A Polynomial Approximation Method for Welfarist Axiology

DRAFT Several philosophers have suggested that it is impossible to formulate a theory of population ethics that simultaneously satisfies all of the necessary conditions set by our ethical intuitions (Arrhenius, 2000; Blackorby et al., 2004). However, we will attempt to demonstrate that, using the Stone-Weierstrass method, starting from scratch with a completely underspecified polynomial approximation function for commensurable cardinal utility (used here as a synonym for welfare) in a domain of commodities and populations, there are possible sets of functions that satisfy many if not all of our ethical intuitions (avoiding the Repugnant and Sadistic Conclusions, and others), thus providing a self-consistent welfarist axiology. DRAFT.