  We survey a variety of cosmological problems where the issue of generality
has arisen. This is aimed at providing a wider context for many claims and
deductions made when philosophers of science choose cosmological problems for
investigation. We show how simple counting arguments can be used to
characterise parts of the general solution of Einstein's equations when various
matter fields are present and with different spatial topologies. Applications
are described to the problem of singularities, static cosmological models,
cosmic no hair theorems, the late-time isotropisation of cosmological models,
and the number of parameters needed to describe a general astronomical
universe.
