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.

We can start with some science fiction. Here on Earth, I enter the Teletransporter. When I press some button, a machine destroys my body, while recording the exact states of all my cells. The information is sent by radio to Mars, where another machine makes, out of organic materials, a perfect copy of my body. The person who wakes up on Mars seems to remember living my life up to the moment when I pressed the button, and he is in (...) every other way just like me. Of those who have thought about such cases, some believe that it would be I who would wake up on Mars. They regard Teletransportation as merely the fastest way of travelling. Others believe that, if I chose to be Teletransported, I would be making a terrible mistake. On their view, the person who wakes up would be a mere Replica of me. (shrink)

Might it be that world itself, independently of what we know about it or how we represent it, is metaphysically indeterminate? This article tackles in turn a series of questions: In what sorts of cases might we posit metaphysical indeterminacy? What is it for a given case of indefiniteness to be 'metaphysical'? How does the phenomenon relate to 'ontic vagueness', the existence of 'vague objects', 'de re indeterminacy' and the like? How might the logic work? Are there reasons for postulating (...) this distinctive sort of indefiniteness? Conversely, are there reasons for denying that there is indefiniteness of this sort? (shrink)

A persistent argument against the transitivity assumption of rational choice theory postulates a repeatable action that generates a significant benefit at the expense of a negligible cost. No matter how many times the action has been taken, it therefore seems reasonable for a decision-maker to take the action one more time. However, matters are so fixed that the costs of taking the action some large number of times outweigh the benefits. In taking the action some large number of times on (...) the grounds that the benefits outweigh the costs every time, the decision-maker therefore reveals intransitive preferences, since once she has taken it this large number of times, she would prefer to return to the situation in which she had never taken the action at all. We defend transitivity against two versions of this argument: one in which it is assumed that taking the action one more time never has any perceptible cost, and one in which it is assumed that the cost of taking the action, though (sometimes) perceptible, is so small as to be outweighed at every step by the significant benefit. We argue that the description of the choice situation in the first version involves a contradiction. We also argue that the reasoning used in the second version is a form of similarity-based decision-making. We argue that when the consequences of using similarity-based decision-making are brought to light, rational decision-makers revise their preferences. We also discuss one method that might be used in performing this revision. (shrink)

Total utilitarianism implies Parfit's repugnant conclusion. For any world containing ten billion very happy people, there is a better world where a vast number of people have lives barely worth living. One common response is to claim that life in Parfit's Z is better than he suggests, and thus that his conclusion is not repugnant. This paper shows that this strategy cannot succeeed. Total utilitarianism also implies a reverse repugnant conclusion. For any world where ten billion people have lives of (...) excruciating agony, there is a worse world where a vast number of people have lives almost worth living. This reverse repugnant conclusion is at least as repugnant as Parfit's original. If we avoid the latter by raising the zero level, then the former becomes more repugnant. We cannot save total utilitarianism by tinkering with the zero level. (shrink)

It is notoriously difficult to find an intuitively satisfactory rule for evaluating populations based on the welfare of the people in them. Standard examples, like total utilitarianism, either entail the Repugnant Conclusion or in some other way contradict common intuitions about the relative value of populations. Several philosophers have presented formal arguments that seem to show that this happens of necessity: our core intuitions stand in contradiction. This paper assesses the state of play, focusing on the most powerful of these (...) ‘impossibility theorems’, as developed by Gustaf Arrhenius. I highlight two ways in which these theorems fall short of their goal: some appeal to a supposedly egalitarian condition which, however, does not properly reflect egalitarian intuitions; the others rely on a background assumption about the structure of welfare which cannot be taken for granted. Nonetheless, the theorems remain important: they give insight into the difficulty, if not perhaps the impossibility, of constructing a satisfactory population axiology. We should aim for reflective equilibrium between intuitions and more theoretical considerations. I conclude by highlighting one possible ingredient in this equilibrium, which, I argue, leaves open a still wider range of acceptable theories: the possibility of vague or otherwise indeterminate value relations. (shrink)

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.

