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.
