Jon, List I remember reading to you that we already had this debate on the hexadic signs and that each one remained on its positions. I see that you have not changed and I see that you are investing the podium according to your own concerns. In the scientific debate everything is allowed except to use the argument of authority. I have not changed either and even I think I have progressed a lot in clarification by creating the "trichotomic machine" ( Marty,Robert, « The trichotomic machine », *Semiotica*, vol. 2019, no 228, mai 2019, p. 173-192, ISSN <https://fr.wikipedia.org/wiki/International_Standard_Serial_Number> 1613-3692 <http://worldcat.org/issn/1613-3692&lang=fr>) which is a universal "machine". You will find a complete description of it at the URL https://www.academia.edu/s/d347b3561a/the-trichotomic-machine-brings-order-among-the-interpretants, with a perfectly clear result, that if you assign any final interpreter to category (3) then there can only exist one class of signs: 3-3-3 for the triadic signs and 3-3-3-3-3-3 for the hexadic signs. We can moreover easily see it from the evidence formulated by Peirce according to which a tertian (3) can only be determined by a tertian (letter to Lady Welby of December 23, 1908) which implies that, going up the chain of determinations, we can only find three. I also show that to talk about the 66 classes we must first find how and in what order are the other 4 trichotomies added by Peirce. If this point is neglected and the existence of decadic signs is posed, then the number of classes explodes because each missing determination in the chain of determinations multiplies by 3 the number of possible classes.
As for the presuppositions between classes it is true, as you rightly notice, that Peirce uses the term "involution" which is at least as difficult to handle (and to translate). The fact remains that the evidence he formulates in his letter to Lady Welby of December 23, 1908 is equivalent to presuppositions as Frege (amended by Strawson) formulated them. It's in this article. This clearly provides the basics of machine operation. In addition, I have shown, thirty years ago now, that Peirce's intuitions on the affinities between classes of signs could be formulated in a well-known lattice order structure (10 or 28 classes… and why not 66 with a collective agreement on choices of determinations. Best regards Robert Marty https://fr.wikipedia.org/wiki/Robert_Marty *"… in scientific inquiry, as in other enterprises, the maxim holds : nothing hazard, nothing gain." *(C. S. Peirce, MS 318, Pragmatism)
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