Abstract
In the paper we will employ set theory to study the formal aspects of quantum mechanics without explicitly making
use of space-time. It is demonstrated that von Neuman and Zermelo numeral sets, previously efectively used in the explanation
of Hardy’s paradox, follow a Heisenberg quantum form. Here monadic union plays the role of time derivative. The logical
counterpart of monadic union plays the part of the Hamiltonian in the commutator. The use of numerals and monadic union in
the classical probability resolution of Hardy’s paradox [1] is supported with the present derivation of a commutator for sets.