Jon, List, I must make a clarification without which the current debate with JAS will once again be useless. However, it will go far beyond this particular confrontation. Indeed, Part 2, which I am currently finishing, and this dialogue, difficult as it may be, show me the urgent need to clarify the concepts we all use, to clarify them again and again, a necessity in the world of multiple definitions and their multiple variations in a multiplicity of fields of knowledge. This is all the more true given that the main source of information, the Collected Papers, is not exempt from criticism regarding its representativeness and the chronological disorder that often prevails in the sequence of themes. However, they are the main reference thanks to their division into items, which has proved particularly valuable in uniting the community. The NEMs of the admirable Carolyn Eisele, although equal in editorial scope to the CP, have attempted, without much success among the community, to give pure mathematics the place that Peirce consistently attributed to it in his work (they should not be confused with the Existential Graphs, which are more concerned with logic). The Essential Peirce, which displays the editorial rigor lacking in the CP, is limited by its very ambition to an inevitably somewhat reductive essential. As soon as I had access to the MS thanks to the 32 rolls of 100 m of microfilm produced at Harvard University, which my research group fact acquired (in the 1970s), I understood that, at least in semiotics and, to a lesser extent, in phenomenology, in order to attempt to settle the question of fundamentals scientifically and therefore definitively, it was imperative to immerse oneself in the MS, aided by the indispensable Robin catalog, a fact I did. I am not going to recount my personal history here, but simply indicate the main stages that have marked it, not to award myself any commemorative medals, but to mark out a path that I consider scientific in the eyes of the Peirce-L entity, the only institution that the community has given itself to debate, on a daily basis, with the inevitable but indispensable turbulence that affects the debates that take place there.
The first step, after consulting all the sources at my disposal, was to draw up as exhaustive a list as possible of definitions of the sign so that it would be representative of all definitions of the sign and allow the scope of the problems to be measured. I found 76, both dated and undated. Next, I had to analyze them, because science, in order to progress, must reduce diversity to unity. I posted them, accompanied by a detailed analysis, on the forum then run by its founder, Joe Ransdell, who decided to publish them on Peirce.org, where they still remain. Some omissions were pointed out to me, but none of them called into question the result of my analysis, namely that until around 1904-1905, Peirce focused his definitions on three entities (Sign, Object, Interpretant) as elements of a triadic relation (Representamen appears in 1896). Subsequently, the definitions concern these same entities but change the focus, introducing two successive determinations of the Sign by the Object and of the Interpretant by the Sign, the effect of which is to generate a determination of the Interpretant by the Object, which generates a triadic relation. There is no further mention of Representamen, except once around 1911. I have called the first one “global triadic” and the second one “analytic triadic.” These are two distinct successive hypostatic abstractions that are a fact by Peirce as an observer of representations and communications in social life in a large number of cultures. The second is the 1990 publication of my book “L'algèbre des signes” <https://www.jbe-platform.com/content/books/9789027278234> (The Algebra of Signs), subtitled “Essai de sémiotique scientifique selon Charles Sanders Peirce” (Essay on Scientific Semiotics according to Charles Sanders Peirce), in which I present a complete model of Peirce's second conceptualization, with both determinations. In fact, I quickly recognized the applicability of the algebraic forms of Category Theory <https://en.wikipedia.org/wiki/Category_theory>, this “general theory of mathematical structures <https://en.wikipedia.org/wiki/Mathematical_structure> and their relations introduced by Samuel Eilenberg <https://en.wikipedia.org/wiki/Samuel_Eilenberg> and Saunders Mac Lane <https://en.wikipedia.org/wiki/Saunders_Mac_Lane> in the middle of the 20th century,” which I had favored in my mathematical research. Published in awkward French, using highly abstract and little-known mathematics, separated from its main target audience by an ocean, it had little chance of finding an audience, even though it can be found as a secondary source in the Charles S. Peirce article in the Stanford Encyclopedia of Philosophy. That is why, for years, I devoted a lot of time to defending it, in English, in publications that most often did not find a reviewer, and I finally admitted that I would not succeed. Last but not least, I turned to the more accessible Theory of Relational Structures, which allowed me to avoid the pitfalls of functors and, above