NeoFregeanism is an intriguing but elusive philosophy of mathematical exis-tence. At crucial points, it goes cryptic and metaphorical. I want to put forward an interpretation of neoFregeanism—perhaps not one that actual neoFregeans will embrace—that makes sense of much of what they say. NeoFregeans should embrace quantier variance.1 1. NeoFregeanism The neoFregeanism of Bob Hale and Crispin Wright is an attempt to resuscitate Frege’s logicism about arithmetic. Its goal is to combine two ideas. First: platonism about arithmetic. There really do exist numbers; numbers are mind-independent. Second: logicism. Arithmetic derives from logic plus denitions. Thus, arithmetic knowledge rests on logical knowledge, even though its object is a realm of mind-independent abstract entities. 1.1 Frege on arithmetic Let us review Frege’s attempt to derive arithmetic from logic plus denitions. “Arithmetic ” here means second-order Peano arithmetic. “Logic ” means (im-predicative) second-order logic.2 The “denition ” is what is now known as Hume’s Principle: Hume’s Principle ∀F∀G(#x:F x=#x:Gx↔Eq(F,G)) ∗Matti Eklund’s work connecting neoFregeanism to questions about the ontology of material objects (2006b, 2006a) sparked my interest in these topics. Thanks to Matti for helpful