Cher JM, Ben and Gary, Thanks for the messages and comments.
I guess I should comment that the work of Prof. Marty, as of many others, was key to the development of forth chapter of my PhD thesis. Jo¨o Queiroz and Priscila Farias did also very interesting related work. You are right when you say that a liner representation of of the classes can be a problem. Indeed, I would say that the correlation bewteen a triadic, hexadic, or decadic sign relation with the cenopythagorean categories always result in a partially ordered set. The use of a Hasse diagram, as of Marty's lattices, stress this point. However, it is well known in lattice theory that any partially ordered set can be sorted and listed, given a criteria to decide what to list first, when a decision is necessary. One of the problems is that this list is taken as the strictly ordered set, and not as a possible list of its elements. See Figure 4.27, at page 264, and the respective comments, of my thesis. Thanks, Luiz > Benjamin Udell wrote: >> 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. > > > For the record, it must be added that a lot of the information found in > this very exhaustive piece of work has readily been available to > researchers since the 80s and before, including the work done by Robert > Marty on lattices (see the chapter on 'partially ordered sets' for an > overview of why the linear representation of the classes of signs from 1 > to 10 is a bit of a problem... > > Also note that the various trichotomies are not ordered. It is purely a > convention to call a trichotomy the first, second, or third trichotomy, > etc. So deducing an ordering of the classes from that information only, > as it has been done many times including on this list, is incorrect. > > /JM > > --- > Message from peirce-l forum to subscriber [EMAIL PROTECTED] > > --- Message from peirce-l forum to subscriber archive@mail-archive.com
