Arity
How many blanks a relation has. “Loves” has two — ___ loves ___ — and “gives” has three: ___ gives ___ to ___. Arity counts the places, never the things filling them, and that distinction decides a very old theological argument.
Arity is a count of blanks. "___ is asleep" has one, "___ loves ___" has two, "___ gives ___ to ___" has three. Logicians also call it adicity, and a relation with three blanks is called triadic or three-place.
The point that matters is what arity does *not* count. Filling three blanks does not require three different things: "Sam gave Sam's book to Sam" fills a three-place relation with one person. So a proof that some relation has exactly three places is not yet a proof that three individuals are involved in it. Nearly every argument for exactly three divine persons proves the first thing and needs the second.
Where this comes up
Sources
- Cody Gilmore, “Slots in Universals”, Oxford Studies in Metaphysics 8 (2013)