This paper demarcates a theoretically interesting class of "evaluational adjectives." This class includes predicates expressing various kinds of normative and epistemic evaluation, such as predicates of personal taste, aesthetic adjectives, moral adjectives, and epistemic adjectives, among others. Evaluational adjectives are distinguished, empirically, in exhibiting phenomena such as discourse-oriented use, felicitous embedding under the attitude verb `find', and sorites-susceptibility in the comparative form. A unified degree-based semantics is developed: What distinguishes evaluational adjectives, semantically, is that they denote context-dependent measure functions ("evaluational (...) perspectives")—context-dependent mappings to degrees of taste, beauty, probability, etc., depending on the adjective. This perspective-sensitivity characterizing the class of evaluational adjectives cannot be assimilated to vagueness, sensitivity to an experiencer argument, or multidimensionality; and it cannot be demarcated in terms of pretheoretic notions of subjectivity, common in the literature. I propose that certain diagnostics for "subjective" expressions be analyzed instead in terms of a precisely specified kind of discourse-oriented use of context-sensitive language. I close by applying the account to `find x PRED' ascriptions. (shrink)

Ethicists and economists commonly assume that if A is all things considered better than B, and B is all things considered better than C, then A is all things considered better than C. Call this principle Transitivity. Although it has great conceptual, intuitive, and empirical appeal, I argue against it. Larry S. Temkin explains how three types of ethical principle, which cannot be dismissed a priori, threaten Transitivity: (a) principles implying that in some cases different factors are relevant to comparing (...) A to C than to comparing A to B or B to C; (b) principles of limited scope; (c) principles implying that morally relevant differences in degree can amount to differences in kind. My counterexamples employ a principle of type (c): pleasures and pains enormously different in intensity differ in kind. Temkin has also endorsed this type of counterexample, using arguments based on earlier drafts of this paper. (shrink)

Axiomatic utility theory plays a foundational role in some accounts of normative principles. In this context, it is sometimes argued that transitivity of “better than” is a logical truth. Larry Temkin and Stuart Rachels use various examples to argue that “better than” is non–transitive, and that transitivity is not a logical truth. These examples typically involve some sort of “discontinuity.” In his discussion of one of these examples, John Broome suggests that we should reject the claim which involves “discontinuity.” We (...) can, I suggest, make sense of the examples which Temkin uses while sacrificing neither transitivity nor “discontinuity.” This response to Temkin's examples involves developing and modifying James Griffin's account of “discontinuity.” If the account of “discontinuity” seems implausible, that is because of a failure to allow for vagueness. A similar argument can be made in the context of the well-known “repugnant conclusion.” Footnotes1 This paper emerged from a discussion in one of John Broome's seminars. I am very grateful to John Broome, Erik Carlson, James Griffin, Wlodek Rabinowicz, Stuart Rachels, and Larry Temkin for allowing me to read various forthcoming manuscripts which are mentioned in the paper. I am also extremely grateful to Gustaf Arrhenius, Walter Bossert, Luc Bovens, John Broome, Richard Cookson, Robin Cubitt, James Griffin, Graham Loomes, Ben McQuillin, Shepley Orr, Wlodek Rabinowicz, Stuart Rachels, Bob Sugden, and two anonymous referees for comments on earlier versions. Any errors or omissions are mine. (shrink)

Larry Temkin famously argues that what he calls spectrum arguments yield strong reason to reject Transitivity, according to which the ‘all-things-considered better than’ relation is transitive. Spectrum arguments do reveal that the conjunctions of independently plausible claims are inconsistent with Transitivity. But I argue that there is very strong independent reason to reject such conjunctions of claims, and thus that the fact that they are inconsistent with Transitivity does not yield strong reason to reject Transitivity.

