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]> 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 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] > > 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: >> >>
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