Thread by @LedermanHarvey

Some thoughts on @tobyordoxford's interesting preprint 1/n

https://twitter.com/tobyordoxford/status/1971241223760543922

Hyperreals offer an important approach to infinite ethics! But I'm not convinced that they are a "proof of concept" that there is a good solution, definitely not convinced they're better than other approaches, and unclear on what progress they help us make. 2/n

Toby is admirably clear about the limitations of the approach in the paper; less clear in the thread. Two sorts of problems for the use of hyperreals in infinite ethics that have been well-known for some time. 3/n

First problem: relativity to choice of ultrafilter. The hyperreals are defined only relative to a choice of ultrafilter. This is an arbitrary choice of which sets count as "large" in the naturals. But it affects how summation is extended! 4/n

Hard to believe there's an ultrafilter that's privileged from the perspective of ethics. Toby suggests ranking one sum better than another iff better for every choice of ultrafilter. But then we're back with the usual "overtaking" criterion, so this isn't a new proposal at all. 5/n

Second problem: relativity to an order on the population. Like usual kinds of infinite summation, this one depends on an order to be defined. But if we're looking at an infinite population, it's implausible that this order matters ethically. 6/n

This is clearest if the infinite population exists at the same time. Why should starting at one point in space be better than another? But even if all people live in succession; living later doesn't make you matter less than living earlier. 7/n

TBC: I think we need to think more about this sort of approach! There's a lot to learn and I'm glad Toby is bringing people's attention to it. But I'm not convinced this is the right direction and I also fear "fancy math" can distract from "deep, well-known conceptual problems" 8/n

My own view is that Finite Anonymity is too weak as a criterion of impartiality, we need to accept incompleteness in infinite rankings, and that a very different (standard) approach is close to the best we can do in that setting. 9/n

arxiv.org/abs/2408.05851

(Oh also: all of this is just about ethics of infinite populations, not on the problems in decision theory, though I suspect similar issues arise there.) 10/10