According to the Repugnant Conclusion: Compared with the existence of many people who would all have some very high quality of life, there is some much larger number of people whose existence would be better, even though these people would all have lives that were barely worth living. I suggest some ways in which we might be able to avoid this conclusion. I try to defend a strong form of lexical superiority.

The Rachels–Temkin spectrum arguments against the transitivity of better than involve good or bad experiences, lives, or outcomes that vary along multiple dimensions—e.g., duration and intensity of pleasure or pain. This paper presents variations on these arguments involving combinations of good and bad experiences, which have even more radical implications than the violation of transitivity. These variations force opponents of transitivity to conclude that something good is worse than something that isn’t good, on pain of rejecting the good altogether. That (...) is impossible, so we must reject the spectrum arguments. (shrink)

A presentation of the Lewis-Sider argument from vagueness for unrestricted composition and possible responses.

This paper deals with problems that vagueness raises for choices involving evaluative tradeoffs. I focus on a species of such choices, which I call ‘qualitative barrier cases.’ These are cases in which a qualitatively significant tradeoff in one evaluative dimension for a given improvement in another dimension could not make an option better all things considered, but a merely quantitative tradeoff for the given improvement might. Trouble arises, however, when one of the options constitutes a borderline case of an evaluative (...) kind. I argue that in such cases we can neither affirm nor deny that trading off losses in one evaluative dimension for gains in another yields a better outcome. Theoretically, this result provides a way to defuse an argument that has been presented by both Larry Temkin and Stuart Rachels that purports to show that the ‘better than’ relation is intransitive. Practically, it allows us to undermine the claim that rational agents are better off withholding their contribution to a public good in certain instances of the free-rider problem, and thus to take an important step towards solving these problems. (shrink)

This paper deals with problems that vagueness raises for choices involving evaluative tradeoffs. I focus on a species of such choices, which I call ‘qualitative barrier cases.’ These are cases in which a qualitatively significant tradeoff in one evaluative dimension for a given improvement in another dimension could not make an option better all things considered, but a merely quantitative tradeoff for the given improvement might. Trouble arises, however, when one of the options constitutes a borderline case of an evaluative (...) kind. I argue that in such cases we can neither affirm nor deny that trading off losses in one evaluative dimension for gains in another yields a better outcome. Theoretically, this result provides a way to defuse an argument that has been presented by both Larry Temkin and Stuart Rachels that purports to show that the ‘better than’ relation is intransitive. Practically, it allows us to undermine the claim that rational agents are better off withholding their contribution to a public good in certain instances of the free-rider problem, and thus to take an important step towards solving these problems. (shrink)

THIS PAPER CORRECTS AN ERROR IN MY EARLIER PAPER, "CONCEPTS OF SUPERVENIENCE" ("PHILOSOPHY AND PHENOMENOLOGICAL RESEARCH", VOLUME 45, 1984), AND PRESENTS FURTHER MATERIAL ON SUPERVENIENCE. THE ERROR IS THE CLAIM THAT "GLOBAL" SUPERVENIENCE ENTAILS "STRONG" SUPERVENIENCE. HOWEVER, IT IS ARGUED THAT THIS FAILURE OF ENTAILMENT ONLY GOES TO SHOW THE INADEQUACY OF GLOBAL SUPERVENIENCE AS AN EXPLICATION OF "DEPENDENCY" OR "DETERMINATION" RELATION, AND, IN PARTICULAR, THAT MATERIALISM FORMULATED IN TERMS OF GLOBAL SUPERVENIENCE APPEARS TOO WEAK. (IT IS POINTED OUT, AMONG (...) OTHER THINGS, THAT GLOBAL SUPERVENIENCE DOES NOT ENTAIL "WEAK" SUPERVENIENCE). A STRONGER FORM OF GLOBAL SUPERVENIENCE, BASED ON "SIMILARITY" RATHER THAN "INDISCERNIBILITY" BETWEEN WORLDS, IS FORMULATED AND BRIEFLY DISCUSSED. (shrink)

