List, Since there has been some discussion regarding genuine triadic relations, I quickly looked up a few (of the many) Peirce references to that relation. For Peirce, a genuine triadic relation is the logical and metaphysical mark or stamp of meaning. It is the structure through which 3ns -- mediation, generality, continuity -- acts in the universe. All semiosis arises through this irreducible triadic form.
Here are some places where Peirce discusses the genuine triadic relation and and a couple referencing the degenerate triadic relation (I checked some but not all of the sources); all but one concern semiosis as such; the other is the famous quotation in which Peirce notes that "The relation of giving is a genuine triadic relation:" (1903, Syllabus of Certain Topics of Logic) “A genuine triadic relation cannot be resolved into any combination of dyadic relations. For example, the relation of sign to its object and its interpretant is genuinely triadic, since if you take away any one of the three, the relation ceases to exist.” 1.345 “The relation of giving is a genuine triadic relation, for it involves a giver, a gift, and a receiver. Take away any one of the three and the relation is destroyed.”1.346 “A degenerate triadic relation is one which is not genuinely triadic, but may be reduced to a mere aggregate of dyadic relations.” 1.347 (ca. 1897–1902, “Logic as Semiotic”) “A sign is a tri-relative entity. It brings together a sign, its object, and its interpretant. This triadic relation is genuine; it cannot be reduced to dyadic relations without losing its essential character.” CP 5.484 (1906, “Prolegomena to an Apology for Pragmaticism”) “Thought is a species of genuine triadic relation. It involves a sign, its object, and its interpretant. The same may be said of communication in general, and indeed of law. Every genuine triadic relation involves a sign.” CP 3.456 (1903, Harvard Lectures on Pragmatism) “Every genuine triadic relation involves a sign, whether it be a sign of word or deed, or any other sort; for every triadic relation implies mediation, and mediation is of the nature of a sign.” and “A mere dyadic relation, like action and reaction, is not a sign, because it involves no mediation. But where there is mediation there is a sign, and where there is a sign, there is mediation.” EP 2:389–390 Best, Gary R
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