all, their natural transformations, which lead to the same conclusions without success. The third stage is the current stage. I resolved to abandon all theories imported from outside and decided to follow exactly in Peirce's footsteps, an idea that came to me when I picked up the Syllabus and the Lowell Lectures of November 1903 I noticed that from the very first lines of the 5th (MS 540), he was thoroughly revising the 2nd, in which he attempted to classify signs using only two trichotomies (those of the object and the interpretant), without really succeeding. On the other hand, in the 5th, entitled “*Nomenclature and Divisions of Triadic Relations, as Far as They Are Determined*,” based on “*The principles and analogies of Phenomenology*,” he specifies how his universal categories make it possible to differentiate the three correlates of an abstract triadic relation, and, on the second page, he makes this fact: Triadic relations are in three ways divisible by trichotomy, according as the First, the Second, or the Third Correlate, respectively, is a mere possibility, an actual existent, or a law. These three trichotomies, *taken together*, divide all triadic relations into ten classes. Here, Peirce spends, without saying so, from the abstract domain of triadic relations, which he calls *a priori*, in which the three categories inherited from the “reduction thesis” are also found, to the *a posteriori* domain in which the three abstract categories of Firstness, Secondness, and Thirdness are embodied in social life, respectively, as “mere possibility, actual existent, or law.” The literature has gone further by relying on rules of determination between correlates stated *later* by Peirce, when he shifted his focus in his second hypostatic abstraction. This is the case in the CP (see Part 1 of Modeling and finalizing Peirce's semiotics with AI <https://www.academia.edu/130131910/Modeling_and_finalizing_Peirces_semiotics_with_AI>, section 2.2, footnote to CP 2.235, p.658 of the electronic edition). This is also the fact that Irving Lieb does, 1977, Appendix B, p.161). In Part 1, I showed that ten classes of triadic relations can be obtained *a priori* as a Theorem of Relational Algebra disconnected from phenomenology, which gives it the same legitimacy as the Pythagorean theorem in Plane Geometry and, as such, must be respected absolutely. In Part 2 (in progress), I continue with the triadic relation classes alone and also obtain the lattice of triadic relation classes a priori, a new Relational Algebra Theorem, whose status as Universal Sign Grammar cannot be disputed. Thus, it is established that the 1903 Syllabus allows us to establish, without internal determinations, the same result that I obtained with Category Theory, and I am confident that, with the obstacle of abstraction now removed, the community will eventually adopt it as Grammatica Speculativa. After this necessary clarification, I come to the debates on Peirce-L, particularly with JAS, who tacitly acknowledges the legitimate existence of the lattice but takes little or no account of my well-founded observations. As he has been presenting himself as a Structural Engineer rather than a Professional Engineer for several years now, I thought that mathematical structures might interest him... In short, I cannot spend my time fact-checking messages that are all the more complex because they are not expressed in the “taken together” that captures the trichotomies of the same movement of thought, but treat each question trichotomy by trichotomy, striving to take into account valid associations two by two, in an attempt to grasp the three trichotomies in the complexity of their interdependencies. When there are six trichotomies, it becomes inextricable. The Bortolini law <https://en.wikipedia.org/wiki/Brandolini%27s_law>, an adage which states: “The amount of energy needed to refute bullshit <https://en.wikipedia.org/wiki/Bullshit> [a philosophical and psychological term] is an order of magnitude <https://en.wikipedia.org/wiki/Order_of_magnitude> bigger than that needed to produce it” would quickly exhaust me and I would not be able to achieve my editorial goal, which is to rewrite an Algebra of Signs, renewed and amplified by decades of experience, in English of course. But I will not lose interest in Peirce-L. I will intervene pragmatically whenever I have the opportunity to show how my models can shed light on the debates. Honorary Professor ; PhD Mathematics ; PhD Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* Le mer. 8 oct. 2025 à 19:20, Jon Alan Schmidt <[email protected]> a écrit : > Robert, List: > > On the contrary, I am not putting the trichotomy for the final > interpretant (If) *itself *in any position whatsoever--only the one for > its *relation *with the sign (S-If), which appears in both Peirce's 1903 > taxonomy as rheme/dicisign/argument and his later taxonomies as > seme/pheme/delome. Again, my purpose in not introducing any of the *other > *interpretant trichotomies is to avoid revisiting our longstanding > disagreement about their logical order for classifying signs, especially > since it is not pertinent to the thread topic of indexicality. Anyone who > would