Reconstructing Arrhenius’s impossibility theorems

Abstract

This paper provides a detailed reconstruction and analysis of Gustaf Arrhenius’s impossibility theorems in population ethics, which aim to demonstrate the incompatibility of various combinations of plausible conditions with the existence of a satisfactory population axiology. The paper presents a more concise and accessible proof structure using a simplified notation and corrects a perceived problem in Arrhenius’s sixth and favored theorem. It argues that his impossibility results hold under weaker versions of some of his conditions and highlights the role of the assumption of fine-grained welfare levels in the plausibility of these conditions. – AI-generated abstract.