence, 

> like others, is by an act of abstraction (in the sense in which 

> forming an abstract noun is abstraction) conceived as identity.

> 

> And we speak of believing in a proposition, having in mind an entire 

> collection of equivalent propositions with their partial interpretants.

> Thus, two persons are said to have the same proposition in mind. The 

> interpretant of a proposition is itself a proposition. Any necessary 

> inference from a proposition is an interpretant of it.

> 

> When we speak of truth and falsity, we refer to the possibility of the 

> proposition being refuted; and this refutation (roughly speaking) 

> takes place in but one way. Namely, an interpretant of the proposition 

> would, if believed, produce the expectation of a certain description 

> of percept on a certain occasion. The occasion arrives: the percept 

> forced upon us is different. This constitutes the falsity of every 

> proposition of which the disappointing prediction was the 

> interpretant. Thus, a false proposition is a proposition of which some 

> interpretant represents that, on an occasion which it indicates, a 

> percept will have a certain character, while the immediate perceptual 

> judgment on that occasion is that the percept has not that character.

> 

> A true proposition is a proposition belief in which would never lead 

> to such disappointment so long as the proposition is not understood 

> otherwise than it was intended.

 

In the article, I formalize Peirce's notion of equivalence in terms of 
*meaning-preserving translations* (MPTs), which specify a class of equivalent 
sentences in some language or languages.  It's easy to define MPTs for formal 
logics, but much harder for natural languages.

 

John


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[PEIRCE-L] Re: { Information = Comprehension × Extension }

[John F Sowa]

Jon,

That's an important topic to explore:

JA

we can take up the issue of propositions in more detail
as it arises in the relevant context.


For a good analysis of the issues, I recommend the following book:
Stjernfelt, Frederik (2014) Natural Propositions: The Actuality
of Peirce’s Doctrine of Dicisigns, Boston: Docent Press.

I wrote a 5-page article on propositions from a Peircean perspective:
http://www.jfsowa.com/logic/proposit.pdf

That article is based on Peirce's notion of equivalence (CP 5.569):

A sign is only a sign in actu by virtue of its receiving an
interpretation, that is, by virtue of its determining another sign
of the same object. This is as true of mental judgments as it is of
external signs. To say that a proposition is true is to say that
every interpretation of it is true. Two propositions are equivalent
when either might have been an interpretant of the other. This
equivalence, like others, is by an act of abstraction (in the sense
in which forming an abstract noun is abstraction) conceived as identity.

And we speak of believing in a proposition, having in mind an entire
collection of equivalent propositions with their partial interpretants.
Thus, two persons are said to have the same proposition in mind. The
interpretant of a proposition is itself a proposition. Any necessary
inference from a proposition is an interpretant of it.

When we speak of truth and falsity, we refer to the possibility of the
proposition being refuted; and this refutation (roughly speaking) takes
place in but one way. Namely, an interpretant of the proposition would,
if believed, produce the expectation of a certain description of percept
on a certain occasion. The occasion arrives: the percept forced upon
us is different. This constitutes the falsity of every proposition of
which the disappointing prediction was the interpretant. Thus, a false
proposition is a proposition of which some interpretant represents
that, on an occasion which it indicates, a percept will have a certain
character, while the immediate perceptual judgment on that occasion is
that the percept has not that character.

A true proposition is a proposition belief in which would never lead
to such disappointment so long as the proposition is not understood
otherwise than it was intended.


In the article, I formalize Peirce's notion of equivalence in terms
of *meaning-preserving translations* (MPTs), which specify a class
of equivalent sentences in some language or languages.  It's easy to
define MPTs for formal logics, but much harder for natural languages.

John

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[PEIRCE-L] Re: { Information = Comprehension × Extension }

[Jon Awbrey]

Peircers,

The easier-on-the-eyes blog version of my first Discussion post —
from which point it is also easier to follow the links to the
first six Selections from Peirce — is here:

{ Information = Comprehension × Extension } • Discussion 1
https://inquiryintoinquiry.com/2017/06/26/information-comprehension-x-extension-%e2%80%a2-discussion-1/

The word “proposition” occurs only twice in the first six Selections,
once in Selection 2 and once in Selection 4, so maybe it's worth our
pausing to see how Peirce uses the word in this place and time:

{ Information = Comprehension × Extension } • Selection 2
https://inquiryintoinquiry.com/2016/05/19/information-comprehension-x-extension-%e2%80%a2-selection-2/

“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, p. 468)


{ Information = Comprehension × Extension } • Selection 4
https://inquiryintoinquiry.com/2016/05/21/information-comprehension-x-extension-%e2%80%a2-selection-4/

“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.”  (Peirce 1866, p. 469)


For now I'll just add those two observations to the hopper,
and we can take up the issue of propositions in more detail
as it arises in the relevant context.

