Charles Sanders Peirce
American logician, mathematician and founder of pragmatism, who worked out the algebra of relations and argued that three-place relations are irreducible. The same body of work supplies both the best formal support for a triadic argument and its cleanest counterexample.
Peirce spent his life on logic, mathematics and the theory of signs, published comparatively little of it, and turned out to have been decades ahead on several fronts at once. The algebra of relations is one of them.
His reduction thesis — three-place relations cannot be built from two-place ones, and anything larger can be built from three-place ones — is the strongest formal result any argument from threeness can appeal to, and it has since been given proofs he never wrote.
He is also the author of the counterexample. Teridentity, the three-place relation of a thing to itself twice over, is irreducibly triadic and has one occupant. Anyone who wants to use Peirce to prove that a triadic structure needs three individuals has to explain why Peirce's own flagship triad does not.
Where this comes up
Sources
- Debby research packet OTC-002, on Peirce's reduction thesis