Is the value of a world just the sum of values contributed by each value-bearing entity in that world? Additively separable axiologies (like total utilitarianism, prioritarianism, and critical level views) say “yes”, but non-separable axiologies (like average utilitarianism, rank-discounted utilitarianism, and variable value views) say “no”. The distinction between additive and non-additive axiologies is practically important: The former support “arguments from astronomical scale” which suggest (among other things) that the far future is vastly more important than the near future, while the latter apparently do not. We show, however, that when there is a large enough “background population” unaffected by our choices, a wide range of non-additive axiologies converge in their practical implications with some additive axiology — for instance, in the limit, average utilitarianism converges with critical-level utilitarianism and various egalitarian theories converge with prioritiarianism. We further argue that we are in fact in the relevant limit — what is true in the limit is true of us. This means, among other things, that arguments from astronomical scale can succeed even if we reject axiological separability.