Gary R., Robert, List: Overall, we seem to be more or less on the same page.
I understand the impetus for using "presupposition" rather than "involution," since the former term is more familiar to modern mathematicians and logicians than the latter. I have no objection to saying that 3ns involves 2ns and 1ns, while 2ns involves 1ns. I just find it more succinct and equally accurate to say that 3ns involves 2ns, which involves 1ns; this already entails that 3ns also involves 1ns. I am not wedded to Peirce's adaptation of Aristotelian terminology (1ns/2ns/3ns = form/matter/entelechy), which is most prevalent in his writings around 1904--e.g., in "New Elements" (EP 2:303-305) and "Sketch of Dichotomic Mathematics" (NEM 4:292-300)--but I find it helpful in certain contexts. I share Gary R.'s interest in learning more about "the conceptual relationship between Peirce's trichotomic category theory and contemporary mathematical category theory if any." I am more familiar with Fernando Zalamea's opinion (which I share) that Peirce's mathematical conception of continuity is more consistent with category theory (synthetic/top-down) than set theory (analytic/bottom-up). Thanks, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Tue, May 5, 2020 at 3:29 PM Gary Richmond <[email protected]> wrote: > Robert, List, > > Robert wrote: > > RM: I spent a year extracting all the definitions of the sign that Peirce > could have imagined and I was not disappointed since I found 76; they're on > peirce.org. I have taken this effort when I realized the incredible > number of scholars who thought in a non-critical way about the definition > of the sign they attributed to Peirce. In particular, I have seen > impossible triangles and confusions, especially with the Saussurian > tradition, with the conceptions of Hjemslev and in the end of Greimas and > his Ecole de Paris. It would have taken a titanic job to denounce all > distortions, fanciful borrowings and undue annexations. > > > That was certainly time *very* well spent by you! I know of no Peirce > scholar who isn't aware of your list of Peirce's 76 definitions of 'sign', > and many who have referenced it in their own work. I myself have read > through it several times over the years. It is surely a major contribution, > especially since, as you commented, there were any "number of scholars who > thought in a non-critical way about the definition of the sign they > attributed to Peirce." > > Your scholarship has certainly contributed to dispelling the many > "distortions, fanciful borrowings and undue annexations" regarding Peirce's > semeiotic. I sometimes think, how much better Peirce's semeiotic might > today be known, understood, further developed and applied, had it not been > for Sassurean thinking having taken hold and rooting itself so deeply in > Continental thinking for most of the 20th century; and, as a consequence, > drawing attention away from Peirce's triadic semeiotic, distorting it with > Sassurean concepts and language, dyadic and nominalistic thinking, etc. To > some extent it seems to me that that remains the case to this very day. > > Shifting to an entirely different topic prompted by your most recent > off-list email to me (I'm afraid the math in it, as the American English > idiom has it, was "above my pay grade"), a question which has come upon the > list before, albeit infrequently, concerns the conceptual relationship > between Peirce's trichotomic category theory and contemporary mathematical > category theory if any. What, may I ask, are your thoughts about that? > > Best, > > Gary R > > "Time is not a renewable resource." gnox > > *Gary Richmond* > *Philosophy and Critical Thinking* > *Communication Studies* > *LaGuardia College of the City University of New York* > > On Tue, May 5, 2020 at 6:19 AM Robert Marty <[email protected]> > wrote: > >> Gary, Jon Alan, List >> >> I fully respect yours concerns and of course it is clear that everyone >> can invest them in the podium that is quite honored. For the part >> concerning me I see no difficulty in using "involution" rather than >> "presupposition" and I do not think I have strayed too far from Peirce with >> "presupposition" since I think I have shown on the basis of Frege's >> definition that the relationships of determination between the elements of >> the phenomena as stated by Peirce verified this assertion. For I just need >> to inscribe the abstract arrows of the mathematical object that I build >> "*without >> reference to their real existence",** within* Peirce's empirical >> discourse. C.S. Peirce, 1976: NEM, vol. IV, 1122 : >> >> *"It is obvious that a Possible cannot determine anything other than a >> Possible, and likewise a Necessitant cannot be determined by anything other >> than a Necessitant** " *( letter to Lady Welby of December 23, 1908) >> >> I understood very early on that I had to trace a personal path in what >> J.M. Chevalier quite rightly called "Le continent peircien" ( >> https://www.academia.edu/3383353/La_d%C3%A9couverte_du_continent_peircien) >> but by justifying at every step a very close and verifiable proximity to >> the fundamental conceptions of phaneroscopy and semiotics. And when we >> received in Perpignan the MS microfilms that we had ordered from the >> Harvard Library (32 reels of 100m each - 3.2 km!) I don't regret my >> decision ... I spent a year extracting all the definitions of the sign that >> Peirce could have imagined and I was not disappointed since I found 76; >> they're on peirce.org. I have taken this effort when I realized the >> incredible number of scholars who thought in a non-critical way about the >> definition of the sign they attributed to Peirce. In particular, I have >> seen impossible triangles and confusions, especially with the Saussurian >> tradition, with the conceptions of Hjemslev and in the end of Greimas and >> his Ecole de Paris. It would have taken a titanic job to denounce all >> distortions, fanciful borrowings and undue annexations. >> >> A practical consequence is that I have not acquired the skill to discuss >> the relevance of the intellectual investments that can be made on the >> podium. Let me reveal the picture came to mind when I read Jon Alan's first >> and almost immediate reaction above; it is not derogatory: I saw a child >> jumping