We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...) additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. (shrink)

You are morally permitted to save your friend at the expense of a few strangers, but not at the expense of very many. However, there seems no number of strangers that marks a precise upper bound here. Consequently, there are borderline cases of groups at the expense of which you are permitted to save your friend. This essay discusses the question of what explains ethical vagueness like this, arguing that there are interesting metaethical consequences of various explanations.

In this paper we advance a new solution to Quinn’s puzzle of the self-torturer. The solution falls directly out of an application of the principle of instrumental reasoning to what we call “vague projects”, i.e., projects whose completion does not occur at any particular or definite point or moment. The resulting treatment of the puzzle extends our understanding of instrumental rationality to projects and ends that cannot be accommodated by orthodox theories of rational choice.

Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.

We introduce a St. Petersburg-like game, which we call the ‘Pasadena game’, in which we toss a coin until it lands heads for the first time. Your pay-offs grow without bound, and alternate in sign (rewards alternate with penalties). The expectation of the game is a conditionally convergent series. As such, its terms can be rearranged to yield any sum whatsoever, including positive infinity and negative infinity. Thus, we can apparently make the game seem as desirable or undesirable as we (...) want, simply by reordering the pay-off table, yet the game remains unchanged throughout. Formally speaking, the expectation does not exist; but we contend that this presents a serious problem for decision theory, since it goes silent when we want it to speak. We argue that the Pasadena game is more paradoxical than the St. Petersburg game in several respects. We give a brief review of the relevant mathematics of infinite series. We then consider and rebut a number of replies to our paradox: that there is a privileged ordering to the expectation series; that decision theory should be restricted to finite state spaces; and that it should be restricted to bounded utility functions. We conclude that the paradox remains live. (shrink)

Temkin presents a new way of thinking about equality and inequality that challenges the assumptions of philosophers, welfare economists, and others, and has significant implications on both a practical and theoretical level.

This paper argues for the existence of a fourth positive generic value relation that can hold between two items beyond ‘better than’, ‘worse than’, and ‘equally good’: namely ‘on a par’.

This book investigates the idea of inequality. According to the author, it does not address the question whether one should care about inequality nor which version is more plausible. Instead, its purpose is “to understand egalitarianism”, to “elucidate the notion of inequality”. The general thesis is that inequality is a “complex notion,” as shown by the fact that there are many different ways of measuring it. This is relentlessly detailed in a series of chapters that many will find rather hard (...) on the brain, with their panoplies of diagrams and technical distinctions, complete with acronyms. Still, the diagrams are clear enough, and the terminology to the point. (shrink)

The aim of this essay is to argue that, if a robust form of moral realism is true, then moral vagueness is ontic vagueness. The argument is by elimination: I show that neither semantic nor epistemic approaches to moral vagueness are satisfactory.

Killing civilians is worse than killing soldiers. Although this principle is widely affirmed, recent military practice and contemporary just war theory have undermined it. This article argues that killing an innocent person is worse the likelier it was, when you acted, that he would be innocent: riskier killings are worse than less risky killings. In war, killing innocent civilians is almost always riskier than killing innocent soldiers. So killing innocent civilians is worse than killing innocent soldiers. Since almost all civilians (...) are innocent in war, and since killing innocent civilians is worse than killing liable soldiers, killing civilians is worse than killing soldiers. (shrink)

One of the main reasons for providing formal semantics for languages is that the mathematical precision afforded by such semantics allows us to study and manipulate the formalization much more easily than if we were to study the relevant natural languages directly. Michael Tye and R. M. Sainsbury have argued that traditional set-theoretic semantics for vague languages are all but useless, however, since this mathematical precision eliminates the very phenomenon (vagueness) that we are trying to capture. Here we meet this (...) objection by viewing formalization as a process of building models, not providing descriptions. When we are constructing models, as opposed to accurate descriptions, we often include in the model extra ‘machinery’ of some sort in order to facilitate our manipulation of the model. In other words, while some parts of a model accurately represent actual aspects of the phenomenon being modelled, other parts might be merely artefacts of the particular model. With this distinction in place, the criticisms of Sainsbury and Tye are easily dealt with—the precision of the semantics is artefactual and does not represent any real precision in vague discourse. Although this solution to this problem is independent of any particular semantics a detailed account of how we would distinguish between representor and artefact within Dorothy Edgington's degree-theoretic semantics is presented. (shrink)

