In a 1900 paper entitled "On the Number Concept", the formalist mathematician David Hilbert proposed a set of axioms from which he hoped arithmetic might be derived. The last of these axioms was an "Axiom of Completeness" stipulating that: "It is not possible to adjoin to the system of numbers any collection of things so that in the combined collection the preceding axioms are satisfied; that is, briefly put, the numbers form a system of objects which cannot be enlarged with the preceding axioms continuing to hold."¹