 Yet appeal to second-order logic in the philosophy of mathematics is by no means uncontroversial. A first objection is that the ontological commitment of second-order logic is higher than the ontological commitment of first-order logic. After all, use of second-order logic seems to commit us to the existence of abstract objects: classes. In response to this problem, Boolos has articulated an interpretation of second-order logic which avoids this commitment to abstract entities (Boolos 1985). His interpretation spells out the truth clauses for the second-order quantifiers in terms of plural expressions, without invoking classes. For instance, an second-order expression of the form \(\exists x F(x)\) is interpreted as: “there are some (first-order objects) x such that they have the property F”. This interpretation is called the plural interpretation of second-order logic. It is controversial whether there is a real difference between the mathematical use of pluralities and of sets (Linnebo 2003). Nevertheless it is clear that an appeal to the plural interpretation of second-order logic will be tempting for nominalist versions of structuralism.