The principal aims of population axiology are to increase the wellbeing
of everyone, to prevent the suffering of future generations, and to make everyone more equal in these respects. A crisis in the pursuit of these goals came when Derek Parfit (1984) suggested that they inevitably result in a repugnant conclusion, that for any happy world, a miserable world of people whose lives were just barely worth living would be better, were it sufficiently populous. Since then, Gustaf Arrhenius (2000) has shown that these same principles also lead to a sadistic conclusion, that it can be better to add people with negative welfare rather than positive welfare
when adding people without affecting the original people’s welfare. What is more, he showed that there is no welfarist axiology that satisfies these three principles and yet avoids the repugnant conclusion. He called this the impossibility theorem for Theory X. This essay maintains that the ninth premiss of the impossibility theorem contains an invalid inference, and therefore presents a disproof of the theorem