  Then it follows from Classical Semantics that many sentences of mathematics are ontologically committed to mathematical objects. To see this, consider a typical mathematical theorem S, which involves some normal extensional occurrence of either singular terms or first-order quantifiers. By Classical Semantics, these expressions purport to refer to or range over mathematical objects. For S to be true, these expressions must succeed in doing what they purport to do. Consequently, for S to be true, there must be mathematical objects in the range of the variables. By Quine’s Criterion this means that S is ontologically committed to mathematical objects.