This paper looks at the phenomenon of ethical vagueness by asking the question, how ought one to reason about what to do when confronted with a case of ethical vagueness? I begin by arguing that we must confront this question, since ethical vagueness is inescapable. I then outline one attractive answer to the question: we ought to maximize expected moral value when confronted with ethical vagueness. This idea yields determinate results for what one rationally ought to do in cases of (...) ethical vagueness. But what it recommends is dependent on which substantive theory of vagueness is true; one can't draw conclusions about how to reason about vagueness in ethics in the absence of concrete assumptions about the nature of vagueness. (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.

This paper attacks the Implicit Reference Class Theory of gradable adjectives and proposes instead a ?pluralist? approach to the semantics of those terms, according to which they can be governed by a variety of different types of standards, one, but only one, of which is the group-indexed standards utilized by the Implicit Reference Class Theory.

This chapter explores the implications of moral vagueness for non-naturalist metaethical theories like those recently championed by Shafer-Landau, Parfit, and others. It characterizes non-naturalism in terms of its commitment to seven theses: Cognitivism, Correspondence, Atomism, Objectivism, Supervenience, Non-reductivism, and Rationalism. It starts by offering a number of reasons for thinking that moral predicates are vague in the same way in which “red,” “tall,” and “heap” are said to be. It then argues that the moral non-naturalist seeking to countenance moral vagueness (...) faces a dilemma: are moral properties vague, or perfectly sharp? On either horn of the dilemma, serious problems arise for some of the central tenets of non-naturalism: vague properties seem to threaten Objectivism, Supervenience, and Non-reductivism; on the other hand, sharp properties raise problems for Supervenience and Rationalism. The difficulties on each horn of the dilemma are real, and while they may not be insuperable, they do, at the very least, drastically limit the things non-naturalists can consistently say about moral properties, facts, and reasons. (shrink)

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 paper argues that we can benefit or harm people by creating them, but only in the sense that we can create things that are good or bad for them. What we cannot do is to confer comparative benefits and harms to people by creating them or failing to create them. You are not better off (or worse off) created than you would have been had you not been created, for nothing has value for you if you do not exist, (...) not even neutral value. (shrink)

We argue that standard definitions of ‘vagueness’ prejudice the question of how best to deal with the phenomenon of vagueness. In particular, the usual understanding of ‘vagueness’ in terms of borderline cases, where the latter are thought of as truth-value gaps, begs the question against the subvaluational approach. According to this latter approach, borderline cases are inconsistent (i.e., glutty not gappy). We suggest that a definition of ‘vagueness’ should be general enough to accommodate any genuine contender in the debate over (...) how to best deal with the sorites paradox. Moreover, a definition of ‘vagueness’ must be able to accommodate the variety of forms sorites arguments can take. These include numerical, total-ordered sorites arguments, discrete versions, continuous versions, as well as others without any obvious metric structure at all. After considering the shortcomings of various definitions of ‘vagueness’, we propose a very general non-question-begging definition. (shrink)

We are often faced with choices that involve the weighing of people's lives against each other, or the weighing of lives against other good things. These are choices both for individuals and for societies. A person who is terminally ill may have to choose between palliative care and more aggressive treatment, which will give her a longer life but at some cost in suffering. We have to choose between the convenience to ourselves of road and air travel, and the lives (...) of the future people who will be killed by the global warming we cause, through violent weather, tropical disease, and heat waves. We also make choices that affect how many lives there will be in the future: as individuals we choose how many children to have, and societies choose tax policies that influence people's choices about having children. These are all problems of weighing lives. How should we weigh lives? Weighing Lives develops a theoretical basis for answering this practical question. It extends the work and methods of Broome's earlier book Weighing Goods to cover the questions of life and death. Difficult problems come up in the process. In particular, Weighing Lives tackles the well-recognized, awkward problems of the ethics of population. It carefully examines the common intuition that adding people to the population is ethically neutral - neither a good nor a bad thing - but eventually concludes this intuition cannot be fitted into a coherent theory of value. In the course of its argument, Weighing Lives examines many of the issues of contemporary moral theory: the nature of consequentialism and teleology; the transitivity, continuity, and vagueness of betterness; the quantitative conception of wellbeing; the notion of a life worth living; the badness of death; and others. This is a work of philosophy, but one of its distinctive features is that it adopts some of the precise methods of economic theory (without introducing complex mathematics). Not only philosophers, but also economists and political theorists concerned with the practical question of valuing life, should find the book's conclusions highly significant to their work. (shrink)

