Gary F, list,
GF: OK, that does help to clarify what categorial trichotomic (or “category theory” as Joe R. called it) and vector analysis are all about. On that basis, I can see how they would be classified as parts or aspects of phenomenology: they are best applied to *phenomena* or types of phenomena. One important thing to remember here, I think, is that "category theory" is an invention of Peirce's. The best place to look for definitions and descriptions of it and its functioning is in his work beginning around 1885 with "One, Two, Three" (EP1, Item 18) and his letters of that period to William James, especially the one written in late October of that year where he first puts forward his "guess of the secret of the sphynx," being, "that three elements are active in the world, first, chance, second, law [he will later clarify this to mean law put into effect, or, force GR], and third, habit-taking." Again, my initial goal has been to try to help explicate Peirce's own theory. GF: They don’t seem as well suited to semiotic (as Peirce developed it post-1902) or, more generally, to triadic *relations*. So I’ll refrain from asking further questions about those things in this thread. I do not at all agree that categorial trichotomic is not suited to Peirce's late semiotic, and, indeed, I believe that its applications to semiotic and triadic relations are two of its *most* significant applications in cenoscopic science. But perhaps, as you seem to be suggesting, we should for now avoid those particular considerations, at least until we have a fuller understanding of category theory as Peirce conceived of it. Otherwise we might be talking past each other. GF: It seems what we need is examples of its application to phenomena (processes, etc.) and demonstrations of the pragmatic value of vector analysis. One theoretical question remains for me, though: does your development of trichotomic (including vector analysis) make any use of the Peircean concept of degeneracy? The reason I ask is that degeneracy in one concept he continues to apply (with no essential change that I can see) from “Trichotomy” on, to his work on semiotic, on logical relations, *and* on the categories. If your trichotomic has no use for it, or for the genuine/degenerate distinction as applied by Peirce, that in itself might clarify the new direction that your work is taking. I have struggled with these questions for some time now. First, I would say that to get a grasp of how trichotomic can be applied one ought fully familiarize oneself with Peirce's "A Guess at the Riddle." Again, as Houser notes, this MS marks Peirce's "deliberate turn to architectonic thought, " a turn which he continues into the famous Monist Metaphysical Series being "The Architecture of Theories," The Doctrine of Necessity Examined," "The Law of Mind," "Man's Glassy Essence," and "Evolutionary Love." If one is looking for Peirce's own conception of trichotomic, there's probably no better place to begin than with "A Guess at the Riddle" followed by an examination of these famous papers. For, as Houser writes: His three categories, which he speculates are isomorphic with the three elements that are active in the universe. . . serve as the structure for organizing the branches of philosophy and science, and it is clear that he anticipated a complete reorganization of human knowledge around his triad of universal conceptions (EP1:245). And here Houser quotes a passage I gave in an earlier post where Peirce comments that such a restructuring of science (including, and perhaps especially, I will continue to argue, semiotics, including its last branch, methodeutic/ pragmatism) would bring about "one of the births of time." Perhaps on Peirce's own authority, then, it makes sense, at least to me, to imagine that categorial trichotomic *might *have as much--or, at least, nearly as much--potential value as Peirce himself saw it as having. In Peirce's work of this period there are also hints as to the answer to another question you've raised: "does your development of trichotomic (including vector analysis) make any use of the Peircean concept of degeneracy?" For starters, Peirce, by the very fact of discussing degeneracy *in *"TRICHOTOMIC" would seem to be suggesting that its development *might* include that notion, and I have come to see that categorial trichotomic does involve both genuine and degenerate relations (how degenerate relations might be diagrammed in trikonic is something I am now only beginning to explore). However, it is important to note that in the 1907 "Pragmatism," for example, that Peirce comments that "the semiosis of the sign" is a *genuine* triadic relation. This leads me to think that vector analysis (which includes a vector which essentially represents "the semiosis of the sign" ) probably doesn't concern itself with degenerate relations, nor has it any need to. Its structure and purpose, while intimately connected to categorial trichotomic as Peirce outlined it, is quite different (but that's another subject). My growing sense, well at the moment really just a guess, is that category theory may have a part to play in "making Peirce pragmatic," which