It is good that John Sowa read us the “Freedom Of Interpretation Act”
right at the start, as it will serve us in good stead down the road,
but again I'll have to leave its consequences until a few folks have
a chance to delve further into Peirce's text, at which point I think
it's significance will become clear.

Regards,

Jon

On 6/27/2017 5:18 PM, John F Sowa wrote:

Jon,

The subject line raises some complex issues:


Information = Comprehension × Extension


A more fundamental term is 'proposition', which is informally
defined as the "meaning" of a sentence.  That meaning is usually
analyzed as comprehension (AKA intension) and extension.

Given that definition (or a more detailed analysis,
such as Frederik Stjernfelt's book) we can talk about
the many different ways of using a proposition:

  1. If you state it, it's a statement.

  2. If you assert it, it's an assertion.

  3. If you assume it, it's an assumption.

  4. If you infer it, it's an inference.

  5. If it's given to you, it's data.

  6. If it informs you, it's information.

  7. If you know it, it's knowledge.

But the same proposition, in different contexts, 
could be any or all of the above.


John



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Re: [PEIRCE-L] Re: { Information = Comprehension × Extension }

[Jerry Rhee]

John, list:

On 6/27/2017 6:08 PM, Jerry Rhee wrote:

> Thanks for making what might otherwise appear confusing and complex, clear
> and simple.


Not I, but Gary said the above

I saw what you were doing... explaining by means of itself.

best,
J


On Tue, Jun 27, 2017 at 10:19 PM, John F Sowa  wrote:

> On 6/27/2017 6:08 PM, Jerry Rhee wrote:
>
>> Thanks for making what might otherwise appear confusing and complex,
>> clear and simple.
>>
>
> I hope I didn't make it too clear and simple -- because I agree with
> Peirce (and with modern lexicographers) that word senses are definitely
> not clear and simple.  I was simply pointing out some issues that Peirce
> had discussed in various ways.  In particular, most of the ways of using
> a proposition happen can be described by nominalized verbs.
>
> In _How to do things with words_, Austin said more about such issues:
> http://pubman.mpdl.mpg.de/pubman/item/escidoc:2271128:3/comp
> onent/escidoc:2271430/austin_1962_how-to-do-things-with-words.pdf
>
> For good observations by modern lexicographers (Sue Atkins and
> Adam Kilgarriff), see the article "I don't believe in word senses":
> https://www.sketchengine.co.uk/wp-content/uploads/I_dont_believe_1997.pdf
>
> John
>
>
> -
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Re: [PEIRCE-L] Re: { Information = Comprehension × Extension }

[John F Sowa]

On 6/27/2017 6:08 PM, Jerry Rhee wrote:
Thanks for making what might otherwise appear confusing and complex, 
clear and simple.


I hope I didn't make it too clear and simple -- because I agree with
Peirce (and with modern lexicographers) that word senses are definitely
not clear and simple.  I was simply pointing out some issues that Peirce
had discussed in various ways.  In particular, most of the ways of using
a proposition happen can be described by nominalized verbs.

In _How to do things with words_, Austin said more about such issues:
http://pubman.mpdl.mpg.de/pubman/item/escidoc:2271128:3/component/escidoc:2271430/austin_1962_how-to-do-things-with-words.pdf 



For good observations by modern lexicographers (Sue Atkins and
Adam Kilgarriff), see the article "I don't believe in word senses":
https://www.sketchengine.co.uk/wp-content/uploads/I_dont_believe_1997.pdf

John

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Re: [PEIRCE-L] Re: { Information = Comprehension × Extension }

[Jerry Rhee]

John, list:

yeah, that was a great post!

J

On Tue, Jun 27, 2017 at 4:34 PM, Gary Richmond 
wrote:

> John,
>
> Thanks for making what might otherwise appear confusing and complex, clear
> and simple.
>
> Best,
>
> Gary R
>
> [image: Gary Richmond]
>
> *Gary Richmond*
> *Philosophy and Critical Thinking*
> *Communication Studies*
> *LaGuardia College of the City University of New York*
> *C 745*
> *718 482-5690 <(718)%20482-5690>*
>
> On Tue, Jun 27, 2017 at 5:18 PM, John F Sowa  wrote:
>
>> Jon,
>>
>> The subject line raises some complex issues:
>>
>> Information = Comprehension × Extension
>>>
>>
>> A more fundamental term is 'proposition', which is informally
>> defined as the "meaning" of a sentence.  That meaning is usually
>> analyzed as comprehension (AKA intension) and extension.
>>
>> Given that definition (or a more detailed analysis, such as
>> Frederik Stjernfelt's book) we can talk about the many different
>> ways of using a proposition:
>>
>>  1. If you state it, it's a statement.
>>
>>  2. If you assert it, it's an assertion.
>>
>>  3. If you assume it, it's an assumption.
>>
>>  4. If you infer it, it's an inference.
>>
>>  5. If it's given to you, it's data.
>>
>>  6. If it informs you, it's information.
>>
>>  7. If you know it, it's knowledge.
>>
>> But the same proposition, in different contexts, could be
>> any or all of the above.
>>
>> John
>>
>>
>> -
>> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
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>> but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the
>> BODY of the message. More at http://www.cspeirce.com/peirce
>> -l/peirce-l.htm .
>>
>>
>>
>>
>>
>>
>
>
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> .
>
>
>
>
>
>

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Re: [PEIRCE-L] Re: { Information = Comprehension × Extension }

[Gary Richmond]

John,

Thanks for making what might otherwise appear confusing and complex, clear
and simple.

