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)

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)

Many people believe that we have responsibility towards the distant future, but exactly how far this responsibility reaches and how we can find a reasonable ethical foundation for it has not been answered in any definitive manner. Future people have no power over us, they form no part of our moral community and it is unclear how we can represent them in a possible original position. All these problems can be circumvented when you take an impersonal decision criterion like maximizing (...) total or average utility. Such a sum-ranking criterion is neutral with respect to distance in time or space: my utility, my neighbour's and that of our descendants all carry the same weight. This makes future people an integral part of present decisions. Time-neutrality was defended by, among others, Sidgwick, Pigou and Ramsey. (shrink)

Suppose that time is infinitely long towards the future, and that each feasible action produces a finite amount of utility at each time. Then, under appropriate conditions, each action produces an infinite amount of utility. Does this mean that utilitarianism lacks the resources to discriminate among such actions? Since each action produces the same infinite amount of utility, it seems that utilitarianism must judge all actions permissible, judge all actions impermissible, or remain completely silent. If the future is infinite, that (...) is, the prospects for utilitarianism look bleak. (shrink)

There is a rich tradition within game theory, decision theory, economics, and philosophy correlating practical rationality with impartiality, and spatial and temporal neutrality. I argue that in some cases we should give priority to people over both times and places, and to times over places. I also show how three plausible dominance principles regarding people, places, and times conflict, so that we cannot accept all three. However, I argue that there are some cases where we should give priority to times (...) over people, suggesting that there is impersonal value to the distribution of high quality life over different times. (shrink)

This article is divided into two main sections. In section 1, I highlight some of the most significant results of Parfit's discussion of self-defeating theories in Part I of Reasons and Persons. I then argue, against Parfit, that, depending on the nature of the good, the structure of consequentialist, or agent-neutral, theories does not preclude the possibility that such theories may be self-defeating. In section 2, I discuss Parfit's ingenious argument against the self-interest theory, to the effect that as a (...) “hybrid” theory, which is “partial” with respect to people but “neutral” with respect to time, the self-interest theory occupies a dangerous middle ground that is open to attack from two sides: on one side, by a “pure” theory that is partial with respect to both people and times, and on the other side, by a “pure” theory that is neutral with respect to both people and times. I then raise doubts, prompted by the form of Parfit's argument, as to whether there is a general requirement that we treat people, places and times the same, except, perhaps, in cases involving special relations. Specifically, I suggest that there may be reason to treat space differently than time, and that there are compelling reasons to treat persons differently than time. (shrink)

Grill (2023) defends the Sum of Averages View (SAV), on which the value of a population is found by summing the average lifetime welfare of each generation or birth cohort. A major advantage of SAV, according to Grill, is that it escapes the Egyptology objection to average utilitarianism. But, we argue, SAV escapes only the most literal understanding of this objection, since it still allows the value of adding a life to depend on facts about other, intuitively irrelevant lives. Moreover, (...) SAV has a decisive drawback not shared with either average or total utilitarianism: it can evaluate an outcome in which every individual is worse off as better overall, even when exactly the same people exist in both outcomes. These problems, we argue, afflict not only Grill’s view but any view that uses a sum of subpopulation averages, apart from the limiting cases of average and total utilitarianism. (shrink)

Theories that use expected utility maximization to evaluate acts have difficulty handling cases with infinitely many utility contributions. In this paper I present and motivate a way of modifying such theories to deal with these cases, employing what I call “Direct Difference Taking”. This proposal has a number of desirable features: it’s natural and well-motivated, it satisfies natural dominance intuitions, and it yields plausible prescriptions in a wide range of cases. I then compare my account to the most plausible alternative, (...) a proposal offered by Arntzenius :31–58, 2014). I argue that while Arntzenius’s proposal has many attractive features, it runs into a number of problems which Direct Difference Taking avoids. (shrink)

The note addresses the problem of how utilitarianism and other finitely additive theories of value should evaluate infinitely long utility streams. We use the axiomatic approach and show that finite anonymity does not apply in an infinite framework. A stronger anonymity demand (fixed step anonymity) is proposed and motivated. Finally, we construct an ordering criterion that combines fixed step anonymity and strong monotonicity.

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must (resolve to) believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

In the context of worlds with infinitely many bearers of utility, we argue that several collections of natural Utilitarian principles--principles which are certainly true in the classical finite Utilitarian context and which any Utilitarian would find appealing--are inconsistent.

A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. (...) Given this, if God exists, our world—considered on the whole—is infinitely valuable. I further contend that this theistic picture makes our world's value unsurpassable. In support of this contention, I consider proposals for how infinitely valuable worlds might be improved upon, focusing on two main ways—adding value-bearers and increasing the value in present value-bearers. I argue that neither of these can improve our world. Depending on how each method is understood, either it would not improve our world, or our world is unsurpassable with respect to it. I conclude by considering the implications of my argument for the problem of evil more generally conceived. (shrink)

Our universe is both chaotic and (most likely) infinite in space and time. But it is within this setting that we must make moral decisions. This presents problems. The first: due to our universe's chaotic nature, our actions often have long-lasting, unpredictable effects; and this means we typically cannot say which of two actions will turn out best in the long run. The second problem: due to the universe's infinite dimensions, and infinite population therein, we cannot compare outcomes by simply (...) adding up their total moral values - those totals will typically be infinite or undefined. Each of these problems poses a threat to aggregative moral theories. But, for each, we have solutions: a proposal from Greaves let us overcome the problem of chaos, and proposals from the infinite aggregation literature let us overcome the problem of infinite value. But a further problem emerges. If our universe is both chaotic and infinite, those solutions no longer work - outcomes that are infinite and differ by chaotic effects are incomparable, even by those proposals. In this paper, I show that we can overcome this further problem. But, to do so, we must accept some peculiar implications about how aggregation works. (shrink)