This paper proposes an account of homonymy reversals, based on Polya-urn processes. It assumes that words need to be conceptually grounded, and that the presence or absence of a class of referents may destabilize established meaning differences, as well as cause new meanings to emerge. The emergence of new meanings is conditioned on an asymetry of frequency between two words, and requires agents with a Theory of Mind. It will be also argued that markedness cannot be explained by frequency alone.