like to discuss the interpretants is welcome to start a new thread > accordingly. > > Peirce himself postulated the arrangement of the three trichotomies in his > 1903 taxonomy as S → Od-S → S-If, and you obviously agree with this since > you have repeatedly employed it in your mathematical lattice approach. In > this thread, I have simply added the two preceding trichotomies from > Peirce's later taxonomies, in the same order that he likewise postulated, > so I do not understand your objection to the Od-S trichotomy coming after > both the Od and S trichotomies. Peirce ultimately identifies a trichotomy > for each of the six correlates *itself*--the sign, its two objects, and > its three interpretants--as well as a *different *trichotomy for each of > the four *external* relations that the sign has with other correlates > (Od-S, S-If, S-Id, Od-S-If). These are the ten trichotomies that yield 66 > sign classes, and he already includes both kinds--one for a correlate (S) > and two for relations (Od-S, S-If)--in his 1903 taxonomy that yields ten > classes. > > Peirce marks only two of the ten trichotomies to indicate his level of > confidence about them. The one for the mode of apprehension of the sign > itself as potisign/actisign/famisign is {sigma}, although he adds, "I think > I might as well have marked this division {delta} instead of {sigma}, > except that perhaps the question may arise whether I ought not to have > recognized a division according as the sign is a *natural sign*, which > has no party to the dialogue as its author, or whether it be an *uttered > sign*, and in the latter case, is the very sign that is getting uttered > or another. But it seems to me that this division turns upon the question > of whether or not the sign uttered is a sign of a sign as its Object" (CP > 8.348, EP 2:484). The one for the mode of presentation of the immediate > object as descriptive/designative/copulant is {mu}, although he adds, "I > would mark it {delta} if I were satisfied with the distinction between > Descriptives and [Designatives]" (CP 8.352, EP 2:485). > > I take no issue with your Venn diagram and accompanying remarks, which > continue to address only the three 1903 trichotomies that are > uncontroversial. What I am questioning is Peirce's initial classification > of the *word *"beauty"--not the *quality *of beauty--as an *abstractive*, > which according to the same draft letter can *only *be an iconic > qualisign/tone; but as I said before, the only *words *that are (at least > arguably) iconic qualisigns/tones are onomatopoeia, such as "buzz" and > "tick tock." Again, in my view, the quality of beauty *itself *can be an > abstractive iconic qualisign/tone, with some *other *quality as its > dynamical object; the *word *"beauty" as a *type *is a rhematic symbolic > collective copulant, with the *general concept* of beauty as its > dynamical object; and the *word *"beauty" as a *token *is often a > rhematic iconic designative concretive, with the quality of beauty as > *actually > embodied* in something as its dynamical object. > > In the end, I agree that "readers can judge for themselves" whether my > comments about speculative grammar are reasonable in light of Peirce's > pioneering work, as well as whether the last paragraph below is an accurate > characterization of our exchanges. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt > > On Tue, Oct 7, 2025 at 12:59 PM robert marty <[email protected]> > wrote: > >> Jon, List, >> >> I can now see that your approach is dominated by your desire to place the >> interpretant If in a position that conforms to your views, which I have >> shown to be on the fringes of the fundamentals of Peirce's semiotics. Our >> readers can judge for themselves. By omitting (a) what we disagree on and >> then pronouncing (b) a kind of default prohibition on the use of >> interpretants in this thread (even though you yourself retain If in your >> personal construction), you are demonstrating your intention to confine the >> debate to a field that you have chosen by proposing a new pentadic sign. >> >> It is incorrect to say that my approach concerns only the ten classes of >> signs. In the past, I employed a method derived from Category Theory, which >> enabled me to identify the ten classes of triadic signs and their lattice >> structure. With the same method (my trichotomic machine[1] >> <#m_-542534831138755480_m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftn1>), >> I obtained the 28 classes of hexadic signs and their lattice. This method >> is applicable to any other sequence of n trichotomies with (n-1) >> determinations, and therefore also to n = 10 (if there were agreement on >> their integration into a sequence of nine successive, well-defined >> determinations, which is far from being the case). And if the approach you >> propose were valid, your 21 classes would immediately be organized into a >> lattice that you can obtain by going to the lattice generator[2] >> <#m_-542534831138755480_m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftn2> >> designed by Patrick Benazet and marking the number 5 in the indicated >> location. >> >> However, it turns out that your approach is not