[peirce-l] Re: 1st image of triangle of boxes (MS799.2)

[Benjamin Udell]

Gary, Joe, list,   I downloaded the chapter from Merkle's dissertation last night and it downloaded quite quickly compared to the daytime when the Internet is busier. What graphics! Very little in the way of my shadings, very much in the way of exactness and complexity. If somebody asked me to do a graphic with, for instance, over 700 relational lines in the right places, I'd promise nothing! Amazing stuff. And he brings together and compares quite a variety of arrangements of Peircean sign classes and related conceptions by various scholars. If the logical and mathematical structure across Peirce's signs interests you, hie thee to Merkle's chapter http://www.dainf.cefetpr.br/~merkle/thesis/CH4.pdf . I saved my copy to disk, that way I don't cause him (or his server) bandwidth charges by downloading it from his server any time I want to see it.   Best, Ben Udell   So far I've looked mainly at the graphics. ----- Original Message ----- From: Gary Richmond To: Peirce Discussion Forum Sent: Sunday, June 18, 2006 6:01 PM Subject: [peirce-l] Re: 1st image of triangle of boxes (MS799.2)   Ben, Joe, list, I would highly recommend for those interested in further exploring the themes of this discussion--and, yes, thanks very much to Joe, Ben and others for providing such a wealth of valuable information, diagrams, etc.--the fourth chapter of Luis Merkle's dissertation to which he recently posted a URL: http://www.dainf.cefetpr.br/~merkle/thesis/CH4.pdf especially Sect. 4.4 (p 233 to the end of the section) and most especially his Figure 4.5 The 10 valid arrangements that satisfy the prescision constraint [the discussion discusses the connection between prescision and categoriality] which shows clearly how Peirce arrived at the numbering of the triangular diagram under consideration, Figure 4.7 Ternary tree of the 10 valid arrangements among the 27 explicating Figure 4.6 Peirce's arborescent diagram of the ten categories of triadic signs (which he used at Harvard in 1903 to illustrate and defend his classification of signs into 10 categories), as well as Peirce's triangular diagram, here Figure 4.8 Peirce's diagram depicting the affinities among the ten categories (with a very helpful insert labeled "Horizontal and vertical adjacency," and perhaps most especially Merkle's Figure 4.9 Collapse of the 10 valid arrangements into a triangular diagram. Merkle adds this gloss to this figure: By imagining the tree as enclosed in a parallelepiped, it is possible to collapse the existing planes into a single one. The result is a triangle with ten elements. Peirce used triangular diagrams to describe the affinities between categories. The collapse above enables an understanding of Peirce's diagrams in the light of ternary trees. I spent quite a bit of time with Merkle's thesis a while back when he first posted it (or parts of it) to the list, but was too involved in other projects at the time to get much into--if at all--on the list. Merkle's work seems to me to put a clear light on many of the points under consideration in this thread. However, one caveat: the file is huge and may take some considerable time to download. Although Merkle's primary interest seems to be informatics, Sect. 4.4 concentrates on sign relations in Peirce.   Gary   Benjamin Udell wrote:   Joe, list, It will be interesting to find out what you thought was wrong about what the editors were saying. Again, thank you for your efforts in this! --- Message from peirce-l forum to subscriber archive@mail-archive.com