Creative Objectivism, a powerful alternative to Constructivism

It is problematic to allow reasoning about infinite sets to be as unconstrained as that about finite sets. Yet Constructivism seems too restrictive in not allowing one to assume that an ideal computer program will either halt or not halt. Creative Objectivism considers as meaningful any property of integers which is determined by a recursively enumerable set of events. This captures the hyperarithmetical sets of integers and beyond thus including some sets that require quantification over the reals. This philosophy assumes mathematics is a human endeavor that creates objective truth by discovering meaningful properties of the integers that are determined by events that can be enumerated in a universe that may be potentially infinite. This philosophy leads to an “experimental” approach to extending mathematics.