  We introduce new formulations of aperiodicity and cofinality for finitely
aligned higher-rank graphs \Lambda, and prove that C*(\Lambda) is simple if and
only if \Lambda is aperiodic and cofinal. The main advantage of our versions of
aperiodicity and cofinality over existing ones is that ours are stated in terms
of finite paths. To prove our main result, we first characterise each of
aperiodicity and cofinality of \Lambda in terms of the ideal structure of
C*(\Lambda). In an appendix we show how our new cofinality condition simplifies
in a number of special cases which have been treated previously in the
literature; even in these settings, our results are new.
