On infinite ethics

Infinite numbers have long perplexed utilitarian ethicists: when dealing with an infinite universe, the existence of infinite positive utility and infinite negative utility presents a challenge. Even defining our current state becomes an uphill battle in such a scenario. Oxford philosopher Toby Ord offers a potential solution through the use of hyperreal numbers, a mathematical concept where infinite sums behave more like finite ones.

For instance, the sum of infinitely many twos is twice the sum of infinitely many ones. While this solution addresses certain issues, it also introduces new complexities, such as the need to choose an "ultrafilter" to pinpoint certain hyperreals, a choice that is not straightforward. Nonetheless, Elias Schmied views this as a significant philosophical breakthrough, making genuine progress in a seemingly insurmountable problem.

The author wonders why we didn't consider this approach in the first place, instead of accepting the conventional notion that infinity plus infinity equals infinity.