Helmut, List, What you call “vertical involvation” is nothing other than the trichotomization of each of the constituent elements of the sign (O, S, I). In his 1903 Syllabus, Peirce introduces the notion of nature, and, of course, we find the three natures ordered in each of the three trichotomies.
On the other hand, what you call “horizontal involvement” when referring to these same elements is not involvement at all, because here we are dealing with the relations (of determination) between these same elements. Finding the classes of signs means finding all the valid combinations of these three trichotomies, where valid means that only triplets of natures that respect the pre-existing order of natures (in the broad sense, i.e., with possible equalities) should be retained. They can be found “manually” by simple bricolage (this was done very early on by Lieb); one can use the well-known rule, indicated by Peirce five years later in a letter to Lady Welby (this is what the editors of the CP do); one can also integrate them into a mathematical model (I did this as early as 1977 using Category Theory (Math)). But if we look at the Syllabus, we see that Peirce, after defining and studying the three trichotomies of O, S, and I, announces, *without proof*, that “taken together” they lead to ten classes of valid signs and ten only. He studies them further, one by one, but not only that, as I will return to later. Convinced that there was a way, I searched for it by placing myself in the same conditions as Peirce in 1903 (5th lecture, MS 540). It was only within the framework of triadic relations that the search should be conducted. By first following Peirce step by step and then naturally extending his trajectory, I was able to achieve the desired goal. You will find all this in detail, with all the useful references, in Part 1, which I have made public. You then mention relations between classes of signs, referring, for example, to the rhematic indexical legisign and the other classes it should imply. This is something completely different, since now that the classes are well defined, it is a question of the “affinities” between these ten classes (CP 2.264). Here too, using this definition, I showed, as early as 1977 in French, published in English in 1982 in Semiotica, that these affinities led to a structure of order well known today as a “lattice.” Peirce was familiar with this structure (I have documented this). In my Part 2, which I will publish soon, I have developed all this in detail, showing with many arguments that Peirce had “the lattice in mind.” I am aware that my response goes well beyond your initial question, but it is the only rational response I could give you since you are wondering whether a bug you detect in your statement is terminological or conceptual. I would add that I present my results in the form of relational algebra theorems and that, as such, they cannot be dismissed on the pretext that they could have been established in 1903. If that were the case, then Pythagoras' theorem would have to be consigned to oblivion! 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 jeu. 23 oct. 2025 à 20:57, Helmut Raulien <[email protected]> a écrit : > Robert, List, > > Thank you for the challenge! As I have understood Gary, I may post this > second post of today, because it is an answer. I hope, this is so? > > First: I finally have accepted, that e.g. the object is a correlate, and > the sign´s relation with it is a relation, and both are different things. > Thanks to you and Jon. I´m a bit ashamed I had been reluctant to see this > before. > > Now to my so-called trichotomy (composition, involvation, classification). > At the very end there may be a little bug in it, and there also are some > questions (see the question marks). Now it only is about the classification > of signs (signs table, ten classes): > > The classification of signs involves two kinds of involvation, by looking > at the signs table: The vertical and the horizontal kind. The vertical > involvement comes from the fact, that a legisign involves sin-, which then > involve qualisigns, a symbol involves indices, then icons, an argument > involves dicents, then rhemes (I use the plural, without claiming, just > guessing, that it is more than one, otherwise the text gets too long). Now, > if the sign is e.g. a rhematic indexical legisign, it should involve (some? > all? How many of each?) signs, that may be built of the elements involved > (above the sign in the table): Rhematic indexical sinsign, rhematic > iconical sinsign, (rhematic iconical) qualisign. > > Horizontal involvation comes from the fact, that a sign involves a > relation with its object, and a relation with its interpretant. This is > involvation, not composition, linguistically adressed by adjectives (the > "...tic" or "....al" of e.g. "rhematic" or "indexical"). > > So, this was, how classification involves involvation. Now, how does > involvation involve composition? The fact, that a sign always involves its > relation with an object and with an interpretant, means, that there is an > irreducible correlation between sign, object, and interpretant. This > correlation is a composition: Sign, object, and interpretant make the > irreducible sign triad. As I wrote, there may be a little bug here: I have > called a conclusion an involvation,, not really knowing, if that is ok. > > What also may be argued, is, that composition might be seen as a kind of > involvation, then there would not be a categorial distinction. That is a > problem, I don´t know yet, whether it is terminological or conceptual. > > Best, Helmut > > > 23. Oktober 2025 um 16:54 > "robert marty" <[email