Weak Superiority, Imprecise Equality and the Repugnant Conclusion – Erratum

Neither Observation 3 nor Observation 4 assumes Non-diminishing Marginal Value. But it does make a difference to assume Non-diminishing Marginal Value. Suppose first we accept Conditions 3 and 4 (i.e. Constant Marginal Value) together with the Archimedean Property (Condition 8). Consider an infinite standard sequence q, 2q, 3q, ..., nq according to Definition 9, where n is any integer, and let b be an object which is better than q. If b were lexically better than q, then the standard sequence q, 2q, 3q, ..., nq would be strictly bounded; but since it is infinite, b being lexically better than q would violate the Archimedean Property. Hence, under Constant Marginal Value, the Archimedean Property excludes any case of lexical betterness. This follows directly from the assumptions and does not depend on any Continuum Argument.