<p>This paper argues that meaning pluralism, the thesis that there can be alternative, inconsistent yet legitimate ways of applying a concept, can be reconciled with the thesis of the rigidity of referring expressions. Taken together, these two theses open the possibility of substantial, radical disagreements between speakers and between communities of speakers. Such disagreements occur when parties apply a concept legitimately yet differently, rendering the conflict rationally and empirically irremediable. This puzzling result arises when a single language evolves into separate branches, giving rise to substantial cross-linguistic disagreements grounded solely in differences between the languages used.</p>