  A detailed and rigorous analysis of G\"odel's proof of his first
incompleteness theorem is presented. The purpose of this analysis is two-fold.
The first is to reveal what G\"odel actually proved to provide a clear and
solid foundation upon which to base future research. The second is to construct
a coherent explication of G\"odel's proof that is not only approachable by the
non-specialist, but also brings to light the core principles underlying
G\"odel's proof.
