 On Frege’s view, a single quantifier can bind an unsaturated position that is associated with a function that takes a single argument. But it is equally true that two quantifiers can bind two unsaturated positions associated with a function that takes a pair of arguments. For example, the proposition that everyone likes everyone can be represented with the formal sentence ‘\(\forall x \forall y [L(x, y)]\)’. Assuming that ‘Romeo’ and ‘Juliet’ indicate arguments, it follows that Romeo likes everyone, and that everyone likes Juliet—\(\forall y [L(r, y)]\) and \(\forall x [L(x, j)]\). And it follows from all three propositions that Romeo likes Juliet: \(L(r, j)\). The rules of inference for Frege’s logic capture this general feature of the universal quantifier. A variable bound by a universal quantifier can be replaced with a name for some individual in the domain. Correlatively, a name can be replaced with a variable bound by an existential quantifier. Given that Romeo likes Juliet, it follows that someone likes Juliet, and Romeo likes someone. Frege’s formalism can capture this as well: \(L(r, j)\); so \(\exists x [L(x, j)] \land \exists x [L(r, x)]\). And given either conjunct in the conclusion, it follows that someone likes someone: \(\exists x \exists y [L(x, y)]\). A single quantifier can also bind multiple argument positions, as in ‘\(\exists x [L(x, x)]\)’, which is true iff someone likes herself. Putting these points schematically: \(\forall x (\dots x \dots)\), so \(\dots n \dots\); and \(\dots n \dots\), so \(\exists x (\dots x \dots)\).