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; <biosemiot...@lists.ut.ee> > 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<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 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 > >
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