Let us say that a thing is gunky just in case every part of that thing has proper parts. The idea that all physical objects are gunky seems sufficiently sweeping, interesting, and plausible that it is worth examining. However, there is a difficulty. The features of an extended object can surely vary continuously. If an object is gunky then it cannot have point-sized parts which have no further parts. But how can one conceive of a continuous variation in features other (...) than as the obtaining of different features at different point sized locations? (shrink)

The spectrum argument purports to show that the better-than relation is not transitive, and consequently that orthodox value theory is built on dubious foundations. The argument works by constructing a sequence of increasingly less painful but more drawn-out experiences, such that each experience in the spectrum is worse than the previous one, yet the final experience is better than the experience with which the spectrum began. Hence the betterness relation admits cycles, threatening either transitivity or asymmetry of the relation. This (...) paper examines recent attempts to block the spectrum argument, using the idea that it is a mistake to affirm that every experience in the spectrum is worse than its predecessor: an alternative hypothesis is that adjacent experiences may be incommensurable in value, or that due to vagueness in the underlying concepts, it is indeterminate which is better. While these attempts formally succeed as responses to the spectrum argument, they have additional, as yet unacknowledged costs that are significant. In order to effectively block the argument in its most typical form, in which the first element is radically inferior to the last, it is necessary to suppose that the incommensurability is particularly acute: what might be called radical incommensurability. We explain these costs, and draw some general lessons about the plausibility of the available options for those who wish to save orthodox axiology from the spectrum argument. (shrink)

Sergio Tenenbaum and Diana Raffman contend that ‘vague projects’ motivate radical revisions to orthodox, utility-maximising rational choice theory. Their argument cannot succeed if such projects merely ground instances of the paradox of the sorites, or heap. Tenenbaum and Raffman are not blind to this, and argue that Warren Quinn’s Puzzle of the Self-Torturer does not rest on the sorites. I argue that their argument both fails to generalise to most vague projects, and is ineffective in the case of the Self-Torturer (...) itself. (shrink)

This chapter discusses the defence of metaphysical indeterminacy by Elizabeth Barnes and Robert Williams and discusses a classical and bivalent theory of such indeterminacy. Even if metaphysical indeterminacy arguably is intelligible, Barnes and Williams argue in favour of it being so and this faces important problems. As for classical logic and bivalence, the chapter problematizes what exactly is at issue in this debate. Can reality not be adequately described using different languages, some classical and some not? Moreover, it is argued (...) that the classical and bivalent theory of Barnes and Williams does not avoid the problems that arise for rival theories. (shrink)

A certain conception of Hell is inconsistent with God's traditional attributes. My argument is novel in focusing on considerations involving vagueness. God is in charge of the selection procedure, so the selection procedure must be just; any just procedure will have borderline cases; but according to the traditional conception, the afterlife is binary and has no borderline cases.

Some comparisons are hard. How should we think about such comparisons? According to John Broome, we should think about them in terms of vagueness. But the vagueness account has remained unpopular thus far. Here I try to bolster it by clarifying the notion of comparative vagueness that lies at its heart.

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)

In this paper, I advance an original view of the structure of space called Infinitesimal Gunk. This view says that every region of space can be further divided and some regions have infinitesimal size, where infinitesimals are understood in the framework of Robinson’s nonstandard analysis. This view, I argue, provides a novel reply to the inconsistency arguments proposed by Arntzenius and Russell, which have troubled a more familiar gunky approach. Moreover, it has important advantages over the alternative views these authors (...) suggested. Unlike Arntzenius’s proposal, it does not introduce regions with no interior. It also has a much richer measure theory than Russell’s proposal and does not retreat to mere finite additivity. (shrink)

It is plausible to claim that it is morally worse to kill an innocent person than to give any number of people a mild one‐hour headache. Alaistar Norcross has argued that consequentialists, at least, should reject this claim. According to him, any harm that can befall a person can be morally outweighed by a sufficient number of very small harms. He gives a general argument for this view, and tries to show, by means of an argument from analogy, that it (...) is less counter‐intuitive than it appears. I show that his main argument relies on a false assumption, and argue that the purported analogy is dubious. (shrink)

