Jon, List, It's clear that you don't know much about binary relations, let alone triadic or hexadic relations. Once again, your response misses the point. The binary relation you note (S-Od) by introducing Od, which cannot have been present in 1903 since it first appeared in a hexadic definition of the sign in 1906 (definition 33), in a new conceptualization of the sign with six elements and five determinations. You always come back to that. However, here Peirce works only with triadic relations, which he class without any internal determination between their respective correlates. He class them according to the valid triplets of natures to which he assigns all three. Your 21 classes are flawed and have no future. I believe I have already answered all of this in my previous posts. It is best that we leave it at that.
Best regards, Robert Marty Honorary Professor ; PhD Mathematics ; PhD Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* Le mer. 15 oct. 2025 à 02:28, Jon Alan Schmidt <[email protected]> a écrit : > Robert, List: > > Just for the sake of clarity, I would like to highlight one important > point about Peirce's 1903 speculative grammar as presented in the Syllabus. > > CSP (quoted by RM): 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. (CP 2.238, EP 2:290) > > > These three trichotomies, one for each of the three *correlates*--which, > taken together, would indeed divide all *triadic relations* into ten > classes--are *not *the three trichotomies that Peirce goes on to identify > a few paragraphs later for dividing all *signs *into ten classes. > > CSP: Signs are divisible by three trichotomies: first, according as the > sign in itself is a mere quality, is an actual existent, or is a general > law; secondly, according as the relation of the sign to its Object consists > in the sign's having some character in itself, or in some existential > relation to that Object, or in its relation to an Interpretant; thirdly, > according as its Interpretant represents it as a sign of possibility, or as > a sign of fact, or a sign of reason. (CP 2.243, EP 2:291) > > > *Only *the first trichotomy, for "the sign in itself," is the same. The > other two are *not *for the object and interpretant *themselves*, but for > the sign's (dyadic) *relations *with its (dynamical) object and (final) > interpretant. This is confirmed in Peirce's later taxonomies, where the > trichotomy for Od-S (not Od itself) is icon/index/symbol and the one for > S-If (not If itself) is rheme/dicisign/argument or (further generalized) > seme/pheme/delome. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Structural Engineer, Synechist Philosopher, Lutheran Christian > www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt > > On Tue, Oct 14, 2025 at 11:36 AM robert marty <[email protected]> > wrote: > >> 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/>* >> > _ _ _ _ _ _ _ _ _ _ > ► 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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