is the working title of a paper my friend and colleague, Aldo de Moor, proposed decades ago, and by which he meant, specifically (although the phrase doesn't strongly suggest it), applying pragmatism, as "critical common-sensism," to certain contemporary, especially organizational and cultural problems. From a more strictly cenoscopic standpoint, Peirce, in that 1907 essay, lists really a rather stunning number of important ontological questions which scientific pragmatism could help resolve (see: EP2:480). So, in both a scientific as well as the more general cultural sense, I find myself more and more focusing on what, if anything, categorial trichotomic, perhaps especially vector analysis, might contribute to such pragmatic problem solving. This is all by way of saying that I want to look again freshly at pragmatism, that aspect of Peirce's work which brought many of us to him in the first place. To that end, I'm currently drafting a post on some of the ideas contained in the 1907 MS mentioned above, so that I'll be focusing on pragmatism as such for the next few weeks. Best, Gary R [image: Gary Richmond] *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* *C 745* *718 482-5690 <718%20482-5690>* On Fri, Jan 8, 2016 at 11:12 AM, <g...@gnusystems.ca> wrote: > Gary R, > > > > OK, that does help to clarify what categorial trichotomic (or “category > theory” as Joe R. called it) and vector analysis are all about. On that > basis, I can see how they would be classified as parts or aspects of > phenomenology: they are best applied to *phenomena* or types of > phenomena. They don’t seem as well suited to semiotic (as Peirce developed > it post-1902) or, more generally, to triadic *relations*. So I’ll refrain > from asking further questions about those things in this thread. > > > > It seems what we need is examples of its application to phenomena > (processes, etc.) and demonstrations of the pragmatic value of vector > analysis. One theoretical question remains for me, though: does your > development of trichotomic (including vector analysis) make any use of the > Peircean concept of degeneracy? The reason I ask is that degeneracy in one > concept he continues to apply (with no essential change that I can see) > from “Trichotomy” on, to his work on semiotic, on logical relations, *and* > on the categories. If your trichotomic has no use for it, or for the > genuine/degenerate distinction as applied by Peirce, that in itself might > clarify the new direction that your work is taking. > > > > Gary f. > > > > *From:* Gary Richmond [mailto:gary.richm...@gmail.com] > *Sent:* 7-Jan-16 15:49 > > Gary F, List, > > > > Thanks for your questions which I'll try to answer as best I can. I say, > "as best I can" since, if Peirce was a backwoodsman in semiotics, I am more > like someone who, while quite appreciative of Peirce having cleared a path > through the semiotic forest, yet find myself lost in the thicket, while > trying to see the forest freshly through the, well, threes. :-) > > > > In addition, the science of logic as semiotic may turn out not to be the > central focus (or even locus) of trichotomic, while so far, perhaps, having > its fullest application there (although Peirce's own use of categorial > analysis in metaphysics and in certain special and applied sciences is > quite suggestive of its potential value for those sciences as well). In any > event, on to your questions. > > > > GF: First, since you refer to it here as “trichotomic science,” I wonder > where (or whether) you would place it in Peirce’s classification of > sciences. > > This is a somewhat vexing question for me. On the one hand, as I remarked > in a recent post, Peirce refers to trichotomic as an 'art', that is, as 'a > special science'. But then he seems to apply it to (1) all branches of his > theoretical science of logic as semeiotic as well as to (2) the > classification of the sciences taken as a whole (and in particular to > cenoscopic science), and perhaps even to (3) theoretical mathematics (he > once remarks that the categories are 'discovered' in phenomenology, but are > given support 'retrospectively', so to speak, in pure mathematics, in what > Ken Ketner has diagrammed as valental graphs in the context of the > Reduction Thesis). > > Sometimes I've argued that besides the two phenomenoogical sciences de > Tienne has identified (and which you and I and a very few others have > discussed, although not recently, and certainly not in depth), that a third > phenomenological science is quasi-necessary if Peirce is to have a basis > for applying his phaneroscopic and iconoscopic findings in phenomenology to > semeiotics (and beyond). > > > > Despite his general antipathy towards phenomenology as a science, Joe > Ransdell, after he'd read my first paper on trikonic and looked at the > slides which Ben Udell and I had created, referred to it as 'category > theory', and this is the name I've retained for it as a possible third > branch of phenomenology. But, at the moment, I am unclear exactly where to > place *trichotomic* in the classification of sciences (note: *trikonic* > is being developed as but a diagrammatic