Infinite utility and Van Liedekerke's impossibility: A solution

Abstract

The challenge of comparing infinite utility streams does not undermine utilitarianism in practice, as the finite lifespan of the universe and sentient beings ensures that expected utility values remain finite. Theoretically, the perceived incompatibility between monotonicity and time-neutrality arises from a misapplication of temporal neutrality to infinite permutations. While the principle of more utility and the overtaking criterion are intuitively compelling, they appear to conflict with time-neutrality when an infinite number of utility repositions are allowed. This conflict is resolved by distinguishing between weak and strong versions of temporal neutrality. Finitistic or weak time-neutrality—which requires indifference only after a finite number of interchanges—remains a valid utilitarian axiom. In contrast, strong temporal neutrality, involving infinite repositionings, is not a necessary requirement because the cumulative effect of an infinite number of zero-difference changes is mathematically indeterminate. By restricting time-neutrality to its finitistic form, utilitarianism consistently upholds monotonicity and the overtaking criterion while navigating the paradoxes of infinity. This approach preserves the theoretical robustness of utilitarian frameworks against claims of impossibility or meta-ethical unacceptability. – AI-generated abstract.