protected]> > *wrote:* > > Helmut, List, > > You asked the question “What is a trichotomy?” a few days ago on another > thread; I replied on October 21, 2025, at 10:22 a.m., giving you Peirce's > precise definition when he trichotomizes the sciences in order to classify > them; here it is: > *It turns out that in most cases the divisions are trichotomic; the First > of the three members relating to universal elements or laws, the Second > arranging classes of forms and seeking to bring them under universal laws, > the Third going into the utmost detail, describing individual phenomena and > endeavoring to explain them*. (An Outline Classification of the Sciences, > CP 1.180; EP2: 258) > > Note: First, Second, and Third are ordinals! > > So, a formal definition, applicable in all circumstances, would be > something like: > > A trichotomy is a tripartite division of a phaneron into three parts > defined by the natures of the elements it contains, each of which is > characterized by one of the three classes: Thirdness, Secondness, and > Firstness. It follows that, since these categories are interdependent and > verify relations of involvement *a priori, *then the elements with which > each part is associated (which, for convenience, I call, as Peirce was, the > fact, respectively, Tertians, Secondans, and Primans) must be such that > Tertians govern Secondans, whose existence is by definition presupposed, > and also Primans, which, by their definition, only exist when incarnated in > Secondans. > > Consequently, if you claim that a triad of concepts is a trichotomy, you > must show that they meet these conditions. The three classes must be > included, and the elements contained in each must be related by > involvement. Your opinion is not enough, and you cannot leave it to your > readers to verify this. It is up to you to prove it... > > 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 jeu. 23 oct. 2025 à 12:21, Helmut Raulien <[email protected]> a écrit : > >> Jon, Robert, List, >> >> to me, the relations between categorial entities become clearer by >> classifying them with the trichotomy "composition, involvement, >> classification" (Maybe this trichotomy is better than "composition, >> determination, classification", I had proposed before, or maybe involvement >> is a kind of determination). With composition I mean a complete and >> irreducible one. Classification may also be called specification or >> subsumption (Salthe). >> >> The triad "sign, object, interpretant" is a composition. "immediate >> object, dynamical object" is a composition, these two make the object. The >> trichotomy "rheme, dicent, argument" is a classification. A dicent >> involves rhemes, but is not composed of them, because they donot make it. >> For having a dicent, their order too is necessary, which information is in >> the dicent. Same with argument: Peirces example with the beans in a bag >> shows, that according to the order of dicents (propositions) in the >> argument, you have either an abduction, an induction, or a deduction (or >> nonsense, if the order is weird). >> >> A symbol involves indexes, which involve icons, a legisign involves >> sinsigns, which involve qualisigns. >> >> I think, that the three interpretants too are a composition, they >> together make the interpretant. But then I´d have to claim, that every >> interpretant consists of these three parts. The final inerpretant may be >> vague or an anticipation for a long time, but should exist from the >> beginning in some way. >> >> Best, Helmut >> 22. Oktober 2025 um 20:21 >> "Jon Alan Schmidt" <[email protected]> >> *wrote:* >> Robert, List: >> >> As always, where there are conflicting claims about Peirce's thought, I >> encourage readers to draw their own conclusions in light of all the textual >> evidence presented and otherwise available. Accordingly, I stand by my >> statement that is contested below, which is from my first post on Monday ( >> https://list.iu.edu/sympa/arc/peirce-l/2025-10/msg00095.html) and >> supported by the following observations and accompanying quotations that I >> included in my first post yesterday ( >> https://list.iu.edu/sympa/arc/peirce-l/2025-10/msg00104.html). >> >> - He says in 1903 that for *any *class where 3ns is predominant, >> there are subclasses of relatively genuine 3ns, relatively reactional 3ns, >> and relatively qualitative 3ns. >> - He also says in 1903 that in *any *triadic relation, the first >> correlate (e.g., sign) is the simplest, the second (e.g., object) is of >> middling complexity, and the third (e.g., interpretant) is the most >> complex. >> - He introduces the hexad of six correlates already in October 1904, >> not 1906 or 1908; and it is a further development of his 1903 speculative >> grammar, not a completely new approach. >> - He employs the terminology of phaneroscopic analysis to explain the >> additional correlates in July 1905--the dynamical/immediate objects are >> genuine/degenerate, and the final/dynamical/immediate interpretants are >> genuinely/secundally/primarily tertian. >> - He again refers to the dynamical object and the final interpretant >> as "genuine" in April 1906, less than a month after writing the letter to >> Lady Welby that is excerpted below. >> >> In any case, that letter never mentions the immediate/dynamical/final >> interpretants, so it cannot plausibly be considered *the *definitive >> account of them. It does go on to talk about the >> intentional/effectual/communicational interpretants, but a few weeks >> later--in the very same paragraph where he states, "The Normal Interpretant >> is the Genuine Interpretant"--Peirce says that he has "omitted the *intended >> *interpretant" because "it may be