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 [[email protected]] Sent: Monday, April 20, 2015 7:17 PM To: [email protected] 1; <[email protected]> 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 <[email protected]<mailto:[email protected]>> 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 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 <[email protected]<mailto:[email protected]> > 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/[email protected]/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 [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
