cardinality
How many things there are — here, how many divine persons. Kept separate from arity, which counts the blanks in a relation: “the Father loves the Son” has two places whoever fills them, while the why-three question asks why the filling stops at a headcount of exactly three.
Cardinality counts occupants; arity counts places. "Loves" has two places no matter how many lovers exist — ___ loves ___ — while the why-three question asks how many divine persons there are. A relation can have exactly the right shape and the wrong headcount, which is why the two questions must not be merged.
Why the distinction decides arguments here: Swinburne's a priori argument claims it is a conceptual necessity that one divine person generates exactly two more; Mawson's reply is that no conceptual truth ranks singletons below couples or couples below throuples — comparative enrichment is not necessity. An argument that three suffices for unselfish love does not by itself show that a fourth is impossible or that a dyad is deficient; each direction needs its own premise.
In this corpus the why-exactly-three case tracks whether any argument closes the gap from "at least two" or "three suffices" to "exactly three, of necessity" — and so far records that gap as open, with Branson's monarchy bounding depth (no chains of origin) rather than breadth (how many from the source).
The mistaken everyday reading is "three is just the number of the relation." Roles and occupants are different counts, and the arguments for each fail differently.