the Interpretant of *another *sign, >> but it is in no sense the interpretant of *that *sign" (R 339:[276r >> <https://iiif.lib.harvard.edu/manifests/view/drs:15255301$522i>], 1906 >> Apr 2). Specifically, as "a determination of the mind of the utterer" (SS >> 196, EP 2:478, 1906 Mar 9), it obviously *cannot *be any of the >> interpretants of the sign that the utterer is *currently *uttering; >> instead, it must be a dynamical interpretant of a *previous *sign >> determined by the same object. I explain this, along with my position that >> the communicational interpretant corresponds to the immediate (not final) >> interpretant, in my 2022 *Semiotica *paper, "Peirce's Evolving >> Interpretants" (https://philpapers.org/go.pl?aid=SCHPEI-12). >> >> I remain puzzled by the assertion that I am placing the trichotomy for >> the final interpretant itself (If) wherever it suits me. On the contrary, >> Peirce's 1903 taxonomy for classifying signs unambiguously puts the >> trichotomy for the sign's *relation *with its (final) interpretant *after >> *the one for the sign's *relation *with its (dynamical) object, which >> comes *after *the one for the sign itself; and he states plainly in 1908 >> that the trichotomies for *all three* interpretants as correlates also >> come *after *the one for the sign itself. I continue to refrain from >> discussing whether their proper logical order is immediate-dynamical-final >> or final-dynamical-immediate, since I am well aware that this is >> controversial among Peirce scholars due to his peculiar reference to the >> destinate/effective/explicit interpretants in that passage (SS 84, EP >> 2:481, 1908 Dec 23). >> >> Regards, >> >> Jon Alan Schmidt - Olathe, Kansas, USA >> Structural Engineer, Synechist Philosopher, Lutheran Christian >> www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt >> >> On Wed, Oct 22, 2025 at 2:29 AM robert marty <[email protected]> >> wrote: >> >>> Jon, List, >>> >>> It is false to assert this: >>> >>> JAS: Phaneroscopic analysis of the *genuine *triadic relation of >>> representing/mediating reveals that every one sign has two objects and >>> three interpretants, for a total of six correlates. >>> >>> Phaneroscopic analysis of a genuine triadic relation reveals nothing of >>> this. This can be seen from the first appearance of the six correlates in >>> 1906: >>> >>> *33 - 1906 - S.S. 196 - Letter to Lady Welby (Draft) dated "1906 March >>> 9".* >>> >>> I use the word "Sign" in the widest sense for any medium for the >>> communication or extension of a Form (or feature). Being medium, it is >>> determined by something, called its Object, and determines something, >>> called its Interpretant or Interpretand. But some distinctions have to be >>> borne in mind in order rightly to understand what is meant by the Object >>> and by the Interpretant. In order that a Form may be extended or >>> communicated, it is necessary that it should have been really embodied in a >>> Subject independently of the communication; and it is necessary that there >>> should be another subject in which the same form is embodied only in >>> consequence of the communication. The Form, (and the Form is the Object of >>> the Sign), as it really determines the former Subject, is quite independent >>> of the sign; yet we may and indeed must say that the object of a sign can >>> be nothing but what that sign represents it to be. Therefore, in order to >>> reconcile these apparently conflicting Truths, it is indispensible to >>> distinguish the immediate object from the dynamical object. >>> >>> The same form of distinction extends to the interpretant. Still, as >>> applied to the interpretant, it is complicated by the circumstance that the >>> sign not only determines the interpretant to represent (or to take the form >>> of) the object, but also determines the interpretant to represent the sign. >>> Indeed in what we may, from one point of view, regard as the principal kind >>> of signs, there is one distinct part appropriated to representing the >>> object, and another to representing how this very sign itself represents >>> that object. The class of signs I refer to are the dicisigns. In "John is >>> in love with Helen" the object signified is the pair, John and Helen. But >>> the "is in love with" signifies the form this sign represents itself to >>> represent John and Helen's Form to be. That this is so is shown by the >>> precise equivalence between any verb in the indicative and the same made >>> the object of "I tell you". "Jesus wept" = "I tell you that Jesus wept". >>> >>> As you can see, the reasons given by Peirce do not mention the >>> phaneroscopy of the triadic sign *at any point. *He describes the six >>> stages of the journey of a form that would be in the object of the sign >>> into the mind through six successive determinations. He arrives at a more >>> complicated sign, a new definition by expansion. >>> >>> We can still see this in CP 4.536 et 4.539, then in 1908 (47 bis – 1908 >>> - Letter to Lady Welby in CP 8.343), CP 8.314 [March 14, 1909], and in CP >>> 8.183 (undated). >>> >>> It seems to me that Jon is attempting to dissolve the triadic sign into >>> the hexadic sign (a more detailed hypostatic abstraction of the semiotic >>> phenomenon according to Peirce) in order to ultimately promote an >>> idiosyncratic pentadic sign with 21 classes in which he engraves his >>> ideology (if not something else ?) by placing the If wherever it suits him. >>> >>> >>> >>> I promised myself I would keep my time to myself and stop fact-checking, >>> but this was too much. >>> >>> >>> 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. 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