  This paper engages the question "Does the consistency of a set of axioms
entail the existence of a model in which they are satisfied?" within the frame
of the Frege-Hilbert controversy. The question is related historically to the
formulation, proof, and reception of G\"odel's Completeness Theorem. Tools from
mathematical logic are then used to argue that there are precise senses in
which Frege was correct to maintain that demonstrating consistency is as
difficult as it can be but also in which Hilbert was correct to maintain that
demonstrating existence given consistency is as easy as it can be.