Orthodox decision theory gives no advice to agents who hold two goods to be incommensurate in value because such agents will have incomplete preferences. According to standard treatments, rationality requires complete preferences, so such agents are irrational. Experience shows, however, that incomplete preferences are ubiquitous in ordinary life. In this paper, we aim to do two things: (1) show that there is a good case for revising decision theory so as to allow it to apply non-vacuously to agents with incomplete (...) preferences, and (2) to identify one substantive criterion that any such non-standard decision theory must obey. Our criterion, Competitiveness, is a weaker version of a dominance principle. Despite its modesty, Competitiveness is incompatible with prospectism, a recently developed decision theory for agents with incomplete preferences. We spend the final part of the paper showing why Competitiveness should be retained, and prospectism rejected. (shrink)

Suppose one sets up a sequence of less and less valuable objects such that each object in the sequence is only marginally worse than its immediate predecessor. Could one in this way arrive at something that is dramatically inferior to the point of departure? It has been claimed that if there is a radical value difference between the objects at each end of the sequence, then at some point there must be a corresponding radical difference between the adjacent elements. The (...) underlying picture seems to be that a radical gap cannot be scaled by a series of steps, if none of the steps itself is radical. We show that this picture is incorrect on a stronger interpretation of value superiority, but correct on a weaker one. Thus, the conclusion we reach is that, in some sense at least, abrupt breaks in such decreasing sequences cannot be avoided, but that such unavoidable breaks are less drastic than has been suggested. In an appendix written by John Broome and Wlodek Rabinowicz, the distinction between two kinds of value superiority is extended from objects to their attributes. (shrink)

A search is under way for a theory that can accommodate our intuitions in population axiology. The object of this search has proved elusive. This is not surprising since, as we shall see, any welfarist axiology that satisfies three reasonable conditions implies at least one of three counter-intuitive conclusions. I shall start by pointing out the failures in three recent attempts to construct an acceptable population axiology. I shall then present an impossibility theorem and conclude with a short discussion of (...) how it might be extended to pluralist axiologies, that is, axiologies that take more values than welfare into account. (shrink)

Book synopsis: Vagueness is currently the subject of vigorous debate in the philosophy of logic and language. Vague terms-such as "tall", "red", "bald", and "tadpole"—have borderline cases ; and they lack well-defined extensions. The phenomenon of vagueness poses a fundamental challenge to classical logic and semantics, which assumes that propositions are either true or false and that extensions are determinate. Another striking problem to which vagueness gives rise is the sorites paradox. If you remove one grain from a heap of (...) sand, surely you must be left with a heap. Yet apply this principle repeatedly as you remove grains one by one, and you end up, absurdly, with a solitary grain that counts as a heap. This anthology collects papers in the field. After an introduction that surveys the field, the essays form four groups, starting with some historically notable pieces. The 1970s saw an explosion of interest in vagueness, and the second group of essays reprints classic papers from this period. The following group of papers represent current work on the logic and semantics of vagueness. The essays in the final group are contributions to the continuing debate about vague objects and vague identity. (shrink)

If the world itself is metaphysically indeterminate in a specified respect, what follows? In this paper, we develop a theory of metaphysical indeterminacy answering this question.

Vagueness is the study of concepts that admit borderline cases. The epistemology of vagueness concerns attitudes we should have towards propositions we know to be borderline. On this basis Andrew Bacon develops a new theory of vagueness in which vagueness is fundamentally a property of propositions, explicated in terms of its role in thought.

Here I compare two accounts of metaphysical indeterminacy (MI): first, the 'meta-level' approach described by Elizabeth Barnes and Ross Cameron in the companion to this paper, on which every state of affairs (SOA) is itself precise/determinate, and MI is a matter of its being indeterminate which determinate SOA obtains; second, my preferred 'object-level' determinable-based approach, on which MI is a matter of its being determinate---or just plain true---that an indeterminate SOA obtains, where an indeterminate SOA is one whose constitutive object (...) has a determinable property, but no unique determinate of that determinable. In S1, I first note an important difference between our accounts, concerning whether MI is taken to induce propositional indeterminacy; in S2, I highlight and defend certain advantages of my account; in S3, I address certain of Barnes and Cameron's objections to my account. (shrink)

