  We argue that in classical and quantum theories of gravity the configuration
space and Hilbert space may not be constructible through any finite procedure.
If this is the case then the "problem of time" in quantum cosmology may be a
pseudo-problem, because the argument that time disappears from the theory
depends on constructions that cannot be realized by any finite beings that live
in the universe. We propose an alternative formulation of quantum cosmological
theories in which it is only necessary to predict the amplitudes for any given
state to evolve to a finite number of possible successor states. The space of
accessible states of the system is then constructed as the universe evolves
from any initial state. In this kind of formulation of quantum cosmology time
and causality are built in at the fundamental level. An example of such a
theory is the recent path integral formulation of quantum gravity of
Markopoulou and Smolin, but there are a wide class of theories of this type.
