[PEIRCE-L] Re: Stjernfelt : Chapter 9

[Jon Awbrey]

Re: Cathy Legg
At: http://permalink.gmane.org/gmane.science.philosophy.peirce/15739

Hi Cathy, brave soul, I'm getting a "resource not found msg"
on that link right at the moment ...

But this one seems to work:

http://researchcommons.waikato.ac.nz/handle/10289/2811

Cheers,

Jon

On 2/24/2015 5:12 PM, Catherine Legg wrote:

Sincere apologies to everyone for the delay in posting. My life has
been a bit chaotic lately.

First of all I want to say how very much I have been enjoying reading
Frederik's book. It combines mastery of the intricacies of Peirce's
semeiotic, early and late (and we all know what a challenge that is),
with a bold march out into contemporary mainstream philosophy of
biology and cognitive science, flying the flag of Peircean ideas. The
book's powerful organising idea of the dicisign's self-referential
'double structure' also has the capacity to blast so much cavilling,
insufficient contemporary nominalistic philosophy of language out of
the water! (Sorry for the somewhat drenching metaphor).

Chapter 9 is a curious excursion on a very specific topic: Peirce's
rationale for "the puzzling sheets containing 99 small
drawings...which accompany MS 725." It seemed that Peirce was playing
with these as a kind of experiment in breaking down the concept of a
"natural class" to its minimal analytical components.

In the background of this discussion is the topic of MS 725: Peirce's
discussion of "Logical Extension and Comprehension" (presented as a
talk in 1867). The tradition of logic contains a lot of discussion of
this distinction (e.g. in Port-Royal Logic, in Mill, in William
Hamilton), where 'extension' referred to 'things picked out', or the
reference of a term, and 'intension' to the ideas evoked, or meaning
of a term. So the subjects of propositions seem more suited to express
extension and the predicates of propositions seem more suited to
express intension. Although strictly speaking, in the proposition "The
cat is on the mat", the phrase 'the cat' does have some intension
insofar as certain ideas about cats pop into my mind when I hear it,
and the phrase 'is on the mat' des have some extension insofar as we
might think there is some (large) set of things that are on mats in
this world of ours.

The tradition was to define an inverse proportionality between
extension and intension, such that by reducing a term's extension we
increase its intension, and vice versa. So if I change "the cat" to
"the brown cat" in the proposition above, I have a term that picks out
fewer things but has a more specific meaning.

But we will see Peirce challenging this simple formula.

Coincidentally I published a paper on this talk of Peirce's in the
Transaction a long time back, connecting it up with discussions of
extensionality and intenionality in C20th philosophy. It's called
"Extension, Intension and Dormitive Virtue". It was just when I was
starting out as a scholar and is not a terribly elegant paper. But if
anyone is interested:
http://researchcommons.waikato.ac.nz/bitstream/handle/10289/2811

I have been wisely advised by our esteemed Peirce-L moderators not to
try to post too much on this chapter in a single go, so I will leave
it there for now, and return anon!

Cheers, Cathy




--

academia: http://independent.academia.edu/JonAwbrey
my word press blog: http://inquiryintoinquiry.com/
inquiry list: http://stderr.org/pipermail/inquiry/
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
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[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Catherine Legg]

Picking up again where I left off...

The logical tradition that Peirce was responding to with his piece "Logical
Extension and Comprehension" was basically a 'term logic', according to
which this rough formula held:

Breadth x Depth = k (where k is some constant)

This implies: the larger the extension (breadth), the smaller the intension
(depth). This formula seems to work for classic terms such as "blue", which
covers more things but is correspondingly less precise than, say, "baby
blue". Or "vehicle" which covers more things but is less precise than, say
"nuclear submarine".

However, Peirce's shift from terms to propositions as a basic analysis of
meaning allows him to question some of this framework. A proposition is now
not a simple 'multiplication' of two 'similar quantities'. A proposition
requires two separate functionalities. The part which provides the
extension (the subject) functions indexically, and the part which provides
the intension (the predicate) functions iconically.

Stjernfelt points out that, under this framework, "far from being a
constant, Breadth x Depth gives a measure of the amount of information
inherent in a proposition" (which can be higher or lower). He notes that
Peirce still retained this idea 25 years later in Kaina Stoicheia.

*QUESTIONS: In what sense, and to what degree might this 'information' be
measured? (If not in some absolute sense, then perhaps relatively, between
propositions?) Doesn't the very notion of measuring this value conflict
with Peirce's contrite fallibilism, which holds that what a given term will
come to mean to us is not something that can be decided in advance of
scientific inquiry? In other words, scientific terms can hold a great deal
of implicit information as well as the explicit information that scientists
are working with at a given time. *

Probably in the light of this kind of worry, Peirce sets himself the task
to trying to analytically define what is a 'natural class'. For natural
classes are precisely those which bear future inquiry, yielding up implicit
information to be made explicit. As Peirce says, think how much more
"electricity" means now than in the days of Dalton. Whereas an a
non-natural ("artificial") class - has nothing more to tell us apart from
the way it was already defined. Peirce gives the example of 'cow' as a
natural class and 'red cow' as artificial.

To this end, he draws two sets of mysterious diagrams, as a kind of
experiment, possibly unfinished. This seems to be an experiment in defining
"properties" or "marks" in the most minimal way possible, then varying them
in the most minimal ways possible, to try to decide what groupings our
scientific inquirer might decide are 'natural'. This is not a simple matter
of making a class for each property, as we do not have a distinction
between natural and artificial classes.

*QUESTION: How does Peirce attempt to draw the distinction, in the two
cases Frederik catalogues?*

List: if you tell me what you think then I will tell you what I think.

Cheers, Cathy





On Tue, Feb 24, 2015 at 10:12 PM, Catherine Legg 
wrote:

> Sincere apologies to everyone for the delay in posting. My life has
> been a bit chaotic lately.
>
> First of all I want to say how very much I have been enjoying reading
> Frederik's book. It combines mastery of the intricacies of Peirce's
> semeiotic, early and late (and we all know what a challenge that is),
> with a bold march out into contemporary mainstream philosophy of
> biology and cognitive science, flying the flag of Peircean ideas. The
> book's powerful organising idea of the dicisign's self-referential
> 'double structure' also has the capacity to blast so much cavilling,
> insufficient contemporary nominalistic philosophy of language out of
> the water! (Sorry for the somewhat drenching metaphor).
>
> Chapter 9 is a curious excursion on a very specific topic: Peirce's
> rationale for "the puzzling sheets containing 99 small
> drawings...which accompany MS 725." It seemed that Peirce was playing
> with these as a kind of experiment in breaking down the concept of a
> "natural class" to its minimal analytical components.
>
> In the background of this discussion is the topic of MS 725: Peirce's
> discussion of "Logical Extension and Comprehension" (presented as a
> talk in 1867). The tradition of logic contains a lot of discussion of
> this distinction (e.g. in Port-Royal Logic, in Mill, in William
> Hamilton), where 'extension' referred to 'things picked out', or the
> reference of a term, and 'intension' to the ideas evoked, or meaning
> of a term. So the subjects of propositions seem more suited to express
> extension and the predicates of propositions seem more suited to
> express intension. Although strictly speaking, in the proposition "The
> cat is on the mat", the phrase 'the cat' does have some intension
> insofar as certain ideas about cats pop into my mind when I hear it,
> and the phrase 'is on the mat' des have some extension inso

[PEIRCE-L] Re: Stjernfelt : Chapter 9

[Jon Awbrey]

Thread:
CL:http://permalink.gmane.org/gmane.science.philosophy.peirce/15739
CL:http://permalink.gmane.org/gmane.science.philosophy.peirce/15776

Cathy, List,

Frederik's thesis went off the track for me in one of the early chapters --
I've been meaning to do the good scholarly thing and articulate exactly
where and why, but other business pre-occupies, so let me just say what
I have come to opine from my own study of Peirce's information theory
in relation to his theory of inquiry.

Peirce's concept of information generalizes Shannon's to the degree
that triadic sign relations generalize dyadic cause-effect notions of
information transmission, but Peircean information is not substantially
different in that it makes sense only in a context of prior uncertainty,
the "irritation of doubt" that drives inquiry, and its measure is based
on the power of signs in a given sign relation to reduce the uncertainty
of an interpreter about an object, if we may use the sop of agent-talk.

In that view, signs bear information on account of their place
in a specified sign relation, and it is a matter of secondary
concern whether the sign is a picture, proposition, term, or
something else entirely, like the state of a computer system.

Regards,

Jon

On 3/3/2015 2:41 PM, Catherine Legg wrote:

Picking up again where I left off...

The logical tradition that Peirce was responding to with his piece "Logical
Extension and Comprehension" was basically a 'term logic', according to
which this rough formula held:

Breadth x Depth = k (where k is some constant)

This implies: the larger the extension (breadth), the smaller the intension
(depth). This formula seems to work for classic terms such as "blue", which
covers more things but is correspondingly less precise than, say, "baby
blue". Or "vehicle" which covers more things but is less precise than, say
"nuclear submarine".

However, Peirce's shift from terms to propositions as a basic analysis of
meaning allows him to question some of this framework. A proposition is now
not a simple 'multiplication' of two 'similar quantities'. A proposition
requires two separate functionalities. The part which provides the
extension (the subject) functions indexically, and the part which provides
the intension (the predicate) functions iconically.

Stjernfelt points out that, under this framework, "far from being a
constant, Breadth x Depth gives a measure of the amount of information
inherent in a proposition" (which can be higher or lower). He notes that
Peirce still retained this idea 25 years later in Kaina Stoicheia.

*QUESTIONS: In what sense, and to what degree might this 'information' be
measured? (If not in some absolute sense, then perhaps relatively, between
propositions?) Doesn't the very notion of measuring this value conflict
with Peirce's contrite fallibilism, which holds that what a given term will
come to mean to us is not something that can be decided in advance of
scientific inquiry? In other words, scientific terms can hold a great deal
of implicit information as well as the explicit information that scientists
are working with at a given time. *

Probably in the light of this kind of worry, Peirce sets himself the task
to trying to analytically define what is a 'natural class'. For natural
classes are precisely those which bear future inquiry, yielding up implicit
information to be made explicit. As Peirce says, think how much more
"electricity" means now than in the days of Dalton. Whereas an a
non-natural ("artificial") class - has nothing more to tell us apart from
the way it was already defined. Peirce gives the example of 'cow' as a
natural class and 'red cow' as artificial.

To this end, he draws two sets of mysterious diagrams, as a kind of
experiment, possibly unfinished. This seems to be an experiment in defining
"properties" or "marks" in the most minimal way possible, then varying them
in the most minimal ways possible, to try to decide what groupings our
scientific inquirer might decide are 'natural'. This is not a simple matter
of making a class for each property, as we do not have a distinction
between natural and artificial classes.

*QUESTION: How does Peirce attempt to draw the distinction, in the two
cases Frederik catalogues?*

List: if you tell me what you think then I will tell you what I think.

Cheers, Cathy





On Tue, Feb 24, 2015 at 10:12 PM, Catherine Legg 
wrote:


Sincere apologies to everyone for the delay in posting. My life has
been a bit chaotic lately.

