There are infinitely many ways the world might be, and there may well be infinitely many people in it. These facts raise moral paradoxes. We explore a conflict between two highly attractive principles: a Pareto principle that says that what is better for everyone is better overall, and a statewise dominance principle that says that what is sure to turn out better is better on balance. We refine and generalize this paradox, showing that the problem is faced by many theories (...) of interpersonal aggregation besides utilitarianism, and by many decision theories besides expected value theory. Considering the range of consistent responses, we find all of them to be quite radical. (shrink)

This chapter will amount to a detailed exposition and exploration of one of the most prominent arguments against the existence of an unsurpassable world: the argument from addition. Endorsed by a variety of thinkers such as St. Thomas Aquinas, Alvin Plantinga, and William Rowe, the argument from addition uses the possibility of adding good things to a candidate unsurpassable world to argue that every world is surpassable. While widely endorsed, the argument has come under recent criticism. By carefully working through (...) a targeted version of the argument, I set out to establish the following: (i) that a world can always contain more good things; (ii) that a suitably restricted additive aggregation principle allows us to say that adding more good things in a certain way is an improvement, and (iii) that objections to the argument from widespread value incomparability fail. (shrink)

For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...) separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (shrink)

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 worlds are made better if we increase the value in every region of space and time, or 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. (shrink)

Suppose that an altruistic agent who is uncertain between evidential and causal decision theory finds herself in a situation where these theories give conflicting verdicts. We argue that even if she has significantly higher credence in CDT, she should nevertheless act in accordance with EDT. First, we claim that the appropriate response to normative uncertainty is to hedge one's bets. That is, if the stakes are much higher on one theory than another, and the credences you assign to each of (...) these theories are not very different, then it is appropriate to choose the option that performs best on the high-stakes theory. Second, we show that, given the assumption of altruism, the existence of correlated decision makers will increase the stakes for EDT but leave the stakes for CDT unaffected. Together these two claims imply that whenever there are sufficiently many correlated agents, the appropriate response is to act in accordance with EDT. (shrink)

Aggregative moral theories face a series of devastating problems when we apply them in a physically realistic setting. According to current physics, our universe is likely _infinitely large_, and will contain infinitely many morally valuable events. But standard aggregative theories are ill-equipped to compare outcomes containing infinite total value so, applied in a realistic setting, they cannot compare any outcomes a real-world agent must ever choose between. This problem has been discussed extensively, and non-standard aggregative theories proposed to overcome it. (...) This paper addresses a further problem of similar severity. Physics tells us that, in our universe, how remotely in time an event occurs is _relative_. But our most promising aggregative theories, designed to compare outcomes containing infinitely many valuable events, are sensitive to how remote in time those events are. As I show, the evaluations of those theories are then relative too. But this is absurd; evaluations of outcomes must be absolute. So we must reject such theories. Is this objection fatal for all aggregative theories, at least in a relativistic universe like ours? I demonstrate here that, by further modifying these theories to fit with the physics, we can overcome it. (shrink)

Is the overall 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-additive axiologies (like average utilitarianism, rank-discounted utilitarianism, and variable value views) say 'no'. This distinction is practically important: additive axiologies support 'arguments from astronomical scale' which suggest (among other things) that it is overwhelmingly important for humanity to avoid premature extinction and ensure the existence of a (...) large future population, while non-additive axiologies need 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 implications with some additive axiology -- for instance, average utilitarianism converges to critical-level utilitarianism and various egalitarian theories converge to prioritiarianism. We further argue that real-world background populations may be large enough to make these limit results practically significant. This means that arguments from astronomical scale, and other arguments in practical ethics that seem to presuppose additive separability, may be truth-preserving in practice whether or not we accept additive separability as a basic axiological principle. (shrink)

This paper focuses on an underexplored challenge in infinite ethics. On realistic assumptions, if our universe is infinite, every nomologically possible history is actual and nothing we ever do makes a difference to the moral quality of the world as a whole. Call this thought Every History. This paper unpacks Every History and explores some of its ethical implications. Specifically, I argue that if Every History is true and the universe turns out to be infinite (1) our lives are globally (...) insignificant, (2) moral principles enjoining the promotion of value need to be given an appropriately scope-restricted interpretation, and (3) impersonal consequentialism faces a serious challenge. (shrink)

It is widely assumed that a literal understanding of someone’s self-deception that p yields the following contradiction. Qua self-deceiver, she does not believe that p, yet – qua self-deceived – she does believe that p. I argue that this assumption is ill-founded. Literalism about self-deception – the view that self-deceivers literally self-deceive – is not committed to this contradiction. On the contrary, properly understood, literalism excludes it.

We show that in infinite worlds the following three conditions are incompatible: The spatiotemporal ordering of individuals is morally irrelevant. All else being equal, the act of bringing about a good outcome with a high probability is better than the act of bringing about the same outcome with a low probability. One act is better than another only if there is a nonzero probability that it brings about a better outcome. The impossibility of combining these conditions shows that it is (...) more costly to endorse than has been previously acknowledged. (shrink)

The idea of the eternal recurrence is that everyone will live the exact same lives again an infinite number of times. Nietzsche appreciates that this would multiply the value of a single life by infinity, justifying intense emotional responses. His unpublished notes provide a cosmological argument for the eternal recurrence that anticipates Poincaré’s recurrence theorem. Nietzsche’s Thus Spoke Zarathustra describes its hero discovering this idea and struggling to accept the recurrence of all bad things. He eventually comes to love the (...) eternal recurrence because it will bring back all the joys of his life, and teaches this idea to others. (shrink)