Example: “Either this sign is red, or this number is even or odd.”
At the outer level, “either … or” connects two components. The first, “This sign is red,” is categorical. The second, “This number is even or odd,” is itself disjunctive.
Unless we distinguish the inner and outer occurrences of “or,” we may incorrectly count three alternatives at the same level. At the outer level the entire inner disjunction functions as one component.