First of all I want to say how very much I have been enjoying reading
Frederik's book. It combines mastery of the intricacies of Peirce's
semeiotic, early and late (and we all know what a challenge that is),
with a bold march out into contemporary mainstream philosophy of
biology and cognitive science, flying the flag of Peircean ideas. The
book's powerful organising idea of the dicisign's self-referential
'double structure' also has the capacity to blast so much cavilling,
insufficient c

[PEIRCE-L] Re: Stjernfelt : Chapter 9

[Jon Awbrey]

Thread:
CL:http://permalink.gmane.org/gmane.science.philosophy.peirce/15739
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15740
CL:http://permalink.gmane.org/gmane.science.philosophy.peirce/15776
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15777
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/15779
BU:http://permalink.gmane.org/gmane.science.philosophy.peirce/15796

Ben, Cathy, Jerry, List,

What I like to call the "ICE formula", Information = Comprehension × Extension,
was already treated at length in the Harvard and Lowell Lectures of 1865-1866,
so I don't think it could have been the dicent theory of propositions, or any
ostensible shift from terms to propositions, that led Peirce to formulate it.

As always, I think it pays to study Peirce's early treatment of information,
as it affords a wealth of concrete detail, example, and motivation that is
often missing from his later accounts.

I can't say I've managed to rationalize Peirce's inclinations toward a theory
of information completely within my own frame of thought yet, but I have been
putting a fair amount of time into doing so.  My notes in progress are here:

http://intersci.ss.uci.edu/wiki/index.php/Information_%3D_Comprehension_%C3%97_Extension

Regards,

Jon

On 3/8/2015 9:21 PM, Benjamin Udell wrote:

Cathy, list,

You wrote,

QUESTIONS: In what sense, and to what degree might this
'information' be measured? (If not in some absolute sense, then
perhaps relatively, between propositions?) Doesn't the very notion
of measuring this value conflict with Peirce's contrite fallibilism,
which holds that what a given term will come to mean to us is not
something that can be decided in advance of scientific inquiry? In
other words, scientific terms can hold a great deal of implicit
information as well as the explicit information that scientists are
working with at a given time.
[End quote]

Presumably the information to be quantified is not that of what a given term 
will come to mean to us, but rather that of
what it means to us now - the difference between making our ideas true, as 
Peirce put it, and making our ideas clear.
What it means to us now is what we now conceive to be its practical bearing in 
general on conduct.

I have to admit I have little to say about how to quantify comprehension, 
denotation, information in Peirce's sense. I
did find this passage:

Writings 1:342-343, Logic Notebook Dec. 15, 1865
http://pds.lib.harvard.edu/pds/view/15255301?n=28&imagesize=600&jp2Res=0.25&printThumbnails=true

In the formula

Extension × Intension = Implication

we may have the values

(1) 0 × 0 = 0
(2) 0 × n = 0
(3) 0 × ∞ = 0
(4) 0 × ∞ = n
(5) 0 × ∞ = ∞
(6) n × 0 = 0
(7) n × n = n
(8) n × ∞ = ∞
(9) ∞ × 0 = 0
(10) ∞ × 0 = n
(11) ∞ × 0 = ∞
(12) ∞ × n = ∞
(13) ∞ × ∞ = ∞

(7) will be the case with any ordinary symbol.

(4) is the ordinary nothing.

(10) the ordinary being.

These are the cases when Implication is n. Now for those where it is 0.

(6) is the case of a sign, (2) of a copy.

(1) would be a sign of nothing or a copy of being which are
undetermined to be representations.

(9) would be being supposing it were not known to be, or being
considered abstractly of the fact that it is.

(3) would be nothing abstracting from the fact that there is
anything so that its opposition is taken away.

A being which isn't, would be a nothing which is unopposed to
anything; hence being abstracted from the fact that it is is
abstracted from all that makes it differ from nothing abstracted
from its opposition and vice versa.

We will now take up the cases where the implication = ∞. (12) is
being of which some determinate quality is supposed to be known.

(8) is a contradiction it being implied that it exists.

(13) is being which is supposed to have all attributes.

(11) would purport to be a complete list of all beings.

(5) would purport to be a complete conjunction of all attributes.
[End quote]

You wrote,

QUESTION: How does Peirce attempt to draw the distinction, in the
two cases Frederik catalogues?
[End quote]

I can't think of anything to say about this either, though the question of 
natural vs. artificial kinds is quite
interesting to me. Similar question in mathematics: Are primes a natural kind? 
What about the class of functions that
share a certain first derivative? The class of pairs of integers that sum to a 
certain integer?

You wrote,

List: if you tell me what you think then I will tell you what I think.
[End quote]

I haven't done too well, nobody else has replied, I guess you ask tough 
questions, but anyway at this point I'm
interested in hearing what you think.

Best, Ben

On 3/3/2015 2:41 PM, Catherine Legg wrote:


Picking 

[PEIRCE-L] Re: Stjernfelt : Chapter 9

[Catherine Legg]

Hi Jon,

Can you please not include those links in your postings? They are confusing
and add nothing to our conversation here. This issue has been raised before
by the list moderators.

"Peirce's concept of information generalizes Shannon's to the degree
that triadic sign relations generalize dyadic cause-effect notions of
information transmission, but Peircean information is not substantially
different in that it makes sense only in a context of prior uncertainty,
the "irritation of doubt" that drives inquiry"

I don't understand what it means to "generalize dyadic cause-effect notions
of information transmission" - sorry.

"In that view, signs bear information on account of their place
in a specified sign relation, and it is a matter of secondary
concern whether the sign is a picture, proposition, term, or
something else entirely, like the state of a computer system."

Here I quite disagree. In my view the distinction between icon, index and
symbol is very basic to Peirce's semiotics, and highly explanatory.

Cheers, Cathy



On Tue, Mar 3, 2015 at 8:50 PM, Jon Awbrey  wrote:

> Thread:
> CL:http://permalink.gmane.org/gmane.science.philosophy.peirce/15739
> CL:http://permalink.gmane.org/gmane.science.philosophy.peirce/15776
>
> Cathy, List,
>
> Frederik's thesis went off the track for me in one of the early chapters --
> I've been meaning to do the good scholarly thing and articulate exactly
> where and why, but other business pre-occupies, so let me just say what
> I have come to opine from my own study of Peirce's information theory
> in relation to his theory of inquiry.
>
> Peirce's concept of information generalizes Shannon's to the degree
> that triadic sign relations generalize dyadic cause-effect notions of
> information transmission, but Peircean information is not substantially
> different in that it makes sense only in a context of prior uncertainty,
> the "irritation of doubt" that drives inquiry, and its measure is based
> on the power of signs in a given sign relation to reduce the uncertainty
> of an interpreter about an object, if we may use the sop of agent-talk.
>
> In that view, signs bear information on account of their place
> in a specified sign relation, and it is a matter of secondary
> concern whether the sign is a picture, proposition, term, or
> something else entirely, like the state of a computer system.
>
> Regards,
>
> Jon
>
> On 3/3/2015 2:41 PM, Catherine Legg wrote:
>
>> Picking up again where I left off...
>>
>> The logical tradition that Peirce was responding to with his piece
>> "Logical
>> Extension and Comprehension" was basically a 'term logic', according to
>> which this rough formula held:
>>
>> Breadth x Depth = k (where k is some constant)
>>
>> This implies: the larger the extension (breadth), the smaller the
>> intension
>> (depth). This formula seems to work for classic terms such as "blue",
>> which
>> covers more things but is correspondingly less precise than, say, "baby
>> blue". Or "vehicle" which covers more things but is less precise than, say
>> "nuclear submarine".
>>
>> However, Peirce's shift from terms to propositions as a basic analysis of
>> meaning allows him to question some of this framework. A proposition is
>> now
>> not a simple 'multiplication' of two 'similar quantities'. A proposition
>> requires two separate functionalities. The part which provides the
>> extension (the subject) functions indexically, and the part which provides
>> the intension (the predicate) functions iconically.
>>
>> Stjernfelt points out that, under this framework, "far from being a
>> constant, Breadth x Depth gives a measure of the amount of information
>> inherent in a proposition" (which can be higher or lower). He notes that
>> Peirce still retained this idea 25 years later in Kaina Stoicheia.
>>
>> *QUESTIONS: In what sense, and to what degree might this 'information' be
>> measured? (If not in some absolute sense, then perhaps relatively, between
>> propositions?) Doesn't the very notion of measuring this value conflict
>> with Peirce's contrite fallibilism, which holds that what a given term
>> will
>> come to mean to us is not something that can be decided in advance of
>> scientific inquiry? In other words, scientific terms can hold a great deal
>> of implicit information as well as the explicit information that
>> scientists
>> are working with at a given time. *
>>
>> Probably in the light of this kind of worry, Peirce sets himself the task
>> to trying to analytically define what is a 'natural class'. For natural
>> classes are precisely those which bear future inquiry, yielding up
>> implicit
>> information to be made explicit. As Peirce says, think how much more
>> "electricity" means now than in the days of Dalton. Whereas an a
>> non-natural ("artificial") class - has nothing more to tell us apart from
>> the way it was already defined. Peirce gives the example of 'cow' as a
>> natural class and 'red cow' as artificial.
>>
>> To this end, he dra

[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Jon Awbrey]

Franklin, List,

I think that was Ben Udell. 

Regards,

Jon

http://inquiryintoinquiry.com

> On Apr 20, 2015, at 7:30 PM, Franklin Ransom  
> wrote:
> 
> Cathy, Frederik, lists,
> 
> Yes, Frederik, that makes sense to me. As I mentioned in my previous post, 
> counting qualities or characters doesn't seem to be helpful. Although it 
> should be possible to enumerate them, to a point, for the purpose of some 
> inquiry.
> 
> As I recall, Jon Awbrey in the last month or two referenced a text from 
> Peirce about the multiplication of breadth and depth using symbols like 1, 0, 
> and the infinity loop, to distinguish cases such as essential depth and 
> breadth, substantial depth and breadth, the idea of nothing, the idea of 
> being, etc. If infinity was indeed used then, Peirce had certainly 
> contemplated infinite depth and infinite breadth, although perhaps not simply 
> in the sense of counting with no end, but in the direct sense of being that 
> which is without limit, so depth without limit or breadth without limit.
> 
> -- Franklin
> 
>> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt  
>> wrote:
>> Dear Franklin, Cathy, Lists - 
>> 
>> A small clarification: Peirce's BxD=A idea, I think, should not be taken a 
>> device for the arithmetic calculation of exact information size - it is 
>> rather the proposal of a general law relating Breadth and Depth. His idea 
>> comes from the simple idea that when intension is zero, there is no 
>> information, while when extension is zero, there is also no information - 
>> and that is the relation of the two factors in a product.  (It is a bit like 
>> his first Boole-inspired definition of universal quantification as a product 
>> - he defines truth as 1, falsity as 0,  then, in order to be true, each 
>> single case of a universal proposition should be true - if any single one of 
>> them is false, the total product of them all will be zero.) 
>> The BXD=A idea allows him to investigate what happens if intension or 
>> extension are in- or decreased, etc. - even if not being able to express 
>> that in precise numbers. 
>> 
>> Best
>> F
>> 
>> 
>>> Den 20/04/2015 kl. 01.14 skrev Franklin Ransom 
>>> :
>>> 
>>> Cathy, lists,
>>> 
>>> Well, look at this way: It is possible for there to be objects in the 
>>> senses which are yet not perceived, because we do not yet have any idea of 
>>> what it is to which we are looking. It takes a hypothesis to introduce a 
>>> new idea to us to explain what it is, which hypothesis we can then put to 
>>> the test. In order to do so, we must determine what kinds of characters to 
>>> look for (deduction helps here) and then look for existent objects 
>>> (induction) to learn whether the purported relations between characters 
>>> obtain in fact, and in this way we come to understand the thing which we 
>>> are experiencing. It is of course induction which gives us more 
>>> information; abduction simply gives us the idea which needs to become 
>>> informed, and deduction is merely explicative, based on relating the idea 
>>> to other ideas and previously gathered information regarding those ideas.
>>> 
>>> Obviously, we cannot conduct induction without end, because that is a 
>>> practical impossibility. Our 'sum', as you put it, far from being always an 
>>> infinity, will very likely never be an infinity in practice, in whatever 
>>> sense you mean to understand the application of infinity to a 'sum' of 
>>> information. Of course, as an ideal, where science, the community of 
>>> inquiry as such, continues to investigate, it is possible for the 
>>> information of an idea to reach a much greater 'sum' than would otherwise 
>>> be possible for individuals such as you or me. But it is a commonplace of 
>>> science that ideas that work and continue to work are understood more 
>>> thoroughly in their relations to other ideas over the course on inquiry. 
>>> This means of course that not only the breadth, but also the depth of the 
>>> idea continues to grow. As a result, typically, rather than tending to make 
>>> comparisons moot, we start to see a hierarchy of ideas and related sciences 
>>> appear.
>>> 
>>> Consider this passage: "The former [Cows] is a natural class, the latter 
>>> [Red Cows] is not. Now one predicate more may be attached to Red Cows than 
>>> to Cows; hence Mr. Mill's attempts to analyze the difference between 
>>> natural and artificial classes is seen to be a failure. For, according to 
>>> him, the difference is that a real kind is distinguished by unknown 
>>> multitudes of properties while an artificial class has only a few 
>>> determinate ones. Again there is an unusual degree of accordance among 
>>> naturalists in making Vertebrates a natural class. Yet the number of 
>>> predicates proper to it is comparatively small" (NP, p.238, quoting 
>>> Peirce). We can see here that further simplifications are introduced, so 
>>> taking what is learned about various vertebrates, a new idea, that

