[peirce-l] Re: NEW ELEMENTS: So what is it all about? (CORRECTION)
Jim, and all,
I've been very much enjoying reading this thread and, indeed, all the
activity of late on the list has been of interest to me. Alas, I
continue to be up to my neck in work so I can't actively participate in
any of the threads at the moment (a condition which no doubt some here
might hope would continue indefinitely :-). But I thought I'd at least
post these companion pieces to the New Elements quotation you posted.
This one simple reinforces those ideas.
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.
Here is a version of the Breadth X Depth = Information analysis:
CP 2.418
What are thus referred to, so far as they are known, are:
First, The informed breadth of the symbol;
Second, The informed depth of the symbol;
Third, The sum of synthetical propositions in which the symbol is
subject or predicate, or the information concerning the symbol.†P1
CP 2.419
By breadth and depth, without an adjective, I shall hereafter mean the
informed breadth and depth.
CP 2.419
It is plain that the breadth and depth of a symbol, so far as they
are not essential, measure the information concerning it, that is, the
synthetical propositions of which it is subject or predicate. This
follows directly from the definitions of breadth, depth, and
information. Hence it follows:
First, That, as long as the information remains constant, the
greater the breadth, the less the depth;
Second, That every increase of information is accompanied by an
increase in depth or breadth, independent of the other quantity;
Third, That, when there is no information, there is either no depth
or no breadth, and conversely.
CP 2.419
These are the true and obvious relations of breadth and depth. They
will be naturally suggested if we term the information the area, and
write--
Breadth X Depth = Area
I was earlier thinking that the formula Breadth X Depth = Information
might parallel what Parmentier called the vector of determination in
semiosis, that "the object determines the sign for the interpretant" in
the order 2/1/3, that is, secondness, then firstness, then thirdness
(this being a logical and not a temporal ordering):
sign
2/1/3 |> interpretant
object
However, since at the moment I cannot find a compelling reason why the
formula Breadth X Depth = Information could not be Depth X Breadth =
Information, and because Peirce comments (in the quote you posted in
response to Ben and which appears below my message) that as concerns
depth, the "reference of the symbol to ground" is "through its
object" (so that perhaps even a quasi-dialectical vector or
order 1/2/3 may be implied), I will tentatively not insist that a
vectorial relation is involved here (but this is very tentative and it
would seem to me possible that indeed the breadth may need to precede
the depth). So:
depth ('reference of the symbol to ground, through its object, that
is, its reference to the common characters of its objects, or its
connotations")
2/1/3 and/or? 1/2/3 |> information ("reference to all the
synthetical propositions in which its objects in common are subject or
predicate")
breadth ("direct reference of the symbol to its objects, or denotation")
Enough for now. Thanks to you and all for stimulating and challenging
posts.
Gary
Jim Piat wrote:
Dear Ben, Joe, Folks--
Ben, I can't always follow your mercurial explorations, elaborations,
counter arguments and interesting asides so I'm just going to quote
Peirce from the penultimate paragraph of the New List (which you may
have already quoted yourself in which case I beg your apology while I
wipe the egg off my face).