aid to trichotomic > analysis/synthesis wherever trichotomic may eventually find its place in > the classification). You also asked: > > > > GF. . .What follows there applies the concept of degeneracy in a way > similar to the treatment of it in the 1903 Syllabus — except that Peirce’s > emphasis in “Trichotomic” seems to be more on *rhetoric* than on*logic*, > in the classical senses of those terms. > > Yes, I agree, that there is more of an emphasis on rhetoric than on logic, > at least at this place in the MS, and specifically rhetoric seen as a > theater art (dramatic expression). Indeed, to me Peirce seems to be "all > over the place" in this MS which looks to me to be yet another sketch of > facets of his trichotomic project. Indeed, Nathan Houser remarks in the > introduction to "TRICHOTOMIC" that its title "is one of the alternatives > Peirce had considered for his projected "One, Two, Three" which became "A > Guess at the Riddle." (EP1:280) One finds in it not only the discussions of > dramatic expression just mentioned, but also brief, really quite sketchy > remarks on 'consciousness', 'the functions of the nervous system', and 'the > properties of protoplam', all analyzed trichotomically. > > GF: Another notable difference is that the earlier work says that “A sign > is a third,” but in the Syllabus, “A *Sign*, or*Representamen*, is a > First” (EP2:272). I wonder whether these differences can be explained by > means of a vectorial analysis. I don’t see how to do that myself, but maybe > you can! > > I'll have to think more about how vectorial analysis may help explain this > discrepancy in Peirce's writing "A sign is a third" in TRICHOTOMIC, while > writing that "A *Sign*, or *Representamen*, is a First" in the *Syllabus, > *but it *may* have something to do with the level of abstraction of the > discussions, a matter which has occasionally, and even recently, been > discussed on the list. This is to say that one can find Peirce referring to > (1) an entire semiosic 'event' as a sign, whereas (2) in other discussions, > and as John Collier has argued, he hypostatically abstracts the object from > the sign from the interpretant. For what it's worth, here's my attempt at > vectorially analyzing both, the later first, as less complicated. > > Case (2): 'sign' as a 1ns might be diagrammed vectorially in this way: > > 2nd, 1ns (. . .the Sign, i.e., Representamen. . .) > > |> 3rd, 3ns (. . . for the Interpretant) > > 1st, 2ns. The Object determines. . . > > Case (1): 'sign' as a 3ns is more problematic. But I think that this may > represent one of the strengths of vector analysis, namely, that the middle ( > *mediating*) position for all six vectors will be either at 1ns, OR 2ns, > OR 3ns (2 of each of course), so that Peirce is seeing this position of the > sign in the diagram above as "mediating between the mind addressed and the > object represented" (EP1:281). So, *very* tentatively, as a mere > preliminary guess, I might diagram this as follows: > > 2nd, 1ns (. . .the Complete Sign, i.e. Immediate O-R-Inter. . .) > > |> 3rd, 3ns (. . . for the Mind addressed) > > 1st, 2nd. The Dynamic Object determines. . > > Now, I can't say I'm completely satisfied with this second diagram (since > interpretant and mind addressed may seem to intersect or overlap--although > I think that for the human interpreter they can be distinguished). But, > again, in my opinion Peirce is in 1888 merely "on the way" to a much more > fully developed (and occasionally corrected) semiotic theory, and the idea > of 'sign' seems to me to be functioning at several different levels in his > thinking then; so there is some ambiguity concerning several terms, e.g. > 'sign' and 'object' (but others as well). So I'm suggesting that this > ambiguity is not fully resolved (perhaps not even fully understood) in > 1888. In the case of 'sign', perhaps it is *never *fully resolved > (disambiguated), while in the case of 'object' it appears to have been > (dynamic vs immeidate object). > > In one sense the ambiguity If that's what it is) regarding the term 'sign' > can be seen as a strength of Peirce's semiotic, and it is only in this > present kind of minute grammatical analysis that we find ourselves > struggling with questions which, it may turn out, will have to be dealt > with at some other level of analysis and reflection. I personally have no > problem seeing 'sign' as both 1ns (as in Case 2 above), but more > *essentially* as 3ns. > > GF: One more question. If we name the three correlates in a triadic > relation (e.g. sign-object-interpretant), does that constitute a > *trichotomy* in your sense of the word? Or do you. . . > > I would call the three correlates in a triadic relation (S-O-I) a > trichotomy as given in diagram (2) above, the Representamen a 1ns (in a > semiosis its mediating between the object and the interpretent). > > Again, thanks for your questions. I hope my answers are helpful to you. > If not, I'll be happy to entertain additional questions. > > > > Best, > > > > Gary R > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > peirce-L@list.iupui.edu . 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