Helmut, List, I will answer the second question first, as the answer (from Peirce) may shed light on the first. My reply is a little late because I don't post several times a day, I don't change thread titles, and I strive to respect exact thinking by scrupulously following Peirce, which prevents me from attributing errors to him that he did not commit.
To understand what a trichotomy is, we must look for where Peirce defines it precisely, because everyone knows that it is closely related to universal categories, but exact thinking must strive to define each term used clearly and unambiguously. Indeed, trichotomies are at work in the classification of the sciences, particularly in the sciences of discovery. It is in the first of the Lowell Lectures of November 1903 that Peirce constructs "the ladder into the Well of Truth by successive trichotomies" (see the Syllabus), a fractal-type progression. I have described it in C.S. Peirce's Reasoned Classification Of The Sciences. I have carefully distinguished between trichotomy and tripartition and have formalized the notion of trichotomy in this chapter. However, in the 5th lecture, in the context of triadic relations (MS 540), I find the following formulation: *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. *(CP 2.238; EP 2: 290) This is not yet a definition, as it is an attribution of nature to correlates, but it is very similar. If we further compare it to the way trichotomies operate in the classification of the sciences: *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) 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, 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. This is why I proposed the 3D diagram of the podium in *"The 'Podium' of Universal Categories and their degenerate cases."* Helmut, your question reflects a trouble you may feel when, proceeding with a tripartite division according to universal categories, you find yourself in the presence of parts which, to be trichotomies, must have relations. If this is indeed the case, then I hope these few reflections will have been helpful to you. As for your first question, it actually contains two questions, since, in my opinion, the last sentence has nothing to do with the others. HR: *This could be explained more explicitly by mentioning the two parts of the object and the three parts of the interpretant, but my point works anyway, so I think* Indeed, the first part of your question concerns the triadic sign. In the second part, it is inconceivable that you could claim to explain a triadic model (whether that of 1903 without determinations or that of 1905 with two determinations) using concepts from a hexadic model conceived in 1908. You are not the only one to make this mistake. If I come back to the first part of your first question, you initially ask, *"Why is there so much emphasis put on the distinction between a correlate (object, interpretant) and the relation between the sign and each of both?"* I find your use of "on" to be excessive. Personally, I have never attached any importance to this. Of course, we can talk about these two relations, because they exist, of course, both in the triadic representamen without determinations and in the triadic sign with two determinations. In the first case, these are dyads induced by the triad; in the second case, there are only O → S and S → I, which, by concatenation, create O → I. Moreover, when I see that we write (S-O) or (S-Od) and talk about trichotomizing this entity without mentioning the trichotomies of the constituents, I believe that we are misinterpreting Peirce and creating confusion. If we analyze it, there is the "-" which is a conventional sign to express a binary relation (a Tertian), but without specifying its direction. I don't see how we could trichotomize this relation independently of the trichotomies of S and O (or Od), because it is the valid combinations of pairs of natures that will dictate the choice of direction. In fact, for Peirce, it is a way of speaking, and these things are implied when he focuses on the sign S. It seems to me that your first question begins by making this observation. Consequently, it contains the correct answer and that you do not need to resort to another, later conception of the sign to explain 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 sam. 18 oct. 2025 à 21:47, Helmut Raulien <[email protected]> a écrit : > Jon, Robert, List, > > I have two questions, the first is, why is there so much emphasis put on > the distinction between a correlate (object, interpretant) and the relation > between the sign and each of both? I think, the object and the interpretant > are already relations with the sign: The object (at least the immediate, > but I think, both parts) doesn´t exist, if it isn´t denoted by, and > determines the sign. The interpretant is already determined by the sign, > and without an anticipated interpretant, the sign would not exist. This > could be explained this more explicitly, by mentioning the two parts of the > object, and the three of the interpretant, but my point works anyway > already so, I think. > My second question is: What is a trichotomy? Is it both about > specification/classification, and composition? From the word root (to cut > something into three pieces) I would say, it only is about composition, > e.g. for sign, object, interpretant. But not for classification, like > rheme, dicent, argument. Because there it is not about parts of something, > but about "either-or" classes. "Either-or" means, these items already are > apart, you cannot cut something into three pieces here. Ok, you can do this > with your mind, but then you don´t cut the real -or imagined- thing apart, > not even prescindingly, but virtually e.g. a sheet of paper, on which > classes are written. Then you have a trichotomy of paper, but not of the > interpretant (aka(?) its relation with the sign). > > Best, Helmut > 17. Oktober 2025 um 19:15 > "Jon Alan Schmidt" <[email protected]> > *wrote:* > Robert, List: > > As I demonstrated by providing the relevant quotations in my previous post > in this thread (CP 2.238&243, EP 2:290-1), although Peirce suggests in 1903 > that *triadic relations* are classified using trichotomies for the nature > of each correlate *itself*, he does not go on to classify *signs *that > way; after all, a sign is *not *a triadic relation, it is the *first > correlate* of such a relation (CP 2.242, EP 2:290). Instead, although the > first trichotomy is indeed according to the nature of the sign *itself*, > the second is according to the nature of the *relation* between the first > and second correlates, the sign and its object; and the third is according > to the nature of the *relation *between the first and third correlates, > the sign and its interpretant. > > These are both *dyadic *relations that are *involved *in the triadic > relation, but the latter is not *reducible *to them, which is why it is a > *genuine > *triadic relation. Peirce recognizes already in 1903 that "In every > genuine Triadic Relation, the First Correlate may be regarded as > determining the Third Correlate in some respect" (CP 2.241, EP 2:290), > i.e., the sign *determines *its interpretant. He later elaborates that > the sign "is both determined by the object *relatively to the > interpretant*, and determines the interpretant *in reference to the > object*" (EP 2:410, 1907), i.e., the sign's dyadic relations with its > object and interpretant are *both *relations of determination--the object > *determines > *the sign to *determine *the interpretant. Again, Peirce uses > trichotomies for these *relations*, not the object and interpretant > *themselves*, to classify signs in 1903. > > Identifying six correlates instead of three is a refinement, not an > *entirely *new conceptualization. What Peirce calls the object in 1903 is > precisely what he later calls the *dynamical *object, as distinguished > from the *immediate *object. We know this because the trichotomy for the > sign's relation with its object in 1903 (icon/index/symbol) is identical to > the one for the sign's relation with its *dynamical *object in his later > taxonomies. Likewise, what Peirce calls the interpretant in 1903 is what he > later calls the *final *interpretant, as distinguished from the > *immediate *and *dynamical *interpretants. We know this because the > trichotomy for the sign's relation with its interpretant in 1903 > (rheme/dicisign/argument) is identical to the one for the sign's relation > with its *final *interpretant in his later taxonomies (further > generalized to 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 Fri, Oct 17, 2025 at 2:48 AM robert marty <[email protected]> > wrote: > >> 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/>* >> > _ _ _ _ _ _ _ _ _ _ ► 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] . ► UNSUBSCRIBE FROM PEIRCE-L > <[email protected]> . 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. > _ _ _ _ _ _ _ _ _ _ > ► 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> . 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