Robert, Jon, List,
thank you both very much for your enlighting posts, I hope many others besides me profit from them. I have undestood things like this:
A correlational triad (e.g. S,O-, or primi-, alter-, medisense) has elements wih the ordinal numbers 1.2.3. My opinion is, that these numbers also (not only in a trichotomy) represent the categories. The first element has one mode, the second two, the third three. I would say, the second is a dichotomy, and the third is a trichotomy. Further, in the S,O,I- triad, it is so, that the third´s trichotomy (the interpretant´s) can be expressed in three different ways: accordingly to perspective (sign´s, object´s, interpretant´s perspective), accordingly to possibility/ existent/ necessity, or accordingly to utterer/ recipient/ commens. Now, to have a logical scheme, I thing it should be so, that the object´s dichotomy can be expressed in two different ways. Immediate-dynamical is the perspective- dichotomy- _expression_, and I think, the other dichotomy- _expression_ would be possible and existent (actual) object.
Now about involution/ involvation: I´d like to call it "involution", if it is about genuine-degenerate, the trichotomic thing. I´d like to call it "involvation" in other cases, such as common speech, a subset affair, when some agent involves something (actively), and "involvement", when I talk about something being involved (passively), or taking part somewhere. I think that is like common speech.
Involvation / subclass relation can go, mirrorwise, in two opposite directions, when we talk about composition versus classification: The group of mammals (their extension) involves the group of rodents, but the intension of "rodent" involves the intension of "mammal": Being a rodent involves being a mammal. Stanley N. Salthe has described this funny thing in his paper "Salthe´12Axiomathes". It is about the two system´s hierarchies composition and subsumption (subsumption he later calls "specification", I call it mostly "classification").
I thought: Why two, with Peirce it always is three, and have put "determination" in between as secondness. If I´m right, and "composition, determination, classification" is a categorial triad, then composition should be a monotomy, determination a dichotomy, and classification a trichotomy. I think this is so: A composition looks the same from any perspective, a determination looks different from the determining from from the determined perspective, and a classification has three perspectives: The subclass (e.g. rodents), the superclass (e.g. mammals), and the way of classification (e.g. genetic taxonomy).
Earlier i wrote, that determination and involvation might be the same, but now I think that involvation is the firstness in the determination- dichotomy: Possible determination. Example: If a member of parliament is involved in a vote, he only possibly determines the vote. It may also be, that, if he were not taking part, the vote result, the decision, would be the same.
Best, Helmut
25. Oktober 2025 um 00:11
wrote:
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
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
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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