BEGIN QUOTE:
The other divisions of terms, propositions, and arguments arise from
the distinction of extension and comprehension. I propose to treat
this subject in a su
[peirce-l] Re: NEW ELEMENTS: So what is it all about? (CORRECTION)
Dear Ben, Joe, Folks-- Ben, I can't always follow your mercurial explorations, elaborations, counter arguments and interesting asides so I'm just going to quote Peirce from the penultimate paragraph of the New List (which you may have already quoted yourself in which case I beg your apology while I wipe the egg off my face). BEGIN QUOTE: The other divisions of terms, propositions, and arguments arise from the distinction of extension and comprehension. I propose to treat this subject in a subsequesnt paper. But I will so far anticipate that, as to say that there is, first, the direct reference of the symbol to its objects, or denotation; second the reference of the symbol to ground, through its object, that is, its reference to the common characters of its objects, or its connotations; and third, its reference to its interpretants through its object, that is , its reference to all the synthetical propositions in which its objects in common are subject or predicate, and this I term the information it embodies. And as every addition to what it denotes, or to what it connotes, is effected by means of a dinstinct proposition of this kind, it follows that the extension and comprehension of a term are in an inverse relation, as long as the information remains the same, and that every increase of information is accompanied by in increas of one or other of these two quantities. It may be observed that extension and comprehension are very often taken in other senses in which this last proposition is not true. END QUOTE: Cheers, Jim Piat --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: NEW ELEMENTS: So what is it all about? (CORRECTION)
Joe, list, >[Joe] CORRECTED VERSION OF PREVIOUS POST : >[Joe] Ben quotes Peirce as follows: >>66~ >>A symbol, in its reference to its object, has a triple reference:-- >>1st, Its direct reference to its object, or the real things which it >>represents; >>2d, Its reference to its ground through its object, or the common characters >>of those objects; >>3d, Its reference to its interpretant through its object, or all the facts >>known about its object. >>What are thus referred to, so far as they are known, are:-- >>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. >>~99 >[Joe] And then says: >>[Ben] "Information" may in some sense incorporates that which involves >>representational relations, but I don't think that that's the dimension of >>represenational relations per se. >[Joe] MY RESPONSE: >[Joe] Well, why not, Ben? Think of "information" in terms of an informing of >something, or of becoming informed by something or about something; .think of >it as an impression of form on something that thus becomes informed by it, >i.e.takes on a certain form in virtue of that. (I am reminded of the locution >"It impresses me (or him or her)"-- or perhaps "he or she is impressed by >such-and-such.") The predicate brings form to the subject, in-forms the >subject. Infomation could be regarded as a certain aspect of representation, >i.e. the dimension of representation as regarded in a certain special way. >Predication is a synthesizing of predicate and subject, as information is a >synthesizing of breadth and depth, an informing of breadth with depth. Peirce also says "comprehension x denotation = information." Would anybody think "iconicity x indexicality = symbolicity"? That would just be false. Or "quality x reaction = representation"? That doesn't look true either. Whence this idea that 1stness & 2ndness would be two dimensions of a planar 3rdness? "Comprehension x denotation = information" has the varieties of possible attribution and distribution already built into the left side of the equation, unseen, all we see is a flat "x" like a bare copula. The propositions are not the predicative relations but the information, the result of predication. Somebody devised the concept of the lambda function to stand for the original idea of the function as the relationship rather than as the output. So maybe I'll need to start talking about a "lambda predication." Attributions and distributions of predicates to subjects, affirmative, negative, probable, logically conditioned -- these simply don't represent the same idea, the same interest and focus, as Peirce's idea of "synthetical propositions in which the symbol is subject or predicate, or the _information_ concerning the symbol." Again it's the multiplication symbol in "comprehension x denotation = information" which looks like the predication relation, but it's unchanging, a final neat little copula. Yet in fact the predicative relation -- as the attribution, frequency, distribution, apportionment, etc. of modifications/outcomes/etc. to substantives/objects/etc. (which can also be expressed as probability values of propositions for instance) -- is a deep and various thing. Deductive mathematical theories of logic, information, probability, etc., have it for their core subject matter. That's a lot of research. They aren't about haecceitous concrete world's substantial things (the pre-eminent metaphysical counterpart to the grammatical subject) and they aren't about general phenomena's suchnesses, common modifications (the pre-eminent metaphysical counterpart to the grammatical predicate.) They aren't special sciences or statistical theory or cenoscopic. It is the very structures of the alternatives involved in attributing, distributing, apportioning