[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Jon, Ben, lists,

Whoops! Sorry about that! I guess it just struck me as a "Jon" kind of
thing to do, with the slow reads going on about Peirce's earlier logical
works. I apologize for the mistake!

-- Franklin

On Mon, Apr 20, 2015 at 7:42 PM, Jon Awbrey  wrote:

> Franklin, List,
>
> I think that was Ben Udell.
>
> Regards,
>
> Jon
>
> http://inquiryintoinquiry.com
>
> On Apr 20, 2015, at 7:30 PM, Franklin Ransom 
> wrote:
>
> Cathy, Frederik, lists,
>
> Yes, Frederik, that makes sense to me. As I mentioned in my previous post,
> counting qualities or characters doesn't seem to be helpful. Although it
> should be possible to enumerate them, to a point, for the purpose of some
> inquiry.
>
> As I recall, Jon Awbrey in the last month or two referenced a text from
> Peirce about the multiplication of breadth and depth using symbols like 1,
> 0, and the infinity loop, to distinguish cases such as essential depth and
> breadth, substantial depth and breadth, the idea of nothing, the idea of
> being, etc. If infinity was indeed used then, Peirce had certainly
> contemplated infinite depth and infinite breadth, although perhaps not
> simply in the sense of counting with no end, but in the direct sense of
> being that which is without limit, so depth without limit or breadth
> without limit.
>
> -- Franklin
>
> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt 
> wrote:
>
>>  Dear Franklin, Cathy, Lists -
>>
>> A small clarification: Peirce's *BxD=A* idea, I think, should not be
>> taken a device for the arithmetic calculation of exact information size -
>> it is rather the proposal of a general law relating Breadth and Depth. His
>> idea comes from the simple idea that when intension is zero, there is no
>> information, while when extension is zero, there is also no information -
>> and that is the relation of the two factors in a product.  (It is a bit
>> like his first Boole-inspired definition of universal quantification as a
>> product - he defines truth as 1, falsity as 0,  then, in order to be true,
>> each single case of a universal proposition should be true - if any single
>> one of them is false, the total product of them all will be zero.)
>> The BXD=A idea allows him to investigate what happens if intension or
>> extension are in- or decreased, etc. - even if not being able to express
>> that in precise numbers.
>>
>>  Best
>> F
>>
>>
>>  Den 20/04/2015 kl. 01.14 skrev Franklin Ransom <
>> pragmaticist.lo...@gmail.com>:
>>
>>  Cathy, lists,
>>
>>  Well, look at this way: It is possible for there to be objects in the
>> senses which are yet not perceived, because we do not yet have any idea of
>> what it is to which we are looking. It takes a hypothesis to introduce a
>> new idea to us to explain what it is, which hypothesis we can then put to
>> the test. In order to do so, we must determine what kinds of characters to
>> look for (deduction helps here) and then look for existent objects
>> (induction) to learn whether the purported relations between characters
>> obtain in fact, and in this way we come to understand the thing which we
>> are experiencing. It is of course induction which gives us more
>> information; abduction simply gives us the idea which needs to become
>> informed, and deduction is merely explicative, based on relating the idea
>> to other ideas and previously gathered information regarding those ideas.
>>
>>  Obviously, we cannot conduct induction without end, because that is a
>> practical impossibility. Our 'sum', as you put it, far from being always an
>> infinity, will very likely never be an infinity in practice, in whatever
>> sense you mean to understand the application of infinity to a 'sum' of
>> information. Of course, as an ideal, where science, the community of
>> inquiry as such, continues to investigate, it is possible for the
>> information of an idea to reach a much greater 'sum' than would otherwise
>> be possible for individuals such as you or me. But it is a commonplace of
>> science that ideas that work and continue to work are understood more
>> thoroughly in their relations to other ideas over the course on inquiry.
>> This means of course that not only the breadth, but also the depth of the
>> idea continues to grow. As a result, typically, rather than tending to make
>> comparisons moot, we start to see a hierarchy of ideas and related sciences
>> appear.
>>
>>  Consider this passage: "The former [Cows] is a natural class, the
>> latter [Red Cows] is not. Now one predicate more may be attached to Red
>> Cows than to Cows; hence Mr. Mill's attempts to analyze the difference
>> between natural and artificial classes is seen to be a failure. For,
>> according to him, the difference is that a real kind is distinguished by
>> unknown multitudes of properties while an artificial class has only a few
>> determinate ones. Again there is an unusual degree of accordance among
>> naturalists in making Vertebrates a natural class. Yet the number of
>> predicates

[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Jon Awbrey]

Franklin,

This looks like the post you had in mind:

BU:article.gmane.org/gmane.science.philosophy.peirce/15796/match=breadth+depth

BU:http://permalink.gmane.org/gmane.science.philosophy.peirce/15796

Regards,

Jon

On 4/20/2015 8:21 PM, Franklin Ransom wrote:

Jon, Ben, lists,

Whoops! Sorry about that! I guess it just struck me as a "Jon" kind of
thing to do, with the slow reads going on about Peirce's earlier logical
works. I apologize for the mistake!

-- Franklin

On Mon, Apr 20, 2015 at 7:42 PM, Jon Awbrey  wrote:


Franklin, List,

I think that was Ben Udell.

Regards,

Jon

http://inquiryintoinquiry.com

On Apr 20, 2015, at 7:30 PM, Franklin Ransom 
wrote:

Cathy, Frederik, lists,

Yes, Frederik, that makes sense to me. As I mentioned in my previous post,
counting qualities or characters doesn't seem to be helpful. Although it
should be possible to enumerate them, to a point, for the purpose of some
inquiry.

As I recall, Jon Awbrey in the last month or two referenced a text from
Peirce about the multiplication of breadth and depth using symbols like 1,
0, and the infinity loop, to distinguish cases such as essential depth and
breadth, substantial depth and breadth, the idea of nothing, the idea of
being, etc. If infinity was indeed used then, Peirce had certainly
contemplated infinite depth and infinite breadth, although perhaps not
simply in the sense of counting with no end, but in the direct sense of
being that which is without limit, so depth without limit or breadth
without limit.

-- Franklin

On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt 
wrote:


  Dear Franklin, Cathy, Lists -

A small clarification: Peirce's *BxD=A* idea, I think, should not be
taken a device for the arithmetic calculation of exact information size -
it is rather the proposal of a general law relating Breadth and Depth. His
idea comes from the simple idea that when intension is zero, there is no
information, while when extension is zero, there is also no information -
and that is the relation of the two factors in a product.  (It is a bit
like his first Boole-inspired definition of universal quantification as a
product - he defines truth as 1, falsity as 0,  then, in order to be true,
each single case of a universal proposition should be true - if any single
one of them is false, the total product of them all will be zero.)
The BXD=A idea allows him to investigate what happens if intension or
extension are in- or decreased, etc. - even if not being able to express
that in precise numbers.

  Best
F


  Den 20/04/2015 kl. 01.14 skrev Franklin Ransom <
pragmaticist.lo...@gmail.com>:

  Cathy, lists,

  Well, look at this way: It is possible for there to be objects in the
senses which are yet not perceived, because we do not yet have any idea of
what it is to which we are looking. It takes a hypothesis to introduce a
new idea to us to explain what it is, which hypothesis we can then put to
the test. In order to do so, we must determine what kinds of characters to
look for (deduction helps here) and then look for existent objects
(induction) to learn whether the purported relations between characters
obtain in fact, and in this way we come to understand the thing which we
are experiencing. It is of course induction which gives us more
information; abduction simply gives us the idea which needs to become
informed, and deduction is merely explicative, based on relating the idea
to other ideas and previously gathered information regarding those ideas.

  Obviously, we cannot conduct induction without end, because that is a
practical impossibility. Our 'sum', as you put it, far from being always an
infinity, will very likely never be an infinity in practice, in whatever
sense you mean to understand the application of infinity to a 'sum' of
information. Of course, as an ideal, where science, the community of
inquiry as such, continues to investigate, it is possible for the
information of an idea to reach a much greater 'sum' than would otherwise
be possible for individuals such as you or me. But it is a commonplace of
science that ideas that work and continue to work are understood more
thoroughly in their relations to other ideas over the course on inquiry.
This means of course that not only the breadth, but also the depth of the
idea continues to grow. As a result, typically, rather than tending to make
comparisons moot, we start to see a hierarchy of ideas and related sciences
appear.

  Consider this passage: "The former [Cows] is a natural class, the
latter [Red Cows] is not. Now one predicate more may be attached to Red
Cows than to Cows; hence Mr. Mill's attempts to analyze the difference
between natural and artificial classes is seen to be a failure. For,
according to him, the difference is that a real kind is distinguished by
unknown multitudes of properties while an artificial class has only a few
determinate ones. Again there is an unusual degree of accordance among
naturalists in making Vertebrates a natura

[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Jon,

Yes, that is exactly it, thank you so much!

