Gary R. Wrote: Yes, let's continue to discuss Peirce's phenomenology, but in another thread after the seminar.
I will second that! I've been wanting to contribute to this discussion, especially in relation to category theory, abduction and utens/docens. However, as we have been caring for 3 lively grandchildren (one an especially lively 3 yr old) for the past week (and the one to come), I haven't managed to produce a coherent thought. I am sneaking time away late evenings to prepare for the second half of this chapter and look forward to that discussion but am glad we will come back to phenomenology later on. Regards, Phyllis Gary Richmond <[email protected]> wrote: >Gary F. List, > >I'm afraid I wasn't able to make much sense of the Zalamea quotation out of >its context. I am, of course, looking forward to his address at the >Congress. In fact, the entire schedule of invited speakers is of >considerable interest to me. > >Jon wrote a piece called "Precursors of Category Theory" which is of >interest. >http://intersci.ss.uci.edu/wiki/index.php/Precursors_of_Category_Theory > >Yes, let's continue to discuss Peirce's phenomenology, but in another >thread after the seminar. > >Best, > >Gary R. > > > >*Gary Richmond* >*Philosophy and Critical Thinking* >*Communication Studies* >*LaGuardia College of the City University of New York* > > >On Sat, Apr 26, 2014 at 5:19 PM, Gary Fuhrman <[email protected]> wrote: > >> Gary R, list, >> >> >> >> I expect we'll learn more about this at the Centennial conference this >> summer, as Zalamea is one of the listed speakers; but here's a couple of >> quotes from his book, *Peirce's Logic of Continuity,* to give a more >> specific idea of what I was referring to (and incidentally to get us back >> to the subject of pragmatism): >> >> >> >> [[ In particular, we claim that an understanding of modern methods in >> topological model theory and in category theory are extremely useful to >> disentangle the riddle of Peirce's continuum. ] p. 35] >> >> >> >> [[ ... the mathematical theory of categories is the environment of >> contemporary mathematics which better can be fused with Peirce's thought, >> and where perhaps the greater number of tools and models can be found to >> faithfully approach both Peirce's general architectonics and Peirce's >> particular ideas. The continuum - vessel and bridge between the general >> and the particular - is therefore specially well suited to be understood >> categorically. The paradigm of the mathematical theory of categories >> -"arrows, >> *not* elements"; synthesis, *not* analysis; relational, contextual, >> external knowledge, *not* monolithic, isolated, internal knowledge -reflects >> nicely Peirce's pragmatic maxim. In >> category theory the pragmatic dimension becomes evident through diverse >> functorial readings ("interpretations") between "concrete categories". As >> invariants of a generic functorial back-and-forth emerge - solidly: >> *theorematically >> *- "real" universal notions, definable in any "abstract category", beyond >> its eventual existence (or non-existence) in given particular categories. >> Category >> Theory thus provides the more sophisticated technical arsenal, available in >> the present state of our culture, which can be used to prove that *there >> do exist real universals*, vindicating forcefully the validity of >> Peirce's scholastic realism. ] p. 46] >> >> >> >> As for other uses of Category Theory in Peircean studies (or in extending >> Peirce's ideas), Jon probably knows more about that than I do. As to >> whether the presence of another "category theory" within Peircean studies >> will cause confusion, that's only a guess on my part, and maybe not a very >> educated one. Anyway I do want to hear more about what you call "category >> theory," regardless of what you call it. (Maybe not in this thread, though.) >> >> >> >> gary f. >> >> >> >> *From:* Gary Richmond [mailto:[email protected]] >> *Sent:* 26-Apr-14 4:08 PM >> >> *To:* Gary Fuhrman >> *Cc:* Peirce-L >> *Subject:* Re: [PEIRCE-L] Re: de Waal Seminar: Chapter 7, Pragmatism >> >> >> >> Gary F. List, >> >> >> >> You wrote: >> >> >> >> On the term "Category Theory", I guess I wasn't very clear, so let me try >> again: It seems to be already an established term *within Peircean >> studies* in the sense that mathematicians use it. As I understand it, >> Fernando Zalamea (and others) are looking into mathematical and logical >> connections between Peirce's work and Category Theory in that established >> sense, and finding those connections fruitful. If that's the case, then I >> think it would cause confusion among Peirceans to *also* use "Category >> Theory" as a term for a subdivision of Peircean phenomenology. The case of >> mathematicians resisting non-mathematical uses of the word "vector" seems >> to me a very different issue >> >> >> >> I don't agree that the consideration of a branch of phenomenology named >> "Category Theory" would result in contusion "within Peircean studies" at >> all. Contemporary mathematicians (and logicians,etc.) are certainly free >> to use any of the tools of those disciplines (and others) developed since >> Peirce's death. But it seems to me that there is a compelling case for a >> third branch of phenomenology which might best be termed "Category Theory," >> and at least one prominent Peircean scholar, namely Joseph Ransdell, called >> it exactly that. For when most Peirceans read 'category' in relation to >> Peirce's work, they immediately think of Peirce's three universal >> categories, not of mathematical category theory (to which, btw, I found >> only a very few brief references within the Zalamea articles I looked at, >> although I didn't research this deeply, and not the "others" you mentioned >> at all). >> >> >> >> And just *how much* emphasis on the possible fruits of applying >> mathematical category theory to