from level 3 on the steps of the podium and I imagined all the >> possible choices he could make to get down. Obviously there are 10 and even >> there are 6 in the inner cylinder 3 in the outside cylinder and only 1 >> outside the two cylinders. To each his obsessions! Since this (dynamic) >> image no longer leaves my mind because I wonder if it does not open another >> way to go to the lattice of the classes of signs that would not go through >> the constraints of purely algebraic formalization. I think about it often >> ... >> >> Best regards >> >> Robert >> Le mar. 5 mai 2020 à 06:04, Gary Richmond <[email protected]> a >> écrit : >> >>> Jon, Robert, List, >>> >>> I began a draft response to your post, Jon, shortly after you wrote it, >>> but things began to move so quickly on the list that my initial thoughts >>> soon seemed to be superseded in the rapid fire exchanges following. So I am >>> glad that you reposted it as it gives me another chance to respond (*if* >>> I can complete it soon enough not to lose it again as things move on). >>> >>> I certainly agree with Jon that your paper, Robert, is most interesting >>> and that your podium diagram effectively represents the relations holding >>> among the three categories. But I also agree with you, Jon, >>> that 'involution' is not only Peirce's term, but indeed expresses the >>> concept of the logical relations holding among the categories more >>> accurately than does 'presupposition', really optimally. I would very >>> slightly modify Jon's expression of these involutional relations: 3ns >>> *involves *2ns *and* 1ns; 2ns *involves *1ns. >>> >>> JAS: Applying this to the "podium" diagram, 1=essence, 2=existence, and >>> 3=reality. What about the inner portions? I suggest that 1/2=inherence, >>> 2/3=persistence, and 1/2/3=governance. >>> >>> GR: I think that inherence, persistence and governance make good >>> terminological sense in consideration of "the inner portions" of the podium >>> based on CP 1.175. But as I see it the Aristotelian terminology of NEM >>> 4:292-300, "form for 1ns, matter for 2ns, and entelechy for 3ns" is >>> potentially misleading, especially if we forget that for Peirce 'form' is, >>> as you commented, Jon, "whatever it is in itself, irrespective of >>> anything else/" (1=essence), matter as "all that it is in reference to >>> something else than itself" (2=existence), and entelechy as "that which >>> brings things together" (3=reality)." >>> >>> In short, I see no reason to employ the Aristotelian terminology, loaded >>> as it is with pre-Peircean notions especially of form. 'Matter' and >>> 'entelechy' fare somewhat better, but still bring with them the >>> Aristotelian associations. I think that it is possible and desirable to >>> move beyond these in Peircean scholarship. >>> >>> Indeed, I found it helpful to my own understanding to substitute >>> Peirce's terms for Aristotle's in distinguishing the inner relations. So: >>> "the determination of "[the existent] by [essence]" (1/2=inherence), >>> "the reaction of [existent] with [existent] " (2=existence), and "a >>> determination of [an existent] to [an essential form]" >>> (1/2/3=governance). >>> >>> Jon, your quoting Colapietro helped clarify the following, I think, >>> truly important notion: that "reality, is *persistence*, is regularity >>> (or, persistence *in/as* regularity?). >>> >>> VC: Existence is the mode of being of an individual substance >>> considered as a continuity of *reactions*; insofar as it is *actually >>> *reacting >>> against other things, it exists. Persistence is the mode of being of such a >>> substance seen as a *continuity *of reactions; insofar as it endures >>> throughout a series of reactions, it persists. In other words, existence >>> (because it is an instance of opposition) designates the aspect of >>> secondness exhibited by any individual substance, while persistence >>> (because it is a case of continuity) designates one of the ways in which it >>> manifests thirdness. (Vincent Colapietro, *Peirce's Approach to the >>> Self: A Semiotic Perspective on Human Subjectivity,* 83). >>> >>> >>> In a word, 'persistence' is the existential form of continuity. >>> >>> JAS: Peirce describes two different classes of possible states of >>> things that may be realized at a lapse of time--*prolonged **states*, >>> which are *realized at any instant within a lapse; *and *gradual * >>> *states**, which are realized only at an entire lapse during which a >>> change occurs from one **prolonged state** to another*, these two >>> states being "logically incompossible" (see NEM 3:1074-1077, c.1905). Such >>> diversity requires *real *qualities to be continuous (1/2/3), rather >>> than isolated (1), and *real *things to persist (2/3), not merely exist >>> (2). (*Boldface* and *underlining *as emphasis added by GR.) >>> >>> To repeat: In a nutshell, real *qualities* are *continuous* (not >>> isolated); real *things* persist (not just exist). >>> >>> I expect to spend more time reflecting on the following quotations >>> (which I've read numerous times over the years) and your succinct comment >>> which separates them. >>> >>> >>> CSP: Time with its continuity logically involves some other kind of >>> continuity than its own. Time, as the universal form of change, cannot >>> exist unless there is something to undergo change [2/3] and to undergo a >>> change continuous in time there must be a continuity of changeable >>> qualities [1/2/3]. (CP 6.132, EP 1:323, 1892) >>> >>> >>> JAS: This is one specific sense in which all three categories are always >>> present within our existing universe. >>> >>> CSP: I chiefly insist upon continuity, or Thirdness, and, in order to >>> secure to thirdness its really commanding function, I find it indispensable >>> fully [to] recognize that it is a third, and that Firstness, or chance, and >>> Secondness, or Brute reaction, are other elements, without the independence >>> of which Thirdness would not have anything upon which to operate. (CP >>> 6.202, 1898) >>> >>> >>> Best, >>> >>> Gary >>> >>> "Time is not a renewable resource." gnox >>> *Gary Richmond* >>> *Philosophy and Critical Thinking* >>> *Communication Studies* >>> >>> *LaGuardia College of the City University of New York* >>> >>>>
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