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than” and “is as good as”. This field has been riddled with “paradoxes” which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. Already in Derek Parfit’s seminal contribution to the topic, an informal paradox — the Mere Addition Paradox — was presented and later contributions have (...) proved similar results.1 All of these contributions, however, have one thing in common: They all involve an adequacy condition that rules out Parfit’s Repugnant Conclusion: The Repugnant Conclusion: For any perfectly equal population with very high positive welfare, there is a population with very low positive welfare which is better, other things being equal.2 A number of theorists, however, have argued that we should accept the Repugnant Conclusion and hence that avoidance of this conclusion is not a convincing adequacy condition for a population axiology. Torbjörn Tännsjö, for example, argues that the Repugnant Conclusion is not at all repugnant but rather “an unsought, but acceptable, consequence of hedonistic utilitarianism”:3.. (shrink)

This is the classic work upon which modern-day game theory is based. What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry (...) it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences. (shrink)

This book presents an exploration of the idea of the common or social good, extended so that alternatives with different populations can be ranked. The approach is, in the main, welfarist, basing rankings on the well-being, broadly conceived, of those who are alive. The axiomatic method is employed, and topics investigated include: the measurement of individual well-being, social attitudes toward inequality of well-being, the main classes of population principles, principles that provide incomplete rankings, principles that rank uncertain alternatives, best choices (...) from feasible sets, and applications. The chapters are divided, with mathematical arguments confined to the second part. The first part is intended to make the arguments accessible to a more general readership. Although the book can be read as a defense of the critical-level generalized-utilitarian class of principles, comprehensive examinations of other classes are included. (shrink)

Introduction to one of the most important, controversial, and suggestive works of moral philosophy ever written.

Lara Buchak sets out a new account of rational decision-making in the face of risk. She argues that the orthodox view is too narrow, and suggests an alternative, more permissive theory: one that allows individuals to pay attention to the worst-case or best-case scenario, and vindicates the ordinary decision-maker.

How many people should there be? Can there be overpopulation: too many people living? I shall present a puzzling argument about these questions, show how this argument can be strengthened, then sketch a possible reply.

This study uses techniques from economics to illuminate fundamental questions in ethics, particularly in the foundations of utilitarianism. Topics considered include the nature of teleological ethics, the foundations of decision theory, the value of equality and the moral significance of a person's continuing identity through time.

In our lives, we aim to achieve welfare for ourselves, that is, to live good lives. But we also have another, more impartial perspective, where we aim to balance our concern for our own welfare against a concern for the welfare of others. This is a perspective of justice. Nils Holtug examines these two perspectives and the relations between them.

Temkin's book is a very original and deeply unsettling work of skeptical philosophy that mounts an important new challenge to contemporary ethics.

In this paper I explore the implications of moral vagueness (viz., the vagueness of moral predicates) for non-naturalist metaethical theories like those recently championed by Shafer-Landau, Parfit, and others. I characterise non-naturalism in terms of its commitment to 7 theses: Cognitivism, Correspondence, Atomism, Objectivism, Supervenience, Non-reductivism, and Rationalism. I start by offering a number of reasons for thinking that moral predicates are vague in the same way in which ‘red’, ‘tall’, and ‘heap’ are said to be. I then argue that (...) the moral non-naturalist seeking to countenance moral vagueness faces a dilemma: are moral properties vague, or perfectly sharp? On either horn of the dilemma, serious problems arise for some of the central tenets of non-naturalism: vague properties seem to threaten Objectivism, Supervenience, and Non-reductivism; on the other hand, sharp properties raise problems for Supervenience and Rationalism. The difficulties on each horn of the dilemma are real, and while they may not be insuperable, they do, at the very least, drastically limit the things non-naturalists can consistently say about moral properties, facts, and reasons. (shrink)

A set of arguments shows that either the Repugnant Conclusion and its variants are true or the better-than relation isn't transitive. Which is it? This is the most important question in population ethics. The answer will point the way to Parfit's elusive Theory X.