well-defined because your >> construction contains a tautology that renders it inconsistent. In fact, >> your proposition is presented by the diagram. Od → Oi → S → Od-S → S-If in >> which each element mentioned, Od, Oi, S, and If, is defined by Peirce. The >> order of the first three trichotomies, as well as the first two >> determinations represented by arrows, and the order of the three elements >> in the letter to Lady Welby dated December 23, 1908. Od-S and S-If are >> your notations for the 7th trichotomy in Peirce's list of 10 trichotomies >> (8.344) and S-If for the 9th. The other two arrows, therefore, each >> represent a relation of determination that you postulate between S and Od-S >> and between Od-S and Od-If. >> >> My argument requires recalling a concept that is taught in high schools. >> It is "function composition."[3] >> <#m_-542534831138755480_m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftn3>The >> general diagram is as follows: >> >> [image: Une image contenant noir, obscurité Le contenu généré par l’IA >> peut être incorrect.] >> >> where h = g o f represents the function h that results from >> concatenating f and g, I refer to your first two arrows, Od → Oi → S, >> calling here for the first arrow and g the second. Then, since the >> determination relation is transitive, we have h = g o f, which is >> therefore well defined, and we can write Od → S, where the arrow represents >> the determination h of Od by S. >> >> Next, you continue with a determination relation S → Od-S where, in your >> own words, "The Od-S trichotomy is according to the sign's relation with >> its dynamical object." However, we have just seen that Od already >> determines S; therefore, according to you, the sign S should determine a >> relation in which this same Od already determines it. At the very least, >> this is a tautology, and your chain of determinations therefore ends here. >> >> I'm not sure if you evaluated Peirce's assertions based on this model. If >> so, the errors you attributed to him would have been wrong. >> >> Furthermore, I believe you have read the following item (CP 8.445, EP2: >> 483) in which Peirce expresses some certainties and many doubts about >> certain trichotomies: >> >> The ten divisions appear to me to be all Trichotomies, but it is possible >> that some of them are not properly so. Of these Ten Trichotomies, I have a >> clear apprehension of some, (which I mark {d} for {délos}), an >> unsatisfactory and doubtful notion of others (which I mark {a} for >> {adélos}), and a tolerable but not thoroughly tried conception of others >> (which I mark {m} for {metrios}, {s} for {schedon}, almost clear, {ch} for >> {chalepös} hardly better than {a}). >> >> >> *Délos* means that something has become clear or obvious. >> *Adélos*, which is its opposite, means unclear, obscure, indistinct, >> uncertain, vague, and random. >> *Métrios: *average, common, standard, even mediocre. >> *Shedon: *almost, nearly, approximately, close to, near >> *. Chalepös:* with difficulty, with great effort, reluctantly; >> generally expresses the idea of something difficult to accept or deal with. >> >> Unfortunately, I have not been able to find this marking by Peirce; it >> does not appear in Irvin Lieb's edition of Letters, nor in Charles >> Hardwick's Semiotics and Significs. However, it may be found in the paper >> edition of Collected Papers, which I no longer have access to. >> >> Finally, for "beauty," I took the trouble to design a Venn diagram in my >> previous post, which took me a lot of work. Have you considered my >> arguments? I never find any reasoned criticism from you. You oppose me with >> what you believe to be an alternative truth that I am compelled to analyze. >> It is an asymmetrical dialogue in which I am the only one observing the >> precepts of scientific debate. I am not leaving the arena, but I will >> henceforth limit my responses to the bare minimum. >> >> Regards, >> >> Robert Marty >> ------------------------------ >> >> [1] >> <#m_-542534831138755480_m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftnref1> >> The >> trichotomic machine, *Semiotica*, vol.2019, n°228, may 2019, p.173-192. >> >> [2] >> <#m_-542534831138755480_m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftnref2> >> http://patrick-benazet.chez-alice.fr/treillis_en_ligne/lattices/ >> >> [3] >> <#m_-542534831138755480_m_6359114605386728293_m_896552944095627187_m_-1645609776511664205_m_740861618061125398_m_8678089565195086344_m_3716165291448862763_m_-2274401180690844238_m_-6720277692175823396_m_1061596010500244148__ftnref3> >> https://en.wikipedia.org/wiki/Function_composition >> >> Honorary Professor ; PhD Mathematics ; PhD Philosophy >> fr.wikipedia.org/wiki/Robert_Marty >> *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* >> > _ _ _ _ _ _ _ _ _ _ > ► 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] > . > ► <a href="mailto:[email protected]";>UNSUBSCRIBE FROM > PEIRCE-L</a> . But, if your subscribed email account is not your default > email account, then go to > https://list.iu.edu/sympa/signoff/peirce-l . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell.
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