Plato’s partition argument infers that the soul has parts from the fact that the soul experiences mental conflict. Alasdair MacIntyre poses a dilemma for the argument that highlights an ambiguity in the concept of mental conflict. According to the first sense of conflict, a soul is in conflict when it has desires whose satisfaction conditions are logically incompatible. According to the second sense of conflict, a soul is in conflict when it has desires which are logically incompatible even when they are unsatisfied. The dilemma is therefore this: if the mental conflict is supposed to be the latter kind of conflict, then the partition argument is valid but is likely unsound; if it’s supposed to be the former kind, then the partition argument has true premises but is invalid. We explain this dilemma in detail and defend a dispositionalist solution to it.