Jon, List,
The term "division" is too ambiguous for me. You can call the elements of a relation so, too. As far as I have understood, a relation is a kind of composition, and a ...tomy is a kind of classification. Rheme, dicent, argument, for example, is a classification, it is kinds (not parts) of the genuine interpretant-sign-relation, which are prescinded. In reality it is a dekatomy: Ten classes of signs, a classification, either-or. This "either-or" does not apply to the two objects, nor to the three interpretants. They appear together. The division between them is only in the mind of the analyst, not in reality. So it is not a classification, but a composition. The DO and the IO have a relation with each other, the IO is the part of the sign, that enables the sign to have a relation with the DO. I don´t know, if itis ok. to say, that a hexad is irreducible, it is an irreducible triad between a monad, an irreducible dyad, and an irreducible triad. The number of correlates is due to depth of analysis: 1. 3. 6, 10, 15, 21, 28, and so on. The distance between two numbers is the distance between the two numbers before plus one.
Best, Helmut
1. November 2025 um 15:22
"Jon Alan Schmidt" <[email protected]>
wrote:Helmut, List:
I am afraid that your use of the terminology here is still incorrect, at least from a Peircean standpoint.
- A dyad is a relation with two correlates, and a triad is a relation with three correlates.
- A dichotomy is a twofold division of something, and a trichotomy is a threefold division of something.
- Immediate/dynamical is a division of the object, not a relation between objects; so, it is a dichotomy, not a dyad.*
- Likewise, immediate/dynamical/final is a division of the interpretant, not a relation among interpretants; so, it is a trichotomy, not a triad.*
- There are no irreducible relations with more than three correlates (e.g., hexad); in accordance with Peirce's reduction thesis, these are always reducible to a combination of dyads and/or triads.
- Some triads are irreducible, but others are reducible to the dyads that they involve; this is precisely the distinction between a genuine triadic relation and a degenerate triadic relation.
- On the other hand, a dyadic relation is genuine where both correlates are existents, and degenerate where at least one correlate is a quality (CP 1.516, c. 1896; CP 1.528, 1903).
- As divisions, not relations, a trichotomy is not reducible to "subset-relations," and a dichotomy is not reducible to "a set and an element."
- It is also not the case that the dynamical object involves the immediate object, nor that the final interpretant involves the dynamical interpretant, which involves the immediate interpretant.**
- It is (at least theoretically) possible for a sign not to have a dynamical interpretant, but every sign has dynamical and immediate objects, and every sign has final and immediate interpretants.
* In one recently published manuscript, Peirce states that "the Object is Dyadic, and the Interpretant is Triadic. We therefore look to see whether there be not two Objects and three Interpretants" (SWS 200, 1905). However, in that context, he is clearly not saying that the object itself is a dyad, nor that the interpretant itself is a triad. Instead, he goes on to discuss the dyadic (dynamical) and monadic (immediate) objects, and then the triadic (final), dyadic (dynamical), and monadic (immediate) interpretants. Hence, the adjectives reflect the nature of the relation that Peirce viewed each correlate as having with the sign at that particular stage in the evolution of his speculative grammar.
** Again, it is essential to distinguish the dichotomy of objects and trichotomy of interpretants from the various trichotomies for classifying signs. Both objects and all three interpretants have such trichotomies in Peirce's late taxonomies, and the relation between any two of them is not involution but determination as logical constraint--when the six trichotomies are arranged in the proper order, each correlate "determines (i.e. renders definitely to be such as it will be)" the next correlate "in a particular manner" (CP 8.361, EP 2:487, 1908 Dec 25). Specifically, "a Possible can determine nothing but a Possible," while "a Necessitant can be determined by nothing but a Necessitant"; and "the Dynamoid Object determines the Immediate Object, which determines the Sign itself, which determines the Destinate Interpretant, which determines the Effective Interpretant, which determines the Explicit Interpretant" (SS 84, EP 2:481, 1908 Dec 23). The only controversy here is whether destinate=final and explicit=immediate or vice-versa.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
On Sat, Nov 1, 2025 at 1:48 AM Helmut Raulien <[email protected]> wrote:
Supplement: Jon, List,what I wrote below, would (in case of ...tomy) count only for the genuine (final interpretant) element of the trichotomy. It would also be so, that signs without a dynamical object would be possible, or without a final or a dynamical interpretant.31. Oktober 2025 um 19:39"Helmut Raulien" <[email protected]>wrote:Jon, List,My (temporal, so-far) assumption, that the object is a dyad, not a dichotomy, and that the interpretant is a triad, not a trichotomy, is based on the following thoughts:
- The hexad is the S,O,I- triad elaborated, or more deeply analysed. So it should be irreducible too. So it should contain more than one triad, also relations between all six elements, interwoven in such a way, that it is irreducible. Which exact manner I don´t know, not being a mathematician. But it should be irreducible relations, not dicho- and trichotomies, which are reducible: A trichotomy is reducible to two subset-relations inside each other, and a dichotomy to a set and an element.
- If the object were a dichotomy, the dynamical object should involve the immediate object. This is only the case in a true sign. But the immediate object might be false, it might contain a false supposition or a hallucination about the dynamical object. Then it would not be involved in it. But the DO then too would determine the IO, as also some true traits of its must also be represented in the IO, for the sign to denote it. That means, there is a relation between DO and IO (a dyad with the relation(s) denotation-determination), but not necessarily an involution. Similar thoughts can be thought about the interpretant.
Before, I had taken involvement as firstness of determination. But this is common-speech-involvement, not involution. Involution is total involvement, and involvement (common speech) mostly is partial: A member of parliament is involved in a decision not with her/his whole body and soul, but only by professional contribution, and temporarily only when speaking or voting.Best, Helmut
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