 In a nominalist reconstruction of mathematics, concrete entities will have to play the role that abstract entities play in platonistic accounts of mathematics, and concrete relations (such as the part-whole relation) have to be used to simulate mathematical relations between mathematical objects. But here problems arise. First, already Hilbert observed that, given the discretization of nature in quantum mechanics, the natural sciences may in the end claim that there are only finitely many concrete entities (Hilbert 1925). Yet it seems that we would need infinitely many of them to play the role of the natural numbers — never mind the real numbers. Where does the nominalist find the required collection of concrete entities? Secondly, even if the existence of infinitely many concrete objects is assumed, it is not clear that even elementary mathematical theories such as Primitive Recursive Arithmetic can be “simulated” by means of nominalistic relations (Niebergall 2000).