Teridentity
Peirce's three-place identity relation: a is identical with a is identical with a. It has three places that cannot be reduced to two, and exactly one individual fills all three — which makes it the standing counterexample to any argument that moves from “the structure has three places” to “there are three of them”.
Peirce needed a way to say, in the algebra of relations, that three things are all the same thing. Teridentity is that relation: it holds of the triple ⟨a, a, a⟩ and of nothing else.
It has an awkward property for anyone who wants to argue from threeness. Teridentity is genuinely three-placed — it cannot be built up out of two-place relations — and it is satisfied by exactly one individual. So here, in the work of the logician most often cited for the irreducibility of triads, is a triad with one occupant. The proof and the counterexample come from the same desk.
Where this comes up
Sources
- Debby research packet OTC-002, on the slot-to-person bridge
- “Is Peirce's Reduction Thesis Gerrymandered?”, Transactions of the C. S. Peirce Society (2022) / arXiv:2406.14058