  We construct a model to study the impact of instantons on the low lying
eigenvalue spectrum of the Dirac operator. The model is by necessity,
approximate, though it does incorporate the important symmetries of the
underlying field theory. The model also reproduces classical results in the
appropriate limits. We find that generic instanton ensembles lead to an
accumulation of eigenvalues around zero, and hence, break chiral symmetry. The
eigenvalue spectrum is divergent however, as the eigenvalue approaches zero.
This leads to a divergent chiral condensate in quenched QCD, and hence, shows
the theory to be pathological. In full QCD we find the novel result of a
divergent spectral density leading to chiral symmetry breaking, but, with a
finite condensate. This result holds for both $N_{f}=1$ and $N_{f}=2$. We also
compute correlation functions and find a massive $\eta^{'}$ and $\sigma$ in the
chiral limit. Whilst the divergence follows a power law, the strength of the
divergence is inversely proportional to the instanton density. To investigate
the impact of the divergence further, we analyse instanton ensembles derived by
"cooling" lattice gauge configurations. An important negative result is that
the chiral condensate is strongly dependent upon the number of cooling sweeps
performed. Whether the problem lies with cooling or with the identification of
topological objects is yet to be resolved.
