The mere addition paradox, parity and vagueness

Abstract

Derek Parfit’s mere addition paradox has generated a large literature. This paper articulates one response to this paradox—which Parfit himself suggested—in terms of a formal account of the relation of parity. I term this response the parity view'. It is consistent with transitivity of at least as good as’, but implies incompleteness of this relation. The parity view is compatible with critical-band utilitarianism if this is adjusted to allow for vagueness. John Broome argues against accounts which involve incompleteness. He thinks they are based on an intuition of neutrality', which is most naturally understood in terms of equality. There is no rationale, on Broome's view, for seeing it as incommensurateness’ which leads to incompleteness. Parity provides one. Broome’s worries that incommensurateness' makes neutrality implausibly greedy’, and that `incommensurateness’ and vagueness are incompatible do not constitute a knock-down case against the parity view. Similar worries arise for his preferred vagueness view.