What makes careless conduct careless is easily one of the deepest and most contested questions in negligence law, tort theory, and moral theory. Answering it involves determining the conditions that make the imposition of risk unjustifiable, wrong, or impermissible. Yet there is a still deeper as well as overlooked and undertheorized question: Why does subjecting others to risk of harm call for justification in the first place? That risk can be impermissibly imposed upon otherspresupposes that imposing risk is the kind (...) of thing that can be impermissible. Unless imposing risk can be impermissible after all, unjustified risking is literally impossible. In this discussion, I explore what I call the moral significance of risking, arguing that the moral significance of risking resides in a certain kind of nonmaterial autonomy interest that is implicated whenever one imposes risk of harm on another. (shrink)

This paper surveys the current philosophical discussion of the ethics of risk imposition, placing it in the context of relevant work in psychology, economics and social theory. The central philosophical problem starts from the observation that it is not practically possible to assign people individual rights not to be exposed to risk, as virtually all activity imposes some risk on others. This is the ‘problem of paralysis’. However, the obvious alternative theory that exposure to risk is justified when its total (...) benefits exceed its total costs faces the standard distributional challenges of consequentialism. Forms of contractualism have been proposed as a solution, but how exactly such theories can be formulated remains problematic, especially when confronted with the difficult cases of mass, novel, risk such as climate change. (shrink)

We argue that there is a marked shift in the moral weight of an increment in a person's well-being when one moves from a case involving only intra-personal trade-offs to a case involving only inter-personal trads-offs. This shift, we propose, is required by the separateness of persons. We also argue that the Priority View put forward by Parfit cannot account for such a shift. We also outline two alternative views, an egalitarian view and a claims-based view, that can account for (...) this shift. (shrink)

This article argues that we must sever the ethics of war termination from the ethics of war initiation: a belligerent who embarks on a just war at time t1 might be under a duty to sue for peace at t2 before it has achieved its just war aims; conversely, a belligerent who embarks on an unjust war at t1 might acquire a justification for continuing at t2. In the course of making that argument, the article evaluates the various ways in (...) which belligerents end their wars. (shrink)

Proportionality in the resort to war determines a limit to the amount of harm it can be permissible to cause for the sake of achieving a just cause. It seems to follow that if a war has caused harm up to that limit but has not achieved the just cause, it should be terminated. I argue, however, that this is a mistake. Judgments of proportionality are entirely prospective and harms suffered or inflicted in the past should in general be ignored. (...) Yet past losses that could be partially redeemed by the achievement of the just cause may be an exception. (shrink)

This article discusses two doctrines of jus ex bello concerning whether and how to end wars. In Section I, I defend the claim that there is a distinct morality of ending wars. Section II rebuts a challenge that the account is too permissive of war. Section III rejects a forward-looking conception of proportionality for jus ex bello. In Section IV, I allow an exception in cases in which the just cause for the war has changed. In Section V, I defend (...) five principles governing how to end a war. (shrink)

In “Imposing Risks,” Judith Thomson gives a case in which, by turning on her stove, she accidentally causes her neighbor’s death. She claims that both the following are true: (1) she ought not to have caused her neighbor’s death; (2) it was permissible for her to turn her stove on. In this paper it is argued that it cannot be that both (1) and (2) are true, that (2) is true, and that therefore (1) is false. How this is so (...) is explained, and the implications of this position regarding the relation between rights and duties is explored. (shrink)

Important moral dilemmas arise in the context of what I have called jus terminatio and Darrel Moellendorf has called jus ex bello—the norms governing the termination of war. I discuss three dilemmas, showing how they also illuminate proportionality and jus ad bellum: morally accounting for new costs that arise during the course of a war; two variants of the “sunk-cost dilemma” in which an agent is permitted to contribute to a project that is all things considered morally unjust, when that (...) project is morally justified on a forward-looking basis; and the problem of moral hazard in peace negotiations. (shrink)