Infinities in ethics
Infinities in ethics pose some difficult problems. For example, if we're in a big world, there are already infinite numbers of good and bad things. Adding or removing finitely many of them leaves infinitely many of both. This means aggregative consequentialist theories (those that maximize the sum of the values of individual structures) will be indifferent between any acts with merely finite effects.
Nick Bostrom wrote a paper discussing various possible solutions to this problem of "infinitarian paralysis" (as well as the "fanaticism" problem of theories that would sacrifice anything for a small chance of an infinite payoff).
For example, one could look at the density of value, use hyperreal numbers, use discounting in time and space, or ignore very small probabilities. These solutions all have their own problems.
- Infinite Ethics, by Nick Bostrom
- Philosophical implications of inflationary cosmology