Peirce's writings on continuity and >> Existential graphs is there in fact anyhow? For example, in this passage >> from Zalamea's "Plasticity and Creativity in the Logic Notebook," it is >> mentioned but once. >> >> http://www.pucsp.br/pragmatismo/dowloads/lectures_papers/zalamea-paper.pdf >> >> >> >> In fact, even if abstraction, order and visual harmony have been embodied, >> for >> >> example, in the paintings of Rothko or in the sculptures of Caro, Peirce's >> heirs have still to understand that compelling mixture in mathematics. If >> Category Theory confirms itself as an appropriate general topos for such >> an encounter, if its technical expression turns out to be describable by >> the logic of Sheaf Theory, and if sheaf logic situates finally at >> the "heart" of a wider Synthetic Philosophy of Mathematics, then we could >> appreciate better the extraordinary power of the LN [Logic Notebook] seeds. >> >> >> >> Furthermore, I have seen mathematicians apply not only category theory but >> vector analysis and other modern mathematical tools to aspects of Peirce's >> work in continuity theory and EGs in particular, with no resultant >> confusion within Peircean studies. So I think you may be fearing a >> 'confusion' which is really highly unlikely to occur. >> >> >> >> Yet at the outset of that same paper just referenced, Zalamea writes >> something relating much more to the idea I have in mind for the use of >> "category theory" within Peirce's classification of the sciences. He begins >> the paper with this remark: >> >> >> >> Peirce's architectonics, far from rigid, is bended by many plastic >> transformations, >> >> deriving from the cenopythagorean categories, the pragmaticist (modal) >> maxim, the logic of abduction, the synechistic hypotheses and the triadic >> classification of sciences, among many other tools capable of molding >> knowledge >> >> >> >> It is Peirce himself who held for a "triadic classification of sciences," >> at least in his late work in the Science of Review, and the exceptional >> sciences which aren't so divided, notably the physical and psychical wings >> of the special, or idioscopic sciences, are themselves each trichotomically >> divided, namely, into descriptive, classificatory, and nomonological >> branches. The categories are a living presence in Peirce's classification. >> >> >> >> So, when considering the movement from the phaneron to extracting >> something from it for use in the sciences immediately following >> phenomenology, i.e., the normative sciences, and seeing that de Tienne had >> explored a possible second phenomenological science, Iconoscopy, I began to >> see that even that move, essential as I think it may be, doesn't take us >> far enough to in the direction of extracting from the phaneron that which >> could be put to cognitive use in the normative sciences. >> >> >> >> So, reflecting on my couple of decades long work on Peirce's applied >> science of Trichotomic, I began to imagine that what it "applied" were the >> findings of an additonal theoretical science, the third branch of >> phenomenology, namely, Category Theory. Now the work that de Tienne and I >> have been doing is at best tentative. But I think Kees' question as to how >> we do extract something from the phaneron for use in the normative sciences >> needs to be addressed. >> >> >> >> You continued: >> >> >> >> It's been a long time since I read De Tienne's paper on "Iconoscopy", and >> I only dimly remember the context in which we discussed that term before, >> so I'll defer to your judgment on that. (I didn't even remember that your >> proposal is to use "phaneroscopy" as only the first branch of >> "phenomenology" ... I'm still in the habit of using those terms synonymously >> in reference to Peirce.) So I guess I shouldn't have ventured a comment on >> that question. >> >> >> >> Since you correctly, and following Peirce, note that the phaneron is one, >> the *analysis* of it seems to require an expansion of phenomenology to >> include other branches. And Peircean categoriality itself led me to posit >> that there may be three, phaneroscopy, iconoscopy, and category theory. >> >> >> >> We do seem to be using the Keesian phrase "extracting something from the >> phaneron" in quite different senses. In my sense, it's not the elements >> that are "extracted" from the phaneron for special attention but some >> phenomenal ingredient of it; so the "essential elements" of the extracted >> idea (or whatever we call it) would be completely different from the >> elements of the phaneron (i.e. the "categories"). For one thing, they >> wouldn't be indecomposable as the elements of the phaneron are. So again >> we're speaking different dialects here, it seems. >> >> >> >> I'm not exactly sure what you're aiming at in making this distinction and >> I may be missing your point completely. But I would suggest that the >> extraction of the indecomposable elements is primarily the work of >> iconoscopy, and that the "essential elements" can be placed into >> trichotomic relations, and that this is the work of category theory. But we >> indeed may be "speaking different dialects here." So I think more work is >> needed in phenomenology for getting from the phaneon to what might be >> usefully extracted from it for the normative sciences? Absolutely. >> Therefore, I hope we keep this conversation going and growing in the next >> few years. But I certainly will continue to use 'category theory' as I >> have, and doubt that many will be confused, or any for very long. >> >> >> >> Now, it's probably time to return to pragmatism, from which we have >> strayed pretty far, I think. >> >> >> >> Best, >> >> >> >> Gary, >> >> >> >> >> >> >> >> >> ----------------------------- >> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >> PEIRCE-L to this message. 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