For the last thirty years or so, there has been a search underway for a theory that can accommodate our intuitions in regard to moral duties to future generations. The object of this search has proved surprisingly elusive. The classical moral theories in the literature all have perplexing implications in this area. Classical Utilitarianism, for instance, implies that it could be better to expand a population even if everyone in the resulting population would be much worse off than in the (...) original. The main problem has been to find an adequate population theory, that is, a theory about the moral value of states of affairs where the number of people, the quality of their lives, and their identities may vary. Since, arguably, any reasonable moral theory has to take these aspects of possible states of affairs into account when determining the normative status of actions, the study of population theory is of general import for moral theory. A number of theories have been proposed in the literature that purport to avoid counterintuitive implications such as the one mentioned above. The suggestions are diverse: introducing novel ways of aggregating welfare into a measure of value, revising the notion of a life worth living, questioning the way we can compare and measure welfare, counting people’s welfare differently depending on the temporal location or the modal features of their lives, and challenging the logic of axiological and normative concepts. We investigate the concepts and assumptions involved in these theories as well as their implications for population theory. In our discussion, we propose a number of intuitively appealing and logically weak adequacy conditions for an acceptable population theory. Finally, we consider whether it is possible to find a theory that satisfies all of these conditions. We prove that no such theory exists. (shrink)

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than ” and “is as good as”. This field has been riddled with paradoxes and impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. All of these results have one thing in common, however. They all involve an adequacy condition that rules out Derek (...) Parfit’s Repugnant Conclusion. Moreover, some theorists have argued that we should accept the Repugnant Conclusion and hence that avoidance of this conclusion is not a convincing adequacy condition for a population axiology. As I shall show in this chapter, however, one can replace avoidance of the Repugnant Conclusion with a logically weaker and intuitively more convincing condition. The resulting theorem involves, to the best of my knowledge, logically weaker and intuitively more compelling conditions than the other theorems presented in the literature. As such, it. (shrink)

How many people should there be? Can there be overpopulation: too many people living? I shall present a puzzling argument about these questions, show how this argument can be strengthened, then sketch a possible reply.

Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously and randomly choose how to resolve (...) the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)

Those who model doxastic states with a set of probability functions, rather than a single function, face a pressing challenge: can they provide a plausible decision theory compatible with their view? Adam Elga and others claim that they cannot, and that the set of functions model should be rejected for this reason. This paper aims to answer this challenge. The key insight is that the set of functions model can be seen as an instance of the supervaluationist approach to vagueness (...) more generally. We can then generate our decision theory by applying the general supervaluationist semantics to decision-theoretic claims. The result: if an action is permissible according to all functions in the set, it’s determinately permissible; if impermissible according to all, determinately impermissible; and – crucially – if permissible according to some, but not all, it’s indeterminate whether it’s permissible. This proposal handles with ease some difficult cases ) on which alternative decision theories falter. One reason this view has been overlooked in the literature thus far is that all parties to the debate presuppose that an acceptable decision theory must classify each action as either permissible or impermissible. But I will argue that this thought is misguided. Seeing the set of functions model as an instance of supervaluationism provides a compelling motivation for the claim that there can be indeterminacy in the rationality of some actions. (shrink)

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations \is better than" and \is as good as". This eld has been riddled with para- doxes and impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. All of these results have one thing in common, however. They all involve an adequacy condition that rules out Derek (...) Par t's Repugnant Conclusion. Moreover, some theorists have argued that we should accept the Repugnant Conclusion and hence that avoidance of this conclusion is not a convincing adequacy condition for a population axiology. As I shall show in this chapter, however, one can replace avoid- ance of the Repugnant Conclusion with a logically weaker and intuitively more convincing condition. The resulting theorem involves, to the best of my knowledge, logically weaker and intuitively more compelling con- ditions than the other theorems presented in the literature. As such, it challenges the very existence of a satisfactory population ethics. (shrink)

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than” and “is as good as”. This field has been riddled with impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies.1 All of these results have one thing in common, however. They all involve an adequacy condition that rules out Derek Parfit’s Repugnant Conclusion: (...) The Repugnant Conclusion: For any perfectly equal population with very high positive welfare, there is a population with very low positive welfare which is better, other things being equal.2 1 The informal Mere Addition Paradox in Parfit (1984), pp. 419ff is the locus classicus. For an informal proof of a similar result with stronger assumptions, see Ng (1989), p. 240. A formal proof with slightly stronger assumptions than Ng’s can be found in Blackorby and Donaldson (1991). For theorems with much weaker assumptions, see my (1999), (2000b), and especially (2000a), (2001), and (2009). 2 See Parfit (1984), p. 388. My formulation is more general than Parfit’s apart from that he doesn’t demand that the people with very high welfare are equally well off. Expressions such as “a population with very high positive welfare”, “a population with very low positive welfare”, etc., are elliptical for the more cumbersome phrases “a population consisting only of lives with.. (shrink)