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 <g...@gnusystems.ca> 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:gary.richm...@gmail.com] > *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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