[peirce-l] Re: Sinsign, Legisign, Qualisign

[Gary Richmond]

Ben, list, By now you've received my completed and corrected message which omits the request for the not-simplified lattice version of my trikonic diagram of the 10 classes (since I very much like your simplified form which I included in the revised message) and adds analytical content. For right now, and also since I've posted too much today, I'd like to address for now just your question of why I called your diagram adding the lattice structure to my trikonic diagram an "abduction."  Well, really, you point to it yourself. What I'm getting at, is that it really is fair to say that the 10-adic triangular arrangement turns out to be quite suitable to depict the lattice for. . . the structure of ordering and non-ordering. Combining the two may also allow for a kind of possible diagram observation and manipulation which either one apart from the other wouldn't. Also, what you are "getting at" in the comment above is clear  once one sees it diagrammed! But I do not think that your bringing together the lattice structure and the trichotomic one is trivial, and it is that combination which I think may constitute a kind of abduction (or maybe it's really a form of diagram manipulation--although perhaps I really do think that to say that the 10-adic triangular structure is suitable for depicting the lattice structure is a kind of abduction). Best, Gary Benjamin Udell wrote: Gary R., list,   (Note: anybody responding, please remember to delete all unneeded graphics & text.)   Gary Richmond wrote, > (one I believe he hasn't posted yet, but which I hope he will, shows a possible correspondence between Robert's lattice structure...   The graphic which I already posted (and which is the first one shown here) pretty much shows it. It's just simplified, and is at a different angle as a whole than Robert's, and is with Robert's vertical arrows slanted in order to be like others. Gary's calling this an "abduction" but, unless he means that I've kidnapped Robert's lattice diagram (I certainly have done _something_ with it! :-) ), the only element of abduction or surmise is that I don't know whether the verticality of some of Robert's arrows in fact is somehow determinate in terms of the lattice representation. I can see how one could argue that it makes "the most sense" but my surmise is that the distinctive slope of those arrows with respect to the others is indeed optional. Aside from that, and aside from the overall orientation and handedness (left/right) of the visual representation, there's little if any surmise in it, instead it's an equivalence (at least up to a point, which I'll get to in a moment). The lattice structure is pretty much "deterministic" -- I mean, that aside from our flipping it horizontally or vertically or whatever, and aside from our turning the "loose-end"-looking vertices to one angle or another, etc., etc., .its vertices are in a definite arrangement. What I'm getting at, is that it really is fair to say that the 10-adic triangular arrangement turns out to be quite suitable to depict the lattice for -- I don't know what it's called -- the structure of ordering and non-ordering. The second graphic is a re-created version of Robert Marty's. The third is a cross between Robert Marty's style and Gary's trikonic style. The fourth shows --- Message from peirce-l forum to subscriber archive@mail-archive.com