Helmut, List: I am pleased to see that Robert and I agree about *involution *being the relation *within *a trichotomy--3ns involves 2ns, which involves 1ns--and *determination *(in the sense of logical constraint) being the relation *between *trichotomies, at least for classifying signs. In Peirce's 1903 taxonomy, the sign itself (qualisign/sinsign/legisign) determines its dyadic *relation *with its object (icon/index/symbol), which determines its dyadic *relation *with its interpretant (rheme/dicisign/argument). In his 1908 taxonomy, the two objects (dynamoid and immediate) determine the sign itself (tone/token/type), which determines the three interpretants (destinate, effective. and explicit).
The sign, its object, and its interpretant are *not *the members of a trichotomy because they do not comprise a *division *of something and the relation of involution is not applicable--it is *not *the case that the interpretant involves the object, which involves the sign. Instead, the relevant trichotomy is a division into monadic/dyadic/triadic *relations*--as I see it, the immediate (degenerate) object and immediate (relatively qualitative or primarily tertian) interpretant are in *monadic *relations with a sign *type*, which is "a definitely significant Form" (CP 4.537, 1906); the dynamical (genuine) object and dynamical (relatively reactional or secundally tertian) interpretant are in *dyadic *relations with a sign *token*, which is "significant only as occurring just when and where it does" (ibid.); and the dynamical (genuine) object and final (relatively genuine or genuinely tertian) interpretant are in a genuine* triadic *relation with the sign *in itself*, which encompasses different types in different languages and other sign systems (see CP 5.138, EP 2:203, 1903). This genuine triadic relation *involves* those various dyadic and monadic relations, but it is not *reducible *to them. On the other hand, the *only *signs that (metaphysically) *exist *are tokens, each of which is in a *degenerate *triadic relation with its dynamical object and dynamical interpretant, i.e., one that *is *reducible to its constituent dyadic relations--the dynamical object determines the sign token, which determines the dynamical interpretant. Here, "determined" means "specialized," i.e., made *more determinate*; in fact, Peirce uses the German word *bestimmt* for what he has in mind (see CP 6.625, 1868; CP 8.177, EP 2:493, 1909 Feb 26; and EP 2:497, 1909 Mar 14). Signs in themselves, as well as types and tones, are *real* but not actual--they do not *exist*, except as embodied in tokens. As Peirce says about a proposition, a sign *per se* "does not exist but governs existents, to which individuals conform" (CP 8.313, 1905 Jan 22). As he says about a word, "It does not exist; it only determines things that do exist" (CP 4.537, 1906). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Fri, Oct 24, 2025 at 4:12 AM robert marty <[email protected]> wrote: > 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/>* > On Fri, Oct 24, 2025 at 3:36 AM Helmut Raulien <[email protected]> wrote: > Jon, List, > > by introducing other terms I don´t want to create a new theory, it´s just, > that something about some terms bothers me: Sometimes the same term > (trichotomy) is used for different things, and sometimes I feel, that > different terms are used for the same thing. The trichotomiy S-O-I is > such, that a dyadic relation, e,g. S-O, or a monad, may be prescinded from > it, but can not exist, because the triad is irreducible. Same with > primisense, altersense, medisense. With the trichotomy > rheme-dicent-argument it is different: Dicents (propositions) exist, rhemes > too. > > About primi-, alter- medisense, one might argue: "But a plant does not > think". But I´d say, the medisense there is not in the individual, but in > the species. > > To your distinction between determination and involution: Isn´t both the > same, just "determination" is top-dpwn-speak, and "involution" bottom-up? > Just an idea (please don´t be false again, idea!). E.g. my property is > both: Something involved by my extended self, and also something, from > which I have constrained all possibilities away, which would prevent it > from being mine. > > Best, Helmut >
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