-- Franklin

On Mon, Apr 20, 2015 at 8:30 PM, Jon Awbrey  wrote:

> Franklin,
>
> This looks like the post you had in mind:
>
> BU:
> article.gmane.org/gmane.science.philosophy.peirce/15796/match=breadth+depth
>
> BU:http://permalink.gmane.org/gmane.science.philosophy.peirce/15796
>
> Regards,
>
> Jon
>
>
> On 4/20/2015 8:21 PM, Franklin Ransom wrote:
>
>> Jon, Ben, lists,
>>
>> Whoops! Sorry about that! I guess it just struck me as a "Jon" kind of
>> thing to do, with the slow reads going on about Peirce's earlier logical
>> works. I apologize for the mistake!
>>
>> -- Franklin
>>
>> On Mon, Apr 20, 2015 at 7:42 PM, Jon Awbrey  wrote:
>>
>>  Franklin, List,
>>>
>>> I think that was Ben Udell.
>>>
>>> Regards,
>>>
>>> Jon
>>>
>>> http://inquiryintoinquiry.com
>>>
>>> On Apr 20, 2015, at 7:30 PM, Franklin Ransom <
>>> pragmaticist.lo...@gmail.com>
>>> wrote:
>>>
>>> Cathy, Frederik, lists,
>>>
>>> Yes, Frederik, that makes sense to me. As I mentioned in my previous
>>> post,
>>> counting qualities or characters doesn't seem to be helpful. Although it
>>> should be possible to enumerate them, to a point, for the purpose of some
>>> inquiry.
>>>
>>> As I recall, Jon Awbrey in the last month or two referenced a text from
>>> Peirce about the multiplication of breadth and depth using symbols like
>>> 1,
>>> 0, and the infinity loop, to distinguish cases such as essential depth
>>> and
>>> breadth, substantial depth and breadth, the idea of nothing, the idea of
>>> being, etc. If infinity was indeed used then, Peirce had certainly
>>> contemplated infinite depth and infinite breadth, although perhaps not
>>> simply in the sense of counting with no end, but in the direct sense of
>>> being that which is without limit, so depth without limit or breadth
>>> without limit.
>>>
>>> -- Franklin
>>>
>>> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt 
>>> wrote:
>>>
>>>Dear Franklin, Cathy, Lists -

 A small clarification: Peirce's *BxD=A* idea, I think, should not be

 taken a device for the arithmetic calculation of exact information size
 -
 it is rather the proposal of a general law relating Breadth and Depth.
 His
 idea comes from the simple idea that when intension is zero, there is no
 information, while when extension is zero, there is also no information
 -
 and that is the relation of the two factors in a product.  (It is a bit
 like his first Boole-inspired definition of universal quantification as
 a
 product - he defines truth as 1, falsity as 0,  then, in order to be
 true,
 each single case of a universal proposition should be true - if any
 single
 one of them is false, the total product of them all will be zero.)
 The BXD=A idea allows him to investigate what happens if intension or
 extension are in- or decreased, etc. - even if not being able to express
 that in precise numbers.

   Best
 F


   Den 20/04/2015 kl. 01.14 skrev Franklin Ransom <
 pragmaticist.lo...@gmail.com>:

   Cathy, lists,

   Well, look at this way: It is possible for there to be objects in the
 senses which are yet not perceived, because we do not yet have any idea
 of
 what it is to which we are looking. It takes a hypothesis to introduce a
 new idea to us to explain what it is, which hypothesis we can then put
 to
 the test. In order to do so, we must determine what kinds of characters
 to
 look for (deduction helps here) and then look for existent objects
 (induction) to learn whether the purported relations between characters
 obtain in fact, and in this way we come to understand the thing which we
 are experiencing. It is of course induction which gives us more
 information; abduction simply gives us the idea which needs to become
 informed, and deduction is merely explicative, based on relating the
 idea
 to other ideas and previously gathered information regarding those
 ideas.

   Obviously, we cannot conduct induction without end, because that is a
 practical impossibility. Our 'sum', as you put it, far from being
 always an
 infinity, will very likely never be an infinity in practice, in whatever
 sense you mean to understand the application of infinity to a 'sum' of
 information. Of course, as an ideal, where science, the community of
 inquiry as such, continues to investigate, it is possible for the
 information of an idea to reach a much greater 'sum' than would
 otherwise
 be possible for individuals such as you or me. But it is a commonplace
 of
 science that ideas that work and continue to work are understood more
 thoroughly in their relations to other ideas over the course on inquiry.
 This means of course that not only the breadth, but also the depth of
 the
 idea continues to grow. As a result,

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Jerry LR Chandler]

List, Catherine: 

On Mar 3, 2015, at 1:41 PM, Catherine Legg wrote:

> The logical tradition that Peirce was responding to with his piece "Logical 
> Extension and Comprehension" was basically a 'term logic', according to which 
> this rough formula held:
> 
> Breadth x Depth = k (where k is some constant)
> 
> 
> QUESTIONS: In what sense, and to what degree might this 'information' be 
> measured? (If not in some absolute sense, then perhaps relatively, between 
> propositions?) Doesn't the very notion of measuring this value conflict with 
> Peirce's contrite fallibilism, which holds that what a given term will come 
> to mean to us is not something that can be decided in advance of scientific 
> inquiry? In other words, scientific terms can hold a great deal of implicit 
> information as well as the explicit information that scientists are working 
> with at a given time.
> 

Once again,  I offer simple answers from the formal view of logic expressed in 
chemistry and the perplex number system:

Information about a chemical can be expressed in terms of the molecular 
formula, one of the fundamental principles of chemistry, historically 
introduced by Lavoisier and Dalton about the turn of the 19 Century, some 60 
years before this text was conceived.

  The molecular formula is the breadth of the material content. It is 
referenced in the table of elements (TOE) and the perplex numerals (aka the 
atomic numbers). It specifies what is present and the RELATIVE ratio of the 
components as a partition of a molecular number as a representation of the 
thing itself. It is an explicit measure of the logical content of the instance 
at hand, as determined by physical analysis. The breadth of information in any 
chemical structure is subject to measurement  The molecular formula of 
individual DNA, RNA and protein molecules are known from physical measurements. 
Are these sufficient example of  breadth of information and its correspondence 
with qualia?

The depth of the information of any member of the TOE or perplex numeral is the 
implicit in it forms of presentations to the senses. The SAME perplex numeral 
can be a member of uncountably many different molecular numbers. The SAME 
chemical symbol can related to several different valence states.  The 
reactivity of each chemical element differs with the context of the immediate 
surroundings.  The changes of attributes of any chemical compound is related to 
basic physical measures.  Many chemical forms same be perceived as solids, 
liquids or gases - exactly the same matter from the physical components but 
radically difference human experiences.  And, by the way, with different 
physical attributes.

The concept of information as 

> Breadth x Depth = k (where k is some constant)

simply means that for a given the same perplex number (as breadth), the same 
depth of sorts or kinds of experiences will be experienced as attributes. If 
the context of the measurements of the depth changes, the depth measurements 
will change. 
In simpler terms, if the experiments are reproducible, consistency is to be 
expected between the the breadth and depth of observation.  Thus, the value of 
each constant is different for each perplex number.  
In even simpler terms, the unity of nature demands consistency.  (This is 
sharply different from the uniformity of nature.)

CSP's use of the notion of multiplication in this context is rather lax, but 
the ground of meaning for the two semantic terms, breadth and depth, seems 
rather simple enough.

Of course, this interpretation of breadth and depth in terms of perplex number 
theory is remote from the meaning of the term (Shannon) "Information" in 
computer sciences (and set theory!). 

With regard to the distinction between term logic and proposition logic, you 
note that the meaning of a term must have a definition, that is, a sentence.  
But, keep in mind the crisp distinction between a philosopher's "predicate" and 
the copulative forces of a copula.

Cheers

jerry





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Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Benjamin Udell]

Cathy, list,

You wrote,

   QUESTIONS: In what sense, and to what degree might this
   'information' be measured? (If not in some absolute sense, then
   perhaps relatively, between propositions?) Doesn't the very notion
   of measuring this value conflict with Peirce's contrite fallibilism,
   which holds that what a given term will come to mean to us is not
   something that can be decided in advance of scientific inquiry? In
   other words, scientific terms can hold a great deal of implicit
   information as well as the explicit information that scientists are
   working with at a given time.
   [End quote]

Presumably the information to be quantified is not that of what a given 
term will come to mean to us, but rather that of what it means to us now 
- the difference between making our ideas true, as Peirce put it, and 
making our ideas clear. What it means to us now is what we now conceive 
to be its practical bearing in general on conduct.


I have to admit I have little to say about how to quantify 
comprehension, denotation, information in Peirce's sense. I did find 
this passage:


Writings 1:342-343, Logic Notebook Dec. 15, 1865
http://pds.lib.harvard.edu/pds/view/15255301?n=28&imagesize=600&jp2Res=0.25&printThumbnails=true

   In the formula

   Extension × Intension = Implication

   we may have the values

   (1) 0 × 0 = 0
   (2) 0 × n = 0
   (3) 0 × ∞ = 0
   (4) 0 × ∞ = n
   (5) 0 × ∞ = ∞
   (6) n × 0 = 0
   (7) n × n = n
   (8) n × ∞ = ∞
   (9) ∞ × 0 = 0
   (10) ∞ × 0 = n
   (11) ∞ × 0 = ∞
   (12) ∞ × n = ∞
   (13) ∞ × ∞ = ∞

   (7) will be the case with any ordinary symbol.

   (4) is the ordinary nothing.

   (10) the ordinary being.

   These are the cases when Implication is n. Now for those where it is 0.

   (6) is the case of a sign, (2) of a copy.

   (1) would be a sign of nothing or a copy of being which are
   undetermined to be representations.

   (9) would be being supposing it were not known to be, or being
   considered abstractly of the fact that it is.

   (3) would be nothing abstracting from the fact that there is
   anything so that its opposition is taken away.

   A being which isn't, would be a nothing which is unopposed to
   anything; hence being abstracted from the fact that it is is
   abstracted from all that makes it differ from nothing abstracted
   from its opposition and vice versa.

   We will now take up the cases where the implication = ∞. (12) is
   being of which some determinate quality is supposed to be known.

   (8) is a contradiction it being implied that it exists.

   (13) is being which is supposed to have all attributes.

   (11) would purport to be a complete list of all beings.

   (5) would purport to be a complete conjunction of all attributes.
   [End quote]

You wrote,

   QUESTION: How does Peirce attempt to draw the distinction, in the
   two cases Frederik catalogues?
   [End quote]

I can't think of anything to say about this either, though the question 
of natural vs. artificial kinds is quite interesting to me. Similar 
question in mathematics: Are primes a natural kind? What about the class 
of functions that share a certain first derivative? The class of pairs 
of integers that sum to a certain integer?


You wrote,

   List: if you tell me what you think then I will tell you what I think.
   [End quote]

I haven't done too well, nobody else has replied, I guess you ask tough 
questions, but anyway at this point I'm interested in hearing what you 
think.


Best, Ben

On 3/3/2015 2:41 PM, Catherine Legg wrote:


Picking up again where I left off...

The logical tradition that Peirce was responding to with his 
piece "Logical Extension and Comprehension" was basically a 'term 
logic', according to which this rough formula held:


Breadth x Depth = k (where k is some constant)

This implies: the larger the extension (breadth), the smaller the 
intension (depth). This formula seems to work for classic terms such 
as "blue", which covers more things but is correspondingly less 
precise than, say, "baby blue". Or "vehicle" which covers more things 
but is less precise than, say "nuclear submarine".


However, Peirce's shift from terms to propositions as a basic analysis 
of meaning allows him to question some of this framework. A 
proposition is now not a simple 'multiplication' of two 'similar 
quantities'. A proposition requires two separate functionalities. The 
part which provides the extension (the subject) functions indexically, 
and the part which provides the intension (the predicate) functions 
iconically.


Stjernfelt points out that, under this framework, "far from being a 
constant, Breadth x Depth gives a measure of the amount of information 
inherent in a proposition" (which can be higher or lower). He notes 
that Peirce still retained this idea 25 years later in Kaina Stoicheia.


*QUESTIONS: In what sense, and to what degree might this 'information' 
be measured? 

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Catherine Legg]

Jerry your chemical example provides an interesting testing ground for a
simple 'breadth x depth' account of meaning. I'm not sure what the
*propositions* would be in this case though, exactly - ?

What is the "crisp distinction between a philosopher's "predicate" and the
copulative forces of a copula" that you're thinking of?

