Gary R., Helmut, List: Picking up where I left off in my post yesterday, Peirce concisely summarizes how categorial involution manifests in triadic relations as follows.
CSP: Every triadic relationship involves three dyadic relationships and three monadic characters; just as every dyadic action involves two monadic characters. A monadic character involves nothing dyadic or triadic; nor does a dyadic action involve anything triadic. But a triad always involves three dyads and three monads; and a dyad involves two monads. (CP 6.331, 1907) Here, "monadic characters" or "monads" correspond to what he calls "correlates" in 1903--a sign is a monad that is *involved *in a triad, not *itself *a triad. The triadic relation in which a sign *represents *its object for its interpretant or (more generally) *mediates *between its object and interpretant (O-S-I) involves three dyadic relations (O-S, S-I, O-I), each of which involves two of the three monadic characters that are involved in the triadic relation (S, O, I). Again, Peirce states in 1903 that the trichotomies for those three correlates/monads *themselves *can be used to obtain ten classes of *triadic relations* (CP 2.238, EP 2:290), while the well-known ten classes of *signs *are instead derived from the trichotomies for just one such monadic character (S) and the two *dyadic relations *that involve it (O-S and S-I; CP 2.243, EP 2:291). As I have noted before, even in Peirce's later taxonomies, there is no separate trichotomy for the dyadic O-I relation because it is the same as the dyadic O-S relation--"the Interpretant, or Third, cannot stand in a mere dyadic relation to the Object, but must stand in such a relation to it as the Representamen itself does" (CP 2.274, EP 2:273). That brings me to Helmut's post below. HR: The three interpretants, as I think now, differently from before, are a triad, and the two objects a dyad. On the contrary, the three interpretants are *not *a triad because they are *not *the three correlates/monads that are involved in a triadic *relation*; instead, they are a trichotomy--a threefold *division *of the interpretant into "a relatively genuine 3ns, a relatively reactional 3ns ... and a relatively qualitative 3ns" (CP 5.72, EP 2:162). "A sign ... has three Interpretants, the *immediate*, to which it is primarily Tertian, the *dynamic*, to which it is secundally Tertian, the *rational*, to which it is genuinely Tertian" (R 339:247r <https://iiif.lib.harvard.edu/manifests/view/drs:15255301$467i>, 1905 Jul 7). Likewise, the two objects are *not *a dyad because they are *not *the two correlates/monads that are involved in a dyadic *relation*; instead, they are a dichotomy--a twofold *division *of the object into a genuine 2ns and a degenerate 2ns. "A sign ... has two Objects, the *immediate*, to which it is *degenerately *Secundan, the *dynamic*, to which it is *genuinely *Secundan" (ibid.). Unlike the trichotomies mentioned above, these phaneroscopic divisions obviously do not identify different classes of signs; instead, they reveal a total of six correlates/monads, each of which has *its own* trichotomy for classifying signs in Peirce's late taxonomies. Putting it all together, the following is my current understanding. - The genuine (dynamical) object and relatively genuine (final) interpretant are involved in a *genuine *triadic relation with the sign *itself *(Od-S-If), which *is not* reducible to their *genuine *dyadic relations with that sign (Od-S and S-If). - The genuine (dynamical) object and relatively reactional (dynamical) interpretant are involved in a *degenerate *triadic relation with a sign *token *(Od-S-Id), which *is *reducible to their *genuine *dyadic relations with that token as an *instance *of the sign (Od-S and S-Id). - The degenerate (immediate) object and relatively qualitative (immediate) interpretant are involved in *degenerate *dyadic relations with a sign token, which is why there are no separate trichotomies for those *internal *relations. Elaborating on the last bullet, a sign type is "a definitely significant Form," and "In order that a Type may be used, it has to be embodied in a Token which shall be a sign of the Type, and thereby of the object the Type signifies" (CP 4.537, 1906). But *how *does a token represent the corresponding type? "We have to distinguish *Symbols*, which are not themselves existent things from *Instances *of them, which are Icons of them" (NEM 3:877, 1908 Dec 5). The token is an *iconic *sign of the type, recognizable as such only by virtue of its *qualities*, so they are the two correlates/monads involved in a *degenerate *dyadic relation--for *any *iconic sign, "the dual relation between the sign and its object is degenerate" (CP 3.362, 1885), and "The relation to its object is a degenerate relation" (NEM 4:242, EP 2:306, 1901). Accordingly, I suggest that the type is the *immediate *object of the token, and that this is why the token has the same *dynamical *object as the type. Moreover, again for *any *iconic sign, "If it conveys information, it is only in the sense in which the object that it is used to represent may be said to convey information" (ibid.). Hence, the token has the same *immediate *interpretant as the type, which in the specific case of a word is its verbal definition. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Wed, Oct 29, 2025 at 11:44 AM Helmut Raulien <[email protected]> wrote: > Jon, Gary, List, > > Involution, if I´m right, appears in trichotomies, and correlation in > triads. The three interpretants, as I think now, differently from before, > are a triad, and the two objects a dyad. Not a tricho- resp. dichotomy! All > categories come together, so how can there be a dyad? Because it is only > prescinded. To me it makes sense to say, that in reality all categories > always appear together. And that even a sign triad with a qualisign has > three correlates, and the full hexad too. Even if the sign is > "possibility". Just then all three resp. six elements pretty much look the > same like each other. The meaning of the word "possibility" implies > anticipation. If it is only possibility, what is the object? Everything, > that determines this possibility. The interpretant is everything, that is > possible. As long, as everything, that determines the possibility, is > everything, it is pure possibiliy, and nothing happens. Only, when the > possibility is restricted, something happens, and then the object isn´t > anymore everything, but a subset of everything: Something. And an > interpretant is determined, which is different from pure possibility. The > interpretant then delivers a new sign, and so on. So, pure possibility is > an unstable thing, it just needs a little haphazard restriction, then > things start, and unfold. Sounds a bit like the beginning of "Science of > Logic" by Hegel, but I don´t like him. Anyway, my point in this post was, > that I think, that in reality (other than in prescinded parts) all > categories always come together, and degeneracy does not mean there, that > any elements are missing, but that some of them look quite similar to each > other. > > Best, Helmut >
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