across a totality, which are of interest. They're about what can be deduced from the given parameters of a universe of discourse, a total population, etc. One abstracts away not only from the haecceitous facts and substantial things of the concrete world but also from the "suchnesses" and common modifications of positive phenomena in general. These attributions, distributions, etc., are such as "indeed," "not," "very probably," "novelly," "if & only if," etc. They get very complicated in ways that often aren't worth the trouble to express through syntactical innovation (which makes people uncomfortable anyway), so we resort early and often to abstractions, often extensionally defined, while any invented syntactic words are forgotten in an old file. Now, as is well known, a deduction adds no information. Yet a good deduction will bring premissed information under a "novel aspect," in Peirce's phrase. Evidently there's some sort of informativeness there in some sense. I've se
[peirce-l] Re: NEW ELEMENTS: So what is it all about? (CORRECTION)
- Original Message - From: "Joseph Ransdell" <[EMAIL PROTECTED]> To: "Peirce Discussion Forum" <[EMAIL PROTECTED]> Sent: Saturday, May 06, 2006 7:16 PM Subject: [peirce-l] Re: NEW ELEMENTS: So what is it all about? (CORRECTION) CORRECTED VERSION OF PREVIOUS POST : Ben quotes Peirce as follows: 66~ A symbol, in its reference to its object, has a triple reference:-- 1st, Its direct reference to its object, or the real things which it represents; 2d, Its reference to its ground through its object, or the common characters of those objects; 3d, Its reference to its interpretant through its object, or all the facts known about its object. What are thus referred to, so far as they are known, are:-- 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. ~99 And then says: "Information" may in some sense incorporates that which involves representational relations, but I don't think that that's the dimension of represenational relations per se. MY RESPONSE: Well, why not, Ben? Think of "information" in terms of an informing of something, or of becoming informed by something or about something; .think of it as an impression of form on something that thus becomes informed by it, i.e.takes on a certain form in virtue of that. (I am reminded of the locution "It impresses me (or him or her)"-- or perhaps "he or she is impressed by such-and-such.") The predicate brings form to the subject, in-forms the subject. Infomation could be regarded as a certain aspect of representation, i.e. the dimension of representation as regarded in a certain special way. Predication is a synthesizing of predicate and subject, as information is a synthesizing of breadth and depth, an informing of breadth with depth. I'll continue with your response later, Ben.. But this seemed worth remarking by itself. (Sorry for the sloppiness of the uncorrected copy originally posted.) Joe Dear Joe, Ben-- I'm talking too much and promise to make this my last comment for the day -- but I want to say that I think representation of meaning is a commonly held implicit definition of information though it may seldom be expressed in those words. I look in the dictionary and find "information: something told or facts learned; news or knowledge". To me all of these definitions imply the meaning of some event has been represented to someone. I think that for Peirce to represent is to inform. And I might add I think Peirce in some ways also anticipated Shannon's measure of information when he analyzed the fixation of belief in terms of removing doubt or reducing uncertainty.I look forward to your further exchanges. Cheers, Jim Piat --- Message from peirce-l forum to subscriber archive@mail-archive.com
[peirce-l] Re: NEW ELEMENTS: So what is it all about? (CORRECTION)
CORRECTED VERSION OF PREVIOUS POST : Ben quotes Peirce as follows: 66~ A symbol, in its reference to its object, has a triple reference:-- 1st, Its direct reference to its object, or the real things which it represents; 2d, Its reference to its ground through its object, or the common characters of those objects; 3d, Its reference to its interpretant through its object, or all the facts known about its object. What are thus referred to, so far as they are known, are:-- 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. ~99 And then says: "Information" may in some sense incorporates that which involves representational relations, but I don't think that that's the dimension of represenational relations per se. MY RESPONSE: Well, why not, Ben? Think of "information" in terms of an informing of something, or of becoming informed by something or about something; .think of it as an impression of form on something that thus becomes informed by it, i.e.takes on a certain form in virtue of that. (I am reminded of the locution "It impresses me (or him or her)"-- or perhaps "he or she is impressed by such-and-such.") The predicate brings form to the subject, in-forms the subject. Infomation could be regarded as a certain aspect of representation, i.e. the dimension of representation as regarded in a certain special way. Predication is a synthesizing of predicate and subject, as information is a synthesizing of breadth and depth, an informing of breadth with depth. I'll continue with your response later, Ben.. But this seemed worth remarking by itself. (Sorry for the sloppiness of the uncorrected copy originally posted.) Joe . -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.385 / Virus Database: 268.5.5/333 - Release Date: 5/5/2006 --- Message from peirce-l forum to subscriber archive@mail-archive.com