Cheers, Cathy

On Tue, Mar 3, 2015 at 9:38 PM, Jerry LR Chandler 
wrote:

> List, Catherine:
>
> On Mar 3, 2015, at 1:41 PM, Catherine Legg wrote:
>
> The logical tradition that Peirce was responding to with his
> piece "Logical Extension and Comprehension" was basically a 'term logic',
> according to which this rough formula held:
>
> Breadth x Depth = k (where k is some constant)
>
>
> *QUESTIONS: In what sense, and to what degree might this 'information' be
> measured? (If not in some absolute sense, then perhaps relatively, between
> propositions?) Doesn't the very notion of measuring this value conflict
> with Peirce's contrite fallibilism, which holds that what a given term will
> come to mean to us is not something that can be decided in advance of
> scientific inquiry? In other words, scientific terms can hold a great deal
> of implicit information as well as the explicit information that scientists
> are working with at a given time.*
>
>
> Once again,  I offer simple answers from the formal view of logic
> expressed in chemistry and the perplex number system:
>
> Information about a chemical can be expressed in terms of the molecular
> formula, one of the fundamental principles of chemistry, historically
> introduced by Lavoisier and Dalton about the turn of the 19 Century, some
> 60 years before this text was conceived.
>
>   The molecular formula is the breadth of the material content. It is
> referenced in the table of elements (TOE) and the perplex numerals (aka the
> atomic numbers). It specifies what is present and the RELATIVE ratio of the
> components as a partition of a molecular number as a representation of the
> thing itself. It is an explicit measure of the logical content of the
> instance at hand, as determined by physical analysis. The breadth of
> information in any chemical structure is subject to measurement  The
> molecular formula of individual DNA, RNA and protein molecules are known
> from physical measurements. Are these sufficient example of  breadth of
> information and its correspondence with qualia?
>
> The depth of the information of any member of the TOE or perplex numeral
> is the implicit in it forms of presentations to the senses. The SAME
> perplex numeral can be a member of uncountably many different molecular
> numbers. The SAME chemical symbol can related to several different valence
> states.  The reactivity of each chemical element differs with the context
> of the immediate surroundings.  The changes of attributes of any chemical
> compound is related to basic physical measures.  Many chemical forms same
> be perceived as solids, liquids or gases - exactly the same matter from the
> physical components but radically difference human experiences.  And, by
> the way, with different physical attributes.
>
> The concept of information as
>
> Breadth x Depth = k (where k is some constant)
>
>
> simply means that for a given the same perplex number (as breadth), the
> same depth of sorts or kinds of experiences will be experienced as
> attributes. If the context of the measurements of the depth changes, the
> depth measurements will change.
> In simpler terms, if the experiments are reproducible, consistency is to
> be expected between the the breadth and depth of observation.  Thus, the
> value of each constant is different for each perplex number.
> In even simpler terms, the unity of nature demands consistency.  (This is
> sharply different from the uniformity of nature.)
>
> CSP's use of the notion of multiplication in this context is rather lax,
> but the ground of meaning for the two semantic terms, breadth and depth,
> seems rather simple enough.
>
> Of course, this interpretation of breadth and depth in terms of perplex
> number theory is remote from the meaning of the term (Shannon)
> "Information" in computer sciences (and set theory!).
>
> With regard to the distinction between term logic and proposition logic,
> you note that the meaning of a term must have a definition, that is, a
> sentence.  But, keep in mind the crisp distinction between a philosopher's
> "predicate" and the copulative forces of a copula.
>
> Cheers
>
> jerry
>
>
>
>
>

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Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Catherine Legg]

Ben that is a fascinating snippet! Thank you.

I think what the snippet shows is that it's worth bearing in mind that
Peirce's paper on logical comprehension and extension was very early - 1867
- and here he is still working in a 'finitist' tradition in metaphysics and
logic, which he manages to shake himself free of in his later
synechism. Under synechism every real object has an infinite number of
attributes, and every meaningful predicate or general term effectively has
an infinite number of aspects, so a simple multiplication of B x D is
pointless.

And now for what I think is the answer to the question I posed:

*QUESTION: How does Peirce attempt to draw the distinction, in the two
cases Frederik catalogues?*

The examples Peirce gives of a natural and artificial class are*
cows*, and *red
cows* respectively.

I think what he thinks distinguishes the two is that the latter, being
arbitrarily defined, has no further properties than those already
enumerated in the definition. So all we can say about the class of red cows
is that they are cows and they are red.

Whereas the natural class can be inquired into further indefinitely. The
class of cows all share - a certain DNA, certain feeding habits, certain
reproductive strategies, etc. Now I suppose one might argue that the class
of red cows has all those properties too, because the red cows are cows.
But I guess the key point is that there is no EXTRA determination being
given by the redness. Whereas if we said, all *Jersey* cows, the
Jerseyness would have certain further characteristics which can be studied,
and thus this is a natural class.

So with the drawings, I think Peirce is trying to make it that case
that certain of the repeatable drawing features covary with certain other
of the features, and not with others, in ways such that we can capture the
minimal structure necessary for us to be able to group the features
together into 'artificial' and 'natural' classes. So the artificial ones
are those where features A and B go together in a series of cases, but no
other features are shared there. The natural ones are ones where features A
and B go together and in those cases are accompanied by further features C
and D.

All this reminds me of a passage I was writing in a paper but then took out
before publication. It is trying to give a minimal definition of
*scholastic realism*, and arguing that it is not ruled out by fiat as
certain Humean picture in philosophy  suggests. I reproduce it below in
case anyone is interested.

And here ends my postings on Chapter 9!
Cheers, Cathy

Hume’s maxim [i.e. 'there are no necessary connections between distinct
existences', 'the only contraries and existence and non-existence' - CL] ,
and associated Modal Combinatorialism, can be usefully summed up as a
*syntactic
approach to modality*. To argue this, let us frame the issue in maximally
general terms. Consider a world consisting of 4 ‘idea / objects’ (*a*, *b*,
*c* and *d*) – which may combine to make larger states of affairs. Imagine
that these idea / objects are all *distinguishable*. Then according to Hume
they must be *separable*. Let us now imagine a toy universe in which the
only contraries are existence and non-existence. In such a universe
ontologically there may exist - and epistemologically we may imagine - all
possible ‘combinations’ of the objects (just one simple two-way combination
is illustrated for purposes of simplicity, represented by the names of our
objects appearing to the left or right of each other):

*aa  ab  ac  ad  ba  bb  bc  bd  ca  cb  cc  cd  da  db  dc  dd…*

Let us now imagine a toy universe in which Modal Combinatorialism is false.
This  just means that not all combinations are realisable. Here is just one
example:

*aa  ab  ad  ba  bb  bd  ca  cb  cc  cd  da  db  dd…*

This toy universe is missing *ac*, *bc* and *dc*, (for some reason, let us
imagine it is to do with the nature of *c*). An intelligent mind inspecting
the world above might think to summarise the combinations missing from it
in a simple statement – something like, ‘*c* can never come last in
combination, unless with another *c*’. This statement is obviously a
rudimentary law, or universal.
 Our point is now merely that the second scenario is not incoherent. It
is not analytically false to conceive extra-logical constraints on the
happy combination of any conceivable object with any other conceivable
object (bearing in mind that of course these objects will have
*natures*). Mathematics...rules
out such combinations regularly: for example, the combination of 2 × 3 with
3 × *x*, for any *x *other than 2. Hume’s Modal Combinatorialism is
therefore a way of killing off a kind of realism about universals without
being honest about it.

--







On Mon, Mar 9, 2015 at 1:21 AM, Benjamin Udell  wrote:

>  Cathy, list,
>
> You wrote,
>
> QUESTIONS: In what sense, and to what degree might this 'information' be
> measured? (If not in some absol

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Cathy, list,

I was hoping to post sooner, but just got around to it; I'm sorry for the
late contribution.

First of all, I find myself in agreement with Frederik's proposed view of
the Kandinskys, namely that they form a part of Peirce's analysis of
natural classes in the manuscript, and probably should have been included
in the publication of the manuscript.

Second, I noticed that on p.255, when enumerating the definitions of
natural classes given from Ms. 725, Frederik writes for the third
definition: "3) classes without an Area". Compare with p.239, where
Frederik quotes the paragraph from Ms. 725: "In other words *cow* is a term
which has an area; *red cow* has no area, except that area which every term
has, namely that it excites a particular emotion in the mind." The third
definition has to be a typo on Frederik's part; it should read "3) classes
with an Area". Of course, Frederik goes on to argue that this way of
defining natural classes is untenable, because artificial classes must have
area too, on Frederik's view. I would like to discuss this problem of
defining natural classification further below.

But first, Cathy, you said above:

"I think what the snippet shows is that it's worth bearing in mind that
Peirce's paper on logical comprehension and extension was very early - 1867
- and here he is still working in a 'finitist' tradition in metaphysics and
logic, which he manages to shake himself free of in his later
synechism. Under synechism every real object has an infinite number of
attributes, and every meaningful predicate or general term effectively has
an infinite number of aspects, so a simple multiplication of B x D is
pointless."

Are you making a criticism of the position that Frederik defends in Chapter
9, arguing that his interpretation does not adequately take into account
the influence of Peirce's synechism on later accounts of his theory of
information? Consider p.236, where Frederik says: "In the geometrical
metaphor adopted from Hamilton, Peirce consequently names this information
concept 'Area':

Breadth x Depth = Area = Information

This formula is a formalization of the common sense intuition that if a
sign says a lot of things about a lot of objects, it contains much
information, but it does not yield to explicit quantification because of
the issue of quantifying intensions (depth). A quarter of a century later,
in the 'Kaina Stocheia' (1904), Peirce retains this theory: 'Besides the
logical depth and breadth, I have proposed (in 1867) the terms *information*
and *area* to denote the total fact (true or false) that in a given state
of knowledge a sign embodies' (EP II, 305)."

On my view, this means that a multiplication of B x D is anything but
pointless. While it is true that Frederik goes on to say that area cannot
be sufficient for identifying natural classes, this is not the same as
saying that area definitions are "pointless". The definition of a natural
class does not exhaustively identify a thing's attributes, but it does form
the basis of further inquiry, wherein the information identified with the
natural class can increase throughout the course of inquiring into that
natural class; whereas this cannot really be true for an artificial class,
which has its area decided by fiat, or so Frederik would have to aver. So
the difference between a natural class and an artificial class is not that
one has area and the other does not; rather it is that a natural class's
area can change and increase over time, while an artificial class's area
cannot. This means that breadth x depth = area = information is still very
much at play and basic to Peirce's theory of logical quantity; in other
words, the multiplication of B x D is not pointless, but still forms the
basis of analyzing the meaning of a term (or proposition, or argument), as
well as forms the basis of its synthesizing with new findings in continuing
inquiry.

It seems to me that you, Cathy, do recognize that a natural class is one
into which we can continue to inquire and learn more about the class, but I
find your analysis then gets confused in rejecting the idea of information
as the product of breadth and depth; this formula is never really rejected
by Peirce, and I don't find that Frederik rejects it either. It only
becomes more nuanced and part of a more complex analysis over the years, or
so I find.


Now, having accepted it for the sake of argument above, I would actually
like to take issue with Frederik's notion that the class *red cows*, or any
artificial class, has an area. In OLEC, Peirce clearly states the following
(see 6th paragraph, "The Conceptions of Quality, Relation, and
Representation, applied to this Subject", available online at Arisbe;
italics in original):

"1st, The informed *breadth* of the symbol;

2d, The informed *depth* of the symbol;

3d, The sum of synthetical propositions in which the symbol is subject or
predicate, or the *information* concerning the symbol.