Best,

Gary R

[image: Gary Richmond]

*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*
*C 745*
*718 482-5690*

On Tue, Jun 27, 2017 at 5:18 PM, John F Sowa  wrote:

> Jon,
>
> The subject line raises some complex issues:
>
> Information = Comprehension × Extension
>>
>
> A more fundamental term is 'proposition', which is informally
> defined as the "meaning" of a sentence.  That meaning is usually
> analyzed as comprehension (AKA intension) and extension.
>
> Given that definition (or a more detailed analysis, such as
> Frederik Stjernfelt's book) we can talk about the many different
> ways of using a proposition:
>
>  1. If you state it, it's a statement.
>
>  2. If you assert it, it's an assertion.
>
>  3. If you assume it, it's an assumption.
>
>  4. If you infer it, it's an inference.
>
>  5. If it's given to you, it's data.
>
>  6. If it informs you, it's information.
>
>  7. If you know it, it's knowledge.
>
> But the same proposition, in different contexts, could be
> any or all of the above.
>
> John
>
>
> -
> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
> PEIRCE-L to this message. PEIRCE-L posts should go to
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> BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm
> .
>
>
>
>
>
>

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Re: [PEIRCE-L] Re: { Information = Comprehension × Extension }

[John F Sowa]

Jon,

The subject line raises some complex issues:


Information = Comprehension × Extension


A more fundamental term is 'proposition', which is informally
defined as the "meaning" of a sentence.  That meaning is usually
analyzed as comprehension (AKA intension) and extension.

Given that definition (or a more detailed analysis, such as
Frederik Stjernfelt's book) we can talk about the many different
ways of using a proposition:

 1. If you state it, it's a statement.

 2. If you assert it, it's an assertion.

 3. If you assume it, it's an assumption.

 4. If you infer it, it's an inference.

 5. If it's given to you, it's data.

 6. If it informs you, it's information.

 7. If you know it, it's knowledge.

But the same proposition, in different contexts, could be
any or all of the above.

John

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[PEIRCE-L] Re: { Information = Comprehension × Extension }

[Jon Awbrey]

Peircers,

Here's my 1st Comment on Selections 1 through 6 —

{ Information = Comprehension × Extension } • Comment 1
===
https://inquiryintoinquiry.com/2016/05/26/information-comprehension-x-extension-%e2%80%a2-comment-1/

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”.

https://inquiryintoinquiry.com/2016/05/19/information-comprehension-x-extension-%E2%80%A2-selection-1/

In the interests 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:

• t_1 = spherical
• t_2 = bright
• t_3 = fragrant
• t_4 = juicy
• t_5 = tropical
• t_6 = fruit

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

• z = t_1 ∙ t_2 ∙ t_3 ∙ t_4 ∙ t_5 ∙ t_6

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”?

https://inquiryintoinquiry.com/2016/05/20/information-comprehension-x-extension-%E2%80%A2-selection-3/
https://inquiryintoinquiry.com/2016/05/22/information-comprehension-x-extension-%E2%80%A2-selection-5/

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 of 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, attached.]

Figure 1. Conjunctive Term z, Taken as Predicate

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 {t_1, t_2, t_3, t_4, t_5, t_6}, 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.

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
=

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

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



Re:
{ Information = Comprehension × Extension } • Discussion 1
==
https://inquiryintoinquiry.com/2017/06/26/information-comprehension-x-extension-%e2%80%a2-discussion-1/


Peircers,

A puzzle in Peirce I have puzzled over for as long as I can remember 
involves the relationship between his theory of signs, marking the 
characters of icons, indices, and symbols, and his theory of inquiry, 
bearing the three inferences of abduction, induction, and deduction.  
I have long felt the resolution would lie in his theory of information, 
epitomized by the formula “Information = Comprehension × Extension”.


Last summer looked ripe for another run at the problem, which I had 
some years before begun tackling in a series of selections from and 
comments on Peirce’s “Logic of Science” lectures at Harvard (1865) 
and the Lowell Institute (1866).


There's a working draft of those selections and comments here:

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

I serialized the selections and comments on my blog as I worked through them.

Introductory Comment
https://inquiryintoinquiry.com/2016/05/18/information-comprehension-x-extension/

(First Six) Selections from Peirce's Lectures
https://inquiryintoinquiry.com/2016/05/19/information-comprehension-x-extension-%e2%80%a2-selection-1/
https://inquiryintoinqu