Kripke’s work on rigid designation and the necessary a posteriori revolutionalized the philosophy of language. It has had almost no effect on conceptual analysis in moral and political theory. In this paper we use Kripkean arguments to analyse the claim of the essential contestability of concepts. We identify two different accounts of essential contestability. The first, Traditional Essential Contestability (TEC), is based on Gallie’s work and applies largely to traditions such as Christianity or liberalism. The second is Value Plural Essential Contestability (VPEC), which most subsequent writers seem to utilize. We analyse TEC, using Kripke’s historical or causal account of proper names and suggest that the subscript strategy can be used to overcome any claims about the essential nature of the contest. We argue that VPEC does not entail the essential contestability of concepts; instead it entails their incoherence. Using Kripke’s analysis of the rigid designation of natural kinds, such incoherence can be analysed modally. We suggest that either the subscript strategy can be used to overcome VPEC or that the concepts are indeed incoherent. Where such incoherence emerges, we need to break complex concepts down into constituent parts and re-analyse until the subscript strategy works. We argue that Kripke’s analysis enables us to break down conceptual dispute to the bare bones of value pluralism, wherein we can see more clearly where disputants’ moral values differ or where our own moral intuitions are in conflict. This can be overcome, since morality is, in part, ‘fictional’, in that social values are ones we construct and reconstruct. Moral values exist to the extent we think they exist. This bootstrapping quality both poses problems for conceptual analysis and enables us to overcome conflict through deliberation.