By breadth and depth, with

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Catherine Legg]

Hi Franklin,

Sorry for taking so long to reply. Thanks for setting me straight on Peirce
still using the idea of breadth x depth later on in his career. I have to
say though that I don't understand how such a metric might work in the
later semiotic, just because it seems to me that the result of such a 'sum'
will *always* be an infinity of an extremely high order, so any comparisons
seem moot. As Peirce notes, propositions can't be counted. Even an
artifically generated term such as 'red' and 'cow' will still partake of
the surprisingness of 'cow' and 'red' taken on their own.

Best regards,
Cathy

On Mon, Mar 30, 2015 at 10:06 PM, Franklin Ransom <
pragmaticist.lo...@gmail.com> wrote:

> Cathy, list,
>
> I was hoping to post sooner, but just got around to it; I'm sorry for the
> late contribution.
>
> First of all, I find myself in agreement with Frederik's proposed view of
> the Kandinskys, namely that they form a part of Peirce's analysis of
> natural classes in the manuscript, and probably should have been included
> in the publication of the manuscript.
>
> Second, I noticed that on p.255, when enumerating the definitions of
> natural classes given from Ms. 725, Frederik writes for the third
> definition: "3) classes without an Area". Compare with p.239, where
> Frederik quotes the paragraph from Ms. 725: "In other words *cow* is a
> term which has an area; *red cow* has no area, except that area which
> every term has, namely that it excites a particular emotion in the mind."
> The third definition has to be a typo on Frederik's part; it should read
> "3) classes with an Area". Of course, Frederik goes on to argue that this
> way of defining natural classes is untenable, because artificial classes
> must have area too, on Frederik's view. I would like to discuss this
> problem of defining natural classification further below.
>
> But first, Cathy, you said above:
>
> "I think what the snippet shows is that it's worth bearing in mind that
> Peirce's paper on logical comprehension and extension was very early - 1867
> - and here he is still working in a 'finitist' tradition in metaphysics and
> logic, which he manages to shake himself free of in his later
> synechism. Under synechism every real object has an infinite number of
> attributes, and every meaningful predicate or general term effectively has
> an infinite number of aspects, so a simple multiplication of B x D is
> pointless."
>
> Are you making a criticism of the position that Frederik defends in
> Chapter 9, arguing that his interpretation does not adequately take into
> account the influence of Peirce's synechism on later accounts of his theory
> of information? Consider p.236, where Frederik says: "In the geometrical
> metaphor adopted from Hamilton, Peirce consequently names this information
> concept 'Area':
>
> Breadth x Depth = Area = Information
>
> This formula is a formalization of the common sense intuition that if a
> sign says a lot of things about a lot of objects, it contains much
> information, but it does not yield to explicit quantification because of
> the issue of quantifying intensions (depth). A quarter of a century later,
> in the 'Kaina Stocheia' (1904), Peirce retains this theory: 'Besides the
> logical depth and breadth, I have proposed (in 1867) the terms
> *information* and *area* to denote the total fact (true or false) that in
> a given state of knowledge a sign embodies' (EP II, 305)."
>
> On my view, this means that a multiplication of B x D is anything but
> pointless. While it is true that Frederik goes on to say that area cannot
> be sufficient for identifying natural classes, this is not the same as
> saying that area definitions are "pointless". The definition of a natural
> class does not exhaustively identify a thing's attributes, but it does form
> the basis of further inquiry, wherein the information identified with the
> natural class can increase throughout the course of inquiring into that
> natural class; whereas this cannot really be true for an artificial class,
> which has its area decided by fiat, or so Frederik would have to aver. So
> the difference between a natural class and an artificial class is not that
> one has area and the other does not; rather it is that a natural class's
> area can change and increase over time, while an artificial class's area
> cannot. This means that breadth x depth = area = information is still very
> much at play and basic to Peirce's theory of logical quantity; in other
> words, the multiplication of B x D is not pointless, but still forms the
> basis of analyzing the meaning of a term (or proposition, or argument), as
> well as forms the basis of its synthesizing with new findings in continuing
> inquiry.
>
> It seems to me that you, Cathy, do recognize that a natural class is one
> into which we can continue to inquire and learn more about the class, but I
> find your analysis then gets confused in rejecting the idea of information
> as the product of bre

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Cathy, lists,

Well, look at this way: It is possible for there to be objects in the
senses which are yet not perceived, because we do not yet have any idea of
what it is to which we are looking. It takes a hypothesis to introduce a
new idea to us to explain what it is, which hypothesis we can then put to
the test. In order to do so, we must determine what kinds of characters to
look for (deduction helps here) and then look for existent objects
(induction) to learn whether the purported relations between characters
obtain in fact, and in this way we come to understand the thing which we
are experiencing. It is of course induction which gives us more
information; abduction simply gives us the idea which needs to become
informed, and deduction is merely explicative, based on relating the idea
to other ideas and previously gathered information regarding those ideas.

Obviously, we cannot conduct induction without end, because that is a
practical impossibility. Our 'sum', as you put it, far from being always an
infinity, will very likely never be an infinity in practice, in whatever
sense you mean to understand the application of infinity to a 'sum' of
information. Of course, as an ideal, where science, the community of
inquiry as such, continues to investigate, it is possible for the
information of an idea to reach a much greater 'sum' than would otherwise
be possible for individuals such as you or me. But it is a commonplace of
science that ideas that work and continue to work are understood more
thoroughly in their relations to other ideas over the course on inquiry.
This means of course that not only the breadth, but also the depth of the
idea continues to grow. As a result, typically, rather than tending to make
comparisons moot, we start to see a hierarchy of ideas and related sciences
appear.

Consider this passage: "The former [Cows] is a natural class, the latter
[Red Cows] is not. Now one predicate more may be attached to Red Cows than
to Cows; hence Mr. Mill's attempts to analyze the difference between
natural and artificial classes is seen to be a failure. For, according to
him, the difference is that a real kind is distinguished by unknown
multitudes of properties while an artificial class has only a few
determinate ones. Again there is an unusual degree of accordance among
naturalists in making Vertebrates a natural class. Yet the number of
predicates proper to it is comparatively small" (NP, p.238, quoting
Peirce). We can see here that further simplifications are introduced, so
taking what is learned about various vertebrates, a new idea, that of
vertebrates, appears which simplifies the characters involved. Conversely,
species under vertebrates will become much more determinate in terms of
their characters, but be simplified with respect to their extension.

You said above: "Under synechism every real object has an infinite number
of attributes, and every meaningful predicate or general term effectively
has an infinite number of aspects, so a simple multiplication of B x D is
pointless." And yet natural kinds appear, in which certain attributes,
predicates, or aspects appear significant, and others do not. It is
precisely the work of abduction to simplify what is observed so that what
is essential is grasped, and not simply a never-ending multitude of
characters. Such simplification is always with respect to a purpose. With
respect to natural kinds, such purpose, or telos, is objective, and we see
nature all around us selecting certain characters over others as more
significant. If this were not true, natural science would be impossible. As
to real objects, yes they have an infinite number, but not all of them are
relevant to the purpose of interaction with the real object. Certain
meaningful attributes are selected for in attention in order to aid conduct
with respect to some purpose at hand. Information relevant to that purpose
is what is sought for.

I do have a couple of questions for you:

For one, would you explain the idea that propositions can't be counted? I
would suppose that when conducting an experiment, the number of times a
fact is determined relates to developing a frequency ratio, which means
that propositions can be counted in this case, when they are instances of
the same kind or type, or close enough. But if we are talking about
propositions which are all different from each other, than I can see the
point, because that is like trying to count qualities, which isn't very
helpful for comparison. But of course, that's not the same thing as having
so many propositions that they go to infinity and thus can't be counted for
that reason. Is this what is meant, that there are supposed to be so many
propositions that they go to infinity? Perhaps it would be helpful if you
referenced the text where Peirce mentions this.

For two, you said "Even an artifically generated term such as 'red' and
'cow' will still partake of the surprisingness of 'cow' and 'red' taken on
their own." What do

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Benjamin Udell]

Franklin, Jon, lists,

Yep, that was me with Peirce's ∞'s and 0's of breadth and depth, March 
8, 2015, at the link:

https://www.mail-archive.com/peirce-l@list.iupui.edu/msg03282.html

- Best, Ben

On 4/20/2015 7:42 PM, Jon Awbrey wrote:


Franklin, List,

I think that was Ben Udell.

Regards,

Jon

http://inquiryintoinquiry.com

On Apr 20, 2015, at 7:30 PM, Franklin Ransom wrote:


Cathy, Frederik, lists,

Yes, Frederik, that makes sense to me. As I mentioned in my previous 
post, counting qualities or characters doesn't seem to be helpful. 
Although it should be possible to enumerate them, to a point, for the 
purpose of some inquiry.


As I recall, Jon Awbrey in the last month or two referenced a text 
from Peirce about the multiplication of breadth and depth using 
symbols like 1, 0, and the infinity loop, to distinguish cases such 
as essential depth and breadth, substantial depth and breadth, the 
idea of nothing, the idea of being, etc. If infinity was indeed used 
then, Peirce had certainly contemplated infinite depth and infinite 
breadth, although perhaps not simply in the sense of counting with no 
end, but in the direct sense of being that which is without limit, so 
depth without limit or breadth without limit.


-- Franklin

On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt wrote:


-
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L 
to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To 
UNSUBSCRIBE, send a message not to PEIRCE-L 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 .

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

And thanks to you too, Ben!

On Mon, Apr 20, 2015 at 8:31 PM, Benjamin Udell  wrote:

>  Franklin, Jon, lists,
>
> Yep, that was me with Peirce's ∞'s and 0's of breadth and depth, March 8,
> 2015, at the link:
> https://www.mail-archive.com/peirce-l@list.iupui.edu/msg03282.html
>
> - Best, Ben
>
> On 4/20/2015 7:42 PM, Jon Awbrey wrote:
>
> Franklin, List,
>
>  I think that was Ben Udell.
>
> Regards,
>
> Jon
>
> http://inquiryintoinquiry.com
>
> On Apr 20, 2015, at 7:30 PM, Franklin Ransom wrote:
>
> Cathy, Frederik, lists,
>
> Yes, Frederik, that makes sense to me. As I mentioned in my previous post,
> counting qualities or characters doesn't seem to be helpful. Although it
> should be possible to enumerate them, to a point, for the purpose of some
> inquiry.
>
> As I recall, Jon Awbrey in the last month or two referenced a text from
> Peirce about the multiplication of breadth and depth using symbols like 1,
> 0, and the infinity loop, to distinguish cases such as essential depth and
> breadth, substantial depth and breadth, the idea of nothing, the idea of
> being, etc. If infinity was indeed used then, Peirce had certainly
> contemplated infinite depth and infinite breadth, although perhaps not
> simply in the sense of counting with no end, but in the direct sense of
> being that which is without limit, so depth without limit or breadth
> without limit.
>
> -- Franklin
>
> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt wrote:
>
>
>
> -
> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
> PEIRCE-L to this message. PEIRCE-L posts should go to
> peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L
> 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
> .
>
>
>
>
>
>

-
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L 
to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To 
UNSUBSCRIBE, send a message not to PEIRCE-L 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 .

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Benjamin Udell]

Franklin, Jon, Cathy, Frederik, lists,

You're welcome, Franklin.

Generally, before we get too stuck on the issue of infinite or zero 
breadth or depth, let's remember what Peirce is doing, actually using 
those extremes to show the implications of the ideas. How many people do 
that? Another way in which we don't have to get bogged down in exact 
finite-numerical determination of breadth and depth is to consider 
simply increases and decreases of breadth and depth and what, among 
logical acts, those changes in parts or total amount of information 
correspond to. An example of what Peirce _/does/_ with breadth and depth 
is in a paragraph in "Upon Logical Comprehension and Extension" (1867) 
http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm 
 . I have 
broken the paragraph up to help the pattern become even clearer. 
(Remember that Breadth a.k.a. Extension times Depth a.k.a. Comprehension 
equals Area a.k.a. Information.)


