Infinite aggregation: expanded addition
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Infinite aggregation: expanded addition Hayden Wilkinson1
Springer Nature B.V. 2020
Abstract How might we extend aggregative moral theories to compare infinite worlds? In particular, how might we extend them to compare worlds with infinite spatial volume, infinite temporal duration, and infinitely many morally valuable phenomena? When doing so, we face various impossibility results from the existing literature. For instance, the view we adopt can endorse the claim that (1) worlds are made better if we increase the value in every region of space and time, or (2) that they are made better if we increase the value obtained by every person. But they cannot endorse both claims, so we must choose. In this paper I show that, if we choose the latter, our view will face serious problems such as generating incomparability in many realistic cases. Opting instead to endorse the first claim, I articulate and defend a spatiotemporal, expansionist view of infinite aggregation. Spatiotemporal views such as this do face some difficulties, but I show that these can be overcome. With modification, they can provide plausible comparisons in cases that we care about most. Keywords Infinite utility streams Utilitarianism Intergenerational equity Pareto Aggregation Infinite value
1 Introduction Suppose you found that the universe around you was infinite—that it extended infinitely far in space or in time and, as a result, contained infinitely many persons. How should this change your moral decision-making? Radically, it seems, if you & Hayden Wilkinson [email protected] 1
School of Philosophy, Australian National University, Canberra, ACT, Australia
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H. Wilkinson
accept a moral theory which gives some consideration to the total value in the world. Let’s assume that our universe is that way. Further, assume that infinitely many of the persons within it will have quite good lives (with positive value greater than some fixed [ 0). The total sum of value in the world is then positively infinite (or else undefined). But suppose you make any change you want to the world. If infinitely many positive-valued lives will still exist, then the total value will still be positively infinite (or else undefined). So you cannot compare the two worlds by their totals. Neither contains greater total value. Here is a more concrete case. You can either rescue one person from death, or rescue five others from death (each of whom would be better off not dying). And, either way, infinitely many other persons with valuable lives will exist throughout the universe. We can represent the outcome of saving one with W1 , and that of saving five with W5 . Each world contains an infinite plurality of persons fpa ; pb ; pc ; . . .g. And here the moral value of each person’s life is represented on an interval scale as 0 (if they die now) or 1 (if they get to enjoy the remainder of their life). W1 : W5 :
pa
pb
pc
pd
pe
pf
pg
ph
pi
pj
1 0
0 1
0 1
0 1
0 1
0 1
1 1
1 1
1 1
1 1
For these worlds, we cannot say
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