Genuine and degenerate thirdness
Peirce's distinction between three-place relations that genuinely mediate — sign, object, interpreter — and ones that only look three-placed. Specialists concede that no one has supplied a test for telling them apart, which is why the distinction cannot be used to disqualify teridentity.
Peirce did not think every three-place relation was equally interesting. Genuine thirdness involves real mediation — a sign brings an object and an interpreter into relation, and no pair of two-place relations does the job. Degenerate thirdness is three-placed in form only.
The obvious reply on behalf of a triadic argument is that teridentity is degenerate and so proves nothing about genuine triads. Two things block it. Specialists working on Peirce's reduction thesis report that "genuine" has in practice been defined as "irreducible" — which makes teridentity genuine, since it is irreducible. And even a successful criterion would only sort relation-shapes into two bins. Nothing in Peirce's description of mediation requires the three roles to be borne by three numerically different individuals.
Where this comes up
Sources
- “Is Peirce's Reduction Thesis Gerrymandered?”, Transactions of the C. S. Peirce Society (2022) / arXiv:2406.14058
- Jacqueline Brunning, “Genuine Triads and Teridentity” (1997)