   It is only by confusing a movement which is accompanied with a
   change of information with one which is not so, that people can
   confound generalization, induction, and abstraction.
   /Generalization/ is an increase of breadth and a decrease of depth,
   without change of information. /Induction/ is a certain increase of
   breadth without a change of depth, by an increase of believed
   information.
   [Well, that's a neat distinction; it clarifies why Peirce speaks of
   verisimilar induction rather than inductive generalization, and
   implies that induction is not attenuative but instead has its
   premisses entailed by its conclusions, despite how Peirce's forms
   for induction look. - BU]
   /Abstraction/ is a decrease of depth without any change of breadth,
   by a decrease of conceived information.
   /Specification/ is commonly used (I should say unfortunately) for an
   increase of depth without any change of breadth, by an increase of
   asserted information.
   /Supposition/ is used for the same process when there is only a
   conceived increase of information.
   /Determination,/ for any increase of depth.
   /Restriction,/ for any decrease of breadth; but more particularly
   without change of depth, by a supposed decrease of information.
   /Descent,/ for a decrease of breadth and increase of depth, without
   change of information.
   [End quote]

When I first saw that years ago, I promptly made it into a table with 
fields, and was only a little disappointed to find that Peirce had not 
classified all possible combinations of increase / decrease of 
comprehension and of extension. He was using the ideas of comprehension 
and extension to classify logical acts already named in logical 
tradition, and I thought, I'll figure out what logic acts correspond to 
the remaining combinations, but I didn't soon figure it out and I 
drifted to other subjects. My point is that Peirce was remarkably 
productive at a philosophical-logic level with the ideas of breadth and 
depth. Okay, I don't know that nobody before him had attempted that sort 
of thing. But it's like walking into a room full of candy bars.


I'm not sure whether he stuck with that definition of determination.

Best, Ben

On 4/20/2015 8:38 PM, Franklin Ransom wrote:


And thanks to you too, Ben!

On Mon, Apr 20, 2015 at 8:31 PM, Benjamin Udell  > wrote:


Franklin, Jon, lists,

Yep, that was me with Peirce's ∞'s and 0's of breadth and depth,
March 8, 2015, at the link:
https://www.mail-archive.com/peirce-l@list.iupui.edu/msg03282.html

- Best, Ben

On 4/20/2015 7:42 PM, Jon Awbrey wrote:


Franklin, List,

I think that was Ben Udell.

Regards,

Jon

http://inquiryintoinquiry.com

On Apr 20, 2015, at 7:30 PM, Franklin Ransom wrote:


Cathy, Frederik, lists,

Yes, Frederik, that makes sense to me. As I mentioned in my
previous post, counting qualities or characters doesn't seem to
be helpful. Although it should be possible to enumerate them, to
a point, for the purpose of some inquiry.

As I recall, Jon Awbrey in the last month or two referenced a
text from Peirce about the multiplication of breadth and depth
using symbols like 1, 0, and the infinity loop, to distinguish
cases such as essential depth and breadth, substantial depth and
breadth, the idea of nothing, the idea of being, etc. If
infinity was indeed used then, Peirce had certainly contemplated
infinite depth and infinite breadth, although perhaps not simply
in the sense of counting with no end, but in the direct sense of
being that which is without limit, so depth without limit or
breadth without limit.

-- Franklin

On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt wrote:


-
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L 
to this message. PEIRCE-L posts should go to pe

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Ben, lists,

With respect to what you just noted about what he does with the breadth,
depth, and information work, I would like to point out that what you note
has to do with the work of inference upon a given state of information.
What I was referring to has to do with defining different states of
information as such. In fact, Peirce does some of that in the OLEC as
well--such as his logical treatment of the concepts of being and nothing,
substantial depth and breadth, etc.

"When I first saw that years ago, I promptly made it into a table with
fields, and was only a little disappointed to find that Peirce had not
classified all possible combinations of increase / decrease of
comprehension and of extension. He was using the ideas of comprehension and
extension to classify logical acts already named in logical tradition, and
I thought, I'll figure out what logic acts correspond to the remaining
combinations, but I didn't soon figure it out and I drifted to other
subjects. My point is that Peirce was remarkably productive at a
philosophical-logic level with the ideas of breadth and depth. Okay, I
don't know that nobody before him had attempted that sort of thing. But
it's like walking into a room full of candy bars."

Haha, yes, I agree with the sentiment that it's like walking into a room
full of candy bars (well, if I liked candy bars, anyway). That's why I find
it so frustrating to not see an updated account in the context of his
mature semiotic theory, a continuation of that remarkable productivity,
especially considering how productive he was otherwise in his mature
semiotic work. "Kaina Stocheia" does that a bit, but I would have hoped for
something more detailed and robust.

"I'm not sure whether he stuck with that definition of determination."

I had also been wondering that about the definition of determination.

-- Franklin


On Mon, Apr 20, 2015 at 9:15 PM, Benjamin Udell  wrote:

>  Franklin, Jon, Cathy, Frederik, lists,
>
> You're welcome, Franklin.
>
> Generally, before we get too stuck on the issue of infinite or zero
> breadth or depth, let's remember what Peirce is doing, actually using those
> extremes to show the implications of the ideas. How many people do that?
> Another way in which we don't have to get bogged down in exact
> finite-numerical determination of breadth and depth is to consider simply
> increases and decreases of breadth and depth and what, among logical acts,
> those changes in parts or total amount of information correspond to. An
> example of what Peirce _*does*_ with breadth and depth is in a paragraph
> in "Upon Logical Comprehension and Extension" (1867)
> http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm . I have
> broken the paragraph up to help the pattern become even clearer. (Remember
> that Breadth a.k.a. Extension times Depth a.k.a. Comprehension equals Area
> a.k.a. Information.)
>
> It is only by confusing a movement which is accompanied with a change of
> information with one which is not so, that people can confound
> generalization, induction, and abstraction.
> *Generalization* is an increase of breadth and a decrease of depth,
> without change of information. *Induction* is a certain increase of
> breadth without a change of depth, by an increase of believed information.
> [Well, that's a neat distinction; it clarifies why Peirce speaks of
> verisimilar induction rather than inductive generalization, and implies
> that induction is not attenuative but instead has its premisses entailed by
> its conclusions, despite how Peirce's forms for induction look. - BU]
> *Abstraction* is a decrease of depth without any change of breadth, by a
> decrease of conceived information.
> *Specification* is commonly used (I should say unfortunately) for an
> increase of depth without any change of breadth, by an increase of asserted
> information.
> *Supposition* is used for the same process when there is only a conceived
> increase of information.
> *Determination,* for any increase of depth.
> *Restriction,* for any decrease of breadth; but more particularly without
> change of depth, by a supposed decrease of information.
> *Descent,* for a decrease of breadth and increase of depth, without
> change of information.
> [End quote]
>
> When I first saw that years ago, I promptly made it into a table with
> fields, and was only a little disappointed to find that Peirce had not
> classified all possible combinations of increase / decrease of
> comprehension and of extension. He was using the ideas of comprehension and
> extension to classify logical acts already named in logical tradition, and
> I thought, I'll figure out what logic acts correspond to the remaining
> combinations, but I didn't soon figure it out and I drifted to other
> subjects. My point is that Peirce was remarkably productive at a
> philosophical-logic level with the ideas of breadth and depth. Okay, I
> don't know that nobody before him had attempted that sort of thing. But
> it's like walk

RE: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Jeffrey Brian Downard]

Frank, Lists,

You say:  "That's why I find it so frustrating to not see an updated account in 
the context of his mature semiotic theory..."

From the discussion of modal dyadic relations:

CP 3.608  Dyadic relations between symbols, or concepts, are matters of logic, 
so far as they are not derived from relations between the objects and the 
characters to which the symbols refer. Noting that we are limiting ourselves to 
modal dyadic relations, it may probably be said that those of them that are 
truly and fundamentally dyadic arise from corresponding relations between 
propositions. To exemplify what is meant, the dyadic relations of logical 
breadth and depth, often called denotation and connotation, have played a great 
part in logical discussions, but these take their origin in the triadic 
relation between a sign, its object, and its interpretant sign; and 
furthermore, the distinction appears as a dichotomy owing to the limitation of 
the field of thought, which forgets that concepts grow, and that there is thus 
a third respect in which they may differ, depending on the state of knowledge, 
or amount of information. To give a good and complete account of the dyadic 
relations of concepts would be impossible without taking into account the 
triadic relations which, for the most part, underlie them; and indeed almost a 
complete treatise upon the first of the three divisions of logic would be 
required.

So, I would think that "Nomenclature and Division of Triadic Relations" should 
be read in light of these remarks.

--Jeff

Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354

From: Franklin Ransom [pragmaticist.lo...@gmail.com]
Sent: Monday, April 20, 2015 7:17 PM
To: peirce-l@list.iupui.edu 1; 
Subject: Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

Ben, lists,

With respect to what you just noted about what he does with the breadth, depth, 
and information work, I would like to point out that what you note has to do 
with the work of inference upon a given state of information. What I was 
referring to has to do with defining different states of information as such. 
In fact, Peirce does some of that in the OLEC as well--such as his logical 
treatment of the concepts of being and nothing, substantial depth and breadth, 
etc.

"When I first saw that years ago, I promptly made it into a table with fields, 
and was only a little disappointed to find that Peirce had not classified all 
possible combinations of increase / decrease of comprehension and of extension. 
He was using the ideas of comprehension and extension to classify logical acts 
already named in logical tradition, and I thought, I'll figure out what logic 
acts correspond to the remaining combinations, but I didn't soon figure it out 
and I drifted to other subjects. My point is that Peirce was remarkably 
productive at a philosophical-logic level with the ideas of breadth and depth. 
Okay, I don't know that nobody before him had attempted that sort of thing. But 
it's like walking into a room full of candy bars."

Haha, yes, I agree with the sentiment that it's like walking into a room full 
of candy bars (well, if I liked candy bars, anyway). That's why I find it so 
frustrating to not see an updated account in the context of his mature semiotic 
theory, a continuation of that remarkable productivity, especially considering 
how productive he was otherwise in his mature semiotic work. "Kaina Stocheia" 
does that a bit, but I would have hoped for something more detailed and robust.

"I'm not sure whether he stuck with that definition of determination."

I had also been wondering that about the definition of determination.

-- Franklin


On Mon, Apr 20, 2015 at 9:15 PM, Benjamin Udell 
mailto:bud...@nyc.rr.com>> wrote:

Franklin, Jon, Cathy, Frederik, lists,

You're welcome, Franklin.

Generally, before we get too stuck on the issue of infinite or zero breadth or 
depth, let's remember what Peirce is doing, actually using those extremes to 
show the implications of the ideas. How many people do that? Another way in 
which we don't have to get bogged down in exact finite-numerical determination 
of breadth and depth is to consider simply increases and decreases of breadth 
and depth and what, among logical acts, those changes in parts or total amount 
of information correspond to. An example of what Peirce _does_ with breadth and 
depth is in a paragraph in "Upon Logical Comprehension and Extension" (1867) 
http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm<http://www.iupui.edu/%7Epeirce/writings/v2/w2/w2_06/v2_06.htm>
 . I have broken the paragraph up to help the pattern become even clearer. 
(Remember that Breadth a.k.a. Extension times Depth a.k.a. Comprehension equals 
Area a.k.a. Information.)