This article criticises one of Stuart Rachels' and Larry Temkin's arguments against the transitivity of 'better than'. This argument invokes our intuitions about our preferences of different bundles of pleasurable or painful experiences of varying intensity and duration, which, it is argued, will typically be intransitive. This article defends the transitivity of 'better than' by showing that Rachels and Temkin are mistaken to suppose that preferences satisfying their assumptions must be intransitive. It makes cler where the argument goes wrong by (...) showing that it is a version of Zeno's paradox of Achilles and the Tortoise. (shrink)

In this paper I respond to Trenton Merricks's (2005) paper ‘Composition and Vagueness’. I argue that Merricks's paper faces the following difficulty: he claims to provide independent motivation for denying one of the premisses of the Lewis-Sider vagueness argument for unrestricted composition, but the alleged motivation he provides begs the question.

In this paper we aim to disentangle the thesis that the future is open from theses that often get associated or even conflated with it. In particular, we argue that the open future thesis is compatible with both the unrestricted principle of bivalence and determinism with respect to the laws of nature. We also argue that whether or not the future (and indeed the past) is open has no consequences as to the existence of (past and) future ontology.

In this paper I develop a framework for understanding ontic vagueness. The project of the paper is two-fold. I first outline a definitional account of ontic vagueness – one that I think is an improvement on previous attempts because it remains neutral on other, independent metaphysical issues. I then develop one potential manifestation of that basic definitional structure. This is a more robust (and much less neutral) account which gives a fully classical explication of ontic vagueness via modal concepts. The (...) overarching aim is to systematically investigate the puzzling question of what exactly it could be for the world itself to be vague. (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)

An argument is offered for this conditional: If our current concept conscious state is sharp rather than vague, and also correct , then common versions of familiar metaphysical theories of consciousness are false--?namely versions of the identity theory, functionalism, and dualism that appeal to complex physical or functional properties in identification, realization, or correlation. Reasons are also given for taking seriously the claim that our current concept conscious state is sharp. The paper ends by surveying the theoretical options left open (...) by the concept's sharpness and the truth of the conditional argued for in the paper. (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.

Totalism is the view that one distribution of well-being is better than another just in case the one contains a greater sum of well-being than the other. Many philosophers, following Parfit, reject totalism on the grounds that it entails the repugnant conclusion: that, for any number of excellent lives, there is some number of lives that are barely worth living whose existence would be better. This paper develops a theory of welfare aggregation—the lexical-threshold view—that allows totalism to avoid the repugnant (...) conclusion, as well as its analogues involving suffering populations and the lengths of individual lives. The theory is grounded in some independently plausible views about the structure of well-being, identifies a new source of incommensurability in population ethics, and avoids some of the implausibly extreme consequences of other lexical views, without violating the intuitive separability of lives. (shrink)

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.

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.

Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.

Intuitively there are many different things that non-derivatively contribute to well-being: pleasure, desire satisfaction, knowledge, friendship, love, rationality, freedom, moral virtue, and appreciation of true beauty. According to pluralism, at least two different types of things non-derivatively contribute to well-being. Lopsided lives score very low in terms of some types of things that putatively non-derivatively contribute to well-being, but very high in terms of other such types of things. I argue that pluralists essentially face a trilemma about lopsided lives: they (...) must either make implausible claims about how they compare in terms of overall well-being with more balanced lives, allow overall well-being to be implausibly hypersensitive to very slight nonevaluative differences, or else adopt implausible seeming limits on what things lives can contain or how much they can contribute to overall well-being. Such problems about lopsided lives thus push us away from pluralism and toward simpler theories of well-being, toward hedonism in particular. (This piece is the subject of Eden Lin’s paper “Well-Being and Hedonic Indispensability”.). (shrink)