arity

illustrated in (39) and (37), however, differ in their adicity.

It is then possible to develop a semantics for first-order set theory (at least if there is an upper bound on the adicity of predicate constants in the language) using logical rather than set-theoretic notions--interpretations are relations, not first-order functions, the domain is replaced by a property true of exactly the individuals and so on.

n] [element of] PRD (where the superscript n denotes the adicity of F) and ([Alpha], [Beta], .

The conclusion is that a language adequate for the description of our experience must employ monadic, dyadic and triadic predicates but need contain no irreducible predicates of higher adicity (commonly expressed in Peirce's terminology as the claim that our experience contains irreducible firstness, secondness and thirdness).

This means that in the most up-to-date presentation of his theory, the primitives would not be predicates of properties/classes as here, but would rather be "multigrade" predicates of individuals with no fixed adicity.