It is only by confusing a movement which 

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Catherine Legg]

Hi Franklin,

Thanks for your reply. I was not objecting to *comparisons* being made
between the breadth and depth of various scientific terms, of the richness
you so ably describe. My objection was to applying a *metric* to that,
which effectively puts it on a linear scale of more or less
information. For that, it seems one must require some way of
quantifying the information in a proposition, say, between zero (no
information) and 1 (total information). And I can't see how that could be
done.

The claim that propositions themselves can't be counted I took from Peirce.
I just had a look through the CP but couldn't locate it, but I did find the
quotes below which are related.

You also asked: "Even an artifically generated term such as 'red' and 'cow'
will still partake of the surprisingness of 'cow' and 'red' taken on their
own." What does surprisingness have to do with what we're discussing?

Just the fact of continued inquiry that you were talking about, which runs
on abduction, which runs on surprise.

Cheers, Cathy

2.706: If I am permitted the extended sense which I have given to the word

"induction," this argument is simply an induction respecting qualities
instead of

respecting things. In point of fact *P*', *P*'', *P*''', etc., constitute a
random sample of the

characters of *M*, and the ratio *r *of them being found to belong to *S*,
the same ratio of

all the characters of *M *are concluded to belong to *S*. This kind of
argument, however,

as it actually occurs, differs very much from induction, owing to the
impossibility of

simply counting qualities as individual things are counted. Characters have
to be

weighed rather than counted. Thus, antimony is bluish-gray: that is a
character.

Bismuth is a sort of rose-gray; it is decidedly different from antimony in
color, and

yet not so very different as gold, silver, copper, and tin are.


also in 5.169 he says:

"mere possibilities are not capable of being counted"

On Mon, Apr 20, 2015 at 12:14 AM, Franklin Ransom <
pragmaticist.lo...@gmail.com> wrote:

> Cathy, lists,
>
> Well, look at this way: It is possible for there to be objects in the
> senses which are yet not perceived, because we do not yet have any idea of
> what it is to which we are looking. It takes a hypothesis to introduce a
> new idea to us to explain what it is, which hypothesis we can then put to
> the test. In order to do so, we must determine what kinds of characters to
> look for (deduction helps here) and then look for existent objects
> (induction) to learn whether the purported relations between characters
> obtain in fact, and in this way we come to understand the thing which we
> are experiencing. It is of course induction which gives us more
> information; abduction simply gives us the idea which needs to become
> informed, and deduction is merely explicative, based on relating the idea
> to other ideas and previously gathered information regarding those ideas.
>
> Obviously, we cannot conduct induction without end, because that is a
> practical impossibility. Our 'sum', as you put it, far from being always an
> infinity, will very likely never be an infinity in practice, in whatever
> sense you mean to understand the application of infinity to a 'sum' of
> information. Of course, as an ideal, where science, the community of
> inquiry as such, continues to investigate, it is possible for the
> information of an idea to reach a much greater 'sum' than would otherwise
> be possible for individuals such as you or me. But it is a commonplace of
> science that ideas that work and continue to work are understood more
> thoroughly in their relations to other ideas over the course on inquiry.
> This means of course that not only the breadth, but also the depth of the
> idea continues to grow. As a result, typically, rather than tending to make
> comparisons moot, we start to see a hierarchy of ideas and related sciences
> appear.
>
> Consider this passage: "The former [Cows] is a natural class, the latter
> [Red Cows] is not. Now one predicate more may be attached to Red Cows than
> to Cows; hence Mr. Mill's attempts to analyze the difference between
> natural and artificial classes is seen to be a failure. For, according to
> him, the difference is that a real kind is distinguished by unknown
> multitudes of properties while an artificial class has only a few
> determinate ones. Again there is an unusual degree of accordance among
> naturalists in making Vertebrates a natural class. Yet the number of
> predicates proper to it is comparatively small" (NP, p.238, quoting
> Peirce). We can see here that further simplifications are introduced, so
> taking what is learned about various vertebrates, a new idea, that of
> vertebrates, appears which simplifies the characters involved. Conversely,
> species under vertebrates will become much more determinate in terms of
> their characters, but be simplified with respect to their extension.
>
> You said above: "Under synechism eve

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Jeff, lists,

I certainly agree that speculative grammar is important for understanding
information in his mature semiotic theory, and that of course the analysis
of triadic relations must play a big role in that. I am merely lamenting
that, despite the rich analyses of triadic relations that Peirce develops
in his mature theory, he makes no detailed account of the consequences for
information theory based upon those analyses. For instance, and in
particular, how we can update the part of OLEC that Ben quoted, regarding
the classification of inferences as changes in logical quantity--depth,
breadth, and area or information.

-- Franklin

On Tue, Apr 21, 2015 at 4:23 AM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Frank, Lists,
>
> You say:  "That's why I find it so frustrating to not see an updated
> account in the context of his mature semiotic theory..."
>
> From the discussion of modal dyadic relations:
>
> CP 3.608  Dyadic relations between symbols, or concepts, are matters of
> logic, so far as they are not derived from relations between the objects
> and the characters to which the symbols refer. Noting that we are limiting
> ourselves to modal dyadic relations, it may probably be said that those of
> them that are truly and fundamentally dyadic arise from corresponding
> relations between propositions. To exemplify what is meant, the dyadic
> relations of logical breadth and depth, often called denotation and
> connotation, have played a great part in logical discussions, but these
> take their origin in the triadic relation between a sign, its object, and
> its interpretant sign; and furthermore, the distinction appears as a
> dichotomy owing to the limitation of the field of thought, which forgets
> that concepts grow, and that there is thus a third respect in which they
> may differ, depending on the state of knowledge, or amount of information.
> To give a good and complete account of the dyadic relations of concepts
> would be impossible without taking into account the triadic relations
> which, for the most part, underlie them; and indeed almost a complete
> treatise upon the first of the three divisions of logic would be required.
>
> So, I would think that "Nomenclature and Division of Triadic Relations"
> should be read in light of these remarks.
>
> --Jeff
>
> Jeff Downard
> Associate Professor
> Department of Philosophy
> NAU
> (o) 523-8354
> 
> From: Franklin Ransom [pragmaticist.lo...@gmail.com]
> Sent: Monday, April 20, 2015 7:17 PM
> To: peirce-l@list.iupui.edu 1; 
> Subject: Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9
>
> Ben, lists,
>
> With respect to what you just noted about what he does with the breadth,
> depth, and information work, I would like to point out that what you note
> has to do with the work of inference upon a given state of information.
> What I was referring to has to do with defining different states of
> information as such. In fact, Peirce does some of that in the OLEC as
> well--such as his logical treatment of the concepts of being and nothing,
> substantial depth and breadth, etc.
>
> "When I first saw that years ago, I promptly made it into a table with
> fields, and was only a little disappointed to find that Peirce had not
> classified all possible combinations of increase / decrease of
> comprehension and of extension. He was using the ideas of comprehension and
> extension to classify logical acts already named in logical tradition, and
> I thought, I'll figure out what logic acts correspond to the remaining
> combinations, but I didn't soon figure it out and I drifted to other
> subjects. My point is that Peirce was remarkably productive at a
> philosophical-logic level with the ideas of breadth and depth. Okay, I
> don't know that nobody before him had attempted that sort of thing. But
> it's like walking into a room full of candy bars."
>
> Haha, yes, I agree with the sentiment that it's like walking into a room
> full of candy bars (well, if I liked candy bars, anyway). That's why I find
> it so frustrating to not see an updated account in the context of his
> mature semiotic theory, a continuation of that remarkable productivity,
> especially considering how productive he was otherwise in his mature
> semiotic work. "Kaina Stocheia" does that a bit, but I would have hoped for
> something more detailed and robust.
>
> "I'm not sure whether he stuck with that definition of determination."
>
> I had also been wondering that about the definition of determination.
>
> -- Franklin
>
>
> On Mon, Apr 20, 2015 at 9:15 PM, Benjamin Udell  bud...@nyc.rr.com>> wrote:
&g

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Cathy, Jeff, lists,

Jeff has taken an interesting approach to trying to meet the issue, but I
will try my own take here.

Cathy, I note that you specify quantifying the information in a
proposition, although this is not the point of the OLEC--that paper has to
do with the information of a symbol, which is something quite different.
Yes, Peirce says that we can also apply information to propositions and to
arguments. But information will not apply to propositions and arguments in
the same way that it does to symbols. (Moreover, I'm not sure it's right to
think of the information as being "in" a symbol, proposition, or argument.)

In the case of the symbol, the information has to do with the sum of
propositions in which it appears as either subject or predicate. It's true
that quantifying every exact instance can be tedious. But in a scientific
inquiry, in which one is conducting experiments and publishing a report of
the results, one should hope that this quantifying is exactly what is being
accomplished and communicated to future inquiry.

As for your objection to applying a metric that brings in a linear scale
from less to more information: Peirce is attempting to do away with the
thinking that the logical quantities are always inversely proportioned, and
proposes instead that a symbol can grow in overall determination. If this
were not possible, we can not talk about learning and the development of
symbols in inquiry. When we treat of the growth of the symbol, this growth
can be viewed both in terms of the objects to which it applies and in terms
of the qualities or characters that apply to it. One or the other
increases. We don't have some outside point of view to decide how close we
are to a perfect state of information, or what Peirce refers to as the
substantial depth and breadth of a symbol. But we can still count the
objects, and we can still enumerate and weigh the characters, and the
amount of objects might increase, and the characters which are deemed
applicable might increase too. I confess I do not see why you find this
objectionable just because we can't quantify in a way that tells just how
close we are to total information.

I notice that your quotes show that counting logical depth doesn't work
out, because qualities or characters (or possibilities, which are what
qualities as Firsts are from the modal point of view) can't be counted. I
myself said this in previous posting on this thread. But Peirce supposes
that they can be weighed instead, which means there is some kind of
measuring of depth as a quantity.

-- Franklin




On Wed, Apr 22, 2015 at 8:01 AM, Catherine Legg  wrote:

> Hi Franklin,
>
> Thanks for your reply. I was not objecting to *comparisons* being made
> between the breadth and depth of various scientific terms, of the richness
> you so ably describe. My objection was to applying a *metric* to that,
> which effectively puts it on a linear scale of more or less
> information. For that, it seems one must require some way of
> quantifying the information in a proposition, say, between zero (no
> information) and 1 (total information). And I can't see how that could be
> done.
>
> The claim that propositions themselves can't be counted I took
> from Peirce. I just had a look through the CP but couldn't locate it, but I
> did find the quotes below which are related.
>
> You also asked: "Even an artifically generated term such as 'red' and
> 'cow' will still partake of the surprisingness of 'cow' and 'red' taken on
> their own." What does surprisingness have to do with what we're discussing?
>
> Just the fact of continued inquiry that you were talking about, which runs
> on abduction, which runs on surprise.
>
> Cheers, Cathy
>
> 2.706: If I am permitted the extended sense which I have given to the word
>
> "induction," this argument is simply an induction respecting qualities
> instead of
>
> respecting things. In point of fact *P*', *P*'', *P*''', etc., constitute
> a random sample of the
>
> characters of *M*, and the ratio *r *of them being found to belong to *S*,
> the same ratio of
>
> all the characters of *M *are concluded to belong to *S*. This kind of
> argument, however,
>
> as it actually occurs, differs very much from induction, owing to the
> impossibility of
>
> simply counting qualities as individual things are counted. Characters
> have to be
>
> weighed rather than counted. Thus, antimony is bluish-gray: that is a
> character.
>
> Bismuth is a sort of rose-gray; it is decidedly different from antimony in
> color, and
>
> yet not so very different as gold, silver, copper, and tin are.
>
>
> also in 5.169 he says:
>
> "mere possibilities are not capable of being counted"
>
>
>

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