- 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.
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, 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.
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
_ _ _ _ _ _ _ _ _ _ ► 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> . 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.
