Among recent objections to Pascal's Wager, two are especially compelling. The first is that decision theory, and specifically the requirement of maximizing expected utility, is incompatible with infinite utility values. The second is that even if infinite utility values are admitted, the argument of the Wager is invalid provided that we allow mixed strategies. Furthermore, Hájek has shown that reformulations of Pascal's Wager that address these criticisms inevitably lead to arguments that are philosophically unsatisfying and historically unfaithful. Both the objections (...) and Hájek's philosophical worries disappear, however, if we represent our preferences using relative utilities rather than a one-place utility function. Relative utilities provide a conservative way to make sense of infinite value that preserves the familiar equation of rationality with the maximization of expected utility. They also provide a means of investigating a broader class of problems related to the Wager. (shrink)

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.

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.

In this paper, I argue for two theses. First, if Christianity is true, then morality should depend on the metaphysics of the afterlife. Second, if Christianity is true, then contemporary moral theory is mistaken. The argument for the first thesis rests on two premises. If rightness depends on an act’s effects on an individual, then—at least in part—it depends on the long-term effects on him. If rightness depends—at least in part—on the long-term effects on an individual, then it depends on (...) the metaphysics of the afterlife. The argument for the second thesis rests on how heaven or hell swamp other considerations. By changing assumptions about the nature of heaven or hell, who goes there, and standard mathematics, we end up with different ethical theories. Some of these assumptions conflict with contemporary moral theory regarding killing, letting die, and saving. (shrink)

Here, we argue for a mathematical equation that captures desert. Our procedure consists of setting out principles that a correct equation must satisfy and then arguing that our set of equations satisfies them. We then consider two objections to the equation. First, an objector might argue that desert and well-being separately contribute to intrinsic goodness, and they do not separately contribute. The concern here is that our equations treat them as separate contributors. Second, our set of desert-equations are unlike equations (...) in science because our equations involve multiple desert-equations with the applicable equation depending on how the variables are filled out. Neither objection succeeds. (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)

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)

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)

What if human joy went on endlessly? Suppose, for example, that each human generation were followed by another, or that the Western religions are right when they teach that each human being lives eternally after death. If any such possibility is true in the actual world, then an agent might sometimes be so situated that more than one course of action would produce an infinite amount of utility. Deciding whether to have a child born this year rather than next is (...) a situation wherein an agent may face several alternatives whose effects could well ramify endlessly on such suppositions, for the child born this year would be a different person—one who preferred different things, performed different actions, and had different descendants—from a child born next year. It has recently been suggested that traditional utilitarianism stumbles on such cases of infinite utility. Specifically, utilitarianism seems to require, for its application, that all experience of pleasure and pain cease at some time in the future or asymptotically approach zero.2 If neither of these conditions holds, then the utility produced by each of two alternative actions may turn out to be infinite, and utilitarianism thus loses its ability to discriminate morally between them. (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)

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)

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)

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)

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.

In this paper, we argue that in a possible world there is a determinate ranking of teams. Our argument rests on the premise: In theory, nothing prevents a determinate better than ranking. This premise in turn rests on assumptions with regard to stipulations regarding ‘better than’ and nature of a competition as well as a right answer theory of interpretation. We then speculate that in some actual leagues in some years, there were determinate rankings. We consider objections that focus on (...) ties, noise, intransitivity, meaning of ‘better than’, and league recognition of the best team. We finish by noting that the issues involved in sport also apply to ranking candidates to occupy roles in our lives. (shrink)

This thesis discusses the possibility of limited moral trade-offs between different people’s welfare. In chapter 2, I introduce the two central limited trade-off conditions. First, according to minimal infinite superiority, significantly benefiting one person matters more than slightly benefiting each of any number of better-off people. Second, according to minimal finite superiority, significantly benefiting many people matters more than slightly benefiting one person. I consider both axiological and deontic interpretations of these conditions. However, I explain why none of the simple (...) classic moral principles—the simple total and the maximin principles—satisfy both conditions. Furthermore, in chapter 3, I strengthen several proved impossibility results according to which no moral theory satisfies weak interpretations of these central trade-off conditions and several other seemingly plausible minimal conditions. I show that giving up structural axiological and deontic conditions is not a satisfactory solution to these paradoxes. In chapter 4, I discuss the modification of a background assumption of these impossibility results on the measurement of welfare. I show that, given a modification that allows for lexicographically ordered welfare components, a total principle can satisfy all the conditions of the impossibility results. However, I argue that such a modification is not entirely satisfactory because it does not apply in certain instances of the paradoxes. In chapter 5, I discuss a further weakening of minimal infinite superiority. However, I show that a suggested possibility result based on this modification is not valid and that further moral conditions, such as minimal finite superiority, need to be modified. Moreover, I argue that these modified conditions and the principle suggested in the possibility proof—a minimax complaint principle—do not capture the basic idea of the two central limited trade-off conditions sufficiently well. In chapter 6, I argue that other principles suggested for the task—the total claim principles—share the same fate as the simple total principles or the minimax complaint principle. In chapter 7, I propose new principles that take their structural roots from voting theory. I show that, in contrast to the other principles discussed, these principles give plausible verdicts where the other principles failed. Finally, in chapter 8, I consider possible objections levelled against this proposal, and I suggest solutions and avenues for future research. (shrink)

The distinction between intrinsic and extrinsic value can be traced back to Plato and Aristotle. I contend that the distinction has never been properly drawn. My main task is to formulate the distinction in a way that avoids the problems of the traditional formulations. ;After defending the traditional Moorean conception of intrinsic value against John Mackie's arguments from relativity and "queerness," and against recent attacks by Elizabeth Anderson and Shelly Kagan, I attempt to define two important types of extrinsic value (...) in terms of intrinsic value. First, I define instrumental value. The main problem with traditional definitions of instrumental value is that they fail to account for the fact that preventing something intrinsically evil from occurring seems to be just as worthwhile as bringing about something intrinsically good. I attempt to account for this fact by introducing a "contextualist" analysis of instrumental value. Next, I present and defend an analysis of contributory value. I compare contributory value with conditional intrinsic value, and present an argument to show that the notion of conditional intrinsic value faces problems that can be avoided by admitting the existence of contributory value. I then expand on the contextualist analysis of instrumental value, and provide an analysis of extrinsic value that explains what is common to instrumental and contributory value. I contend that my analysis can also account for other types of extrinsic value---for example, signatory value---and I defend my analysis against recent objections by Alastair Norcross involving the extrinsic values of actions. ;Finally, I argue that contributory value can help to solve a current problem in environmental ethics. The problem is this: how can it be that the last member of a species is more valuable than a similar member of a flourishing species ? I argue that diversity of goods increases the value of a whole; therefore, the last member of an endangered species has contributory value in virtue of its contribution to the world's biological diversity. (shrink)