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Next: Introduction
Abstract:
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.