  In the landscape, if there is to be any prospect of scientific prediction, it
is crucial that there be states which are distinguished in some way. The
obvious candidates are states which exhibit symmetries. Here we focus on states
which exhibit discrete symmetries. Such states are rare, but one can speculate
that they are cosmological attractors. We investigate the problem in model
landscapes and cosmologies which capture some of the features of candidate flux
landscapes. In non-supersymmetric theories we find no evidence that such states
might be cosmologically favored. In supersymmetric theories, simple arguments
suggest that states which exhibit $R$ symmetries might be. Our considerations
lead us to raise questions about some popular models of eternal inflation.
