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)

There are 1,000 of us and one victim. We each increase the level at which a ‘discomfort machine’ operates on the victim – leading to great discomfort. Suppose that consecutive levels of the machine are so similar that the victim cannot distinguish them. Have we acted permissibly? According to the ‘no-difference argument’ the answer is ‘yes’ because each of our actions was guaranteed to make the victim no worse off. This argument is of interest because, if it is sound, similar (...) arguments threaten intuitive moral verdicts about many cases in which a large number of individual choices cumulatively make a great difference, while each choice seems to make no difference on its own. But the argument is not sound, as is shown by a simple objection based on a plausible dominance principle – an objection that avoids challenges that have been brought against previous criticisms of the no-difference argument. (shrink)

According to a widely held view, rationality demands that the preferences of a person be transitive. The transitivity assumption is an axiom in standard theories of rational choice. It is also prima facie very plausible. I argue here that transitivity is not a necessary condition of rationality; it is a constraint only in some cases. The argument presented here is based on the non-linearity of differential utility functions. This paper has four parts. First, I present an argument against the transitivity (...) assumption (I, II). Second, I discuss some objections; this will also bring out some features of the view defended here, like the essentially comparative nature of choice (III). Then, I discuss certain proposals that promise to avoid my conclusion (IV). Finally, I go into some implications concerning the nature of rational decision making (V). To accept some intransitivities as rational does not make our life easier; it can even lead to hard choices. However, it does not lead to skepticism about rational choice. (shrink)

Ethics in the tradition of Derek Parfit’s Reasons and Persons is riddled with sorites-like arguments, which lead us by what seem innocent steps to seemingly false conclusions. Take, for example, spectrum arguments for the Repugnant Conclusion that appeal to slight differences in quality of life. Several authors have taken the view that, since spectrum arguments are structurally analogous to sorites arguments, the correct response to spectrum arguments is structurally analogous to the correct response to sorites arguments. This sorites analogy is (...) here argued against. There are potential structural disanalogies between spectrum arguments and sorites arguments. But even if these arguments are relevantly structurally analogous, they differ in their content in ways that show the sorites analogy to be implausible. Two content-based disanalogies are here explored—one is inspired by Parfit’s work on reductionism, and the other involves hypersensitivity. The chapter concludes with a methodological lesson. (shrink)

We argue that all comparative expressions in natural language obey a principle that we call Comparability: if x and y are at least as F as themselves, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns (...) of inference that seem manifestly valid, that the purported failures of Comparability would have absurd consequences, and that the influential arguments against Comparability are less compelling than they may have initially seemed. (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.

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

Discussion of temptation has figured prominently in recent debates concerning instrumental rationality. In light of some particularly interesting cases in which giving in to temptation involves acting in accordance with one’s current evaluative rankings, two lines of thought have been developed: one appeals to the possibility of deviating from a well-grounded resolution, and the other appeals to the possibility of being insufficiently responsive to the prospect of future regret. But the current appeals to resolutions and regret and some of the (...) verdicts provided face some serious challenges. Building on recent work concerning instrumental rationality, and delving into some important complications concerning human psychology, I revisit the relevant cases of temptation and analyze them in a way that puts resolutions, rational failure, and regret in their proper places. In the process, I highlight and explain the significance of the neglected fact that resolutions can introduce effective anchor points, which can serve agents faced with temptation well, even if the resolutions are abandoned. (shrink)

This paper tries to explain why racial profiling involves a serious injustice and to do so in a way that avoids the problems of existing philosophical accounts. An initially plausible view maintains that racial profiling is pro tanto wrong in and of itself by violating a constraint on fair treatment that is generally violated by acts of statistical discrimination based on ascribed characteristics. However, consideration of other cases involving statistical discrimination suggests that violating a constraint of this kind may not (...) be an especially serious wrong in and of itself. To fully capture the significant wrong that occurs when racial profiling is targeted at black Americans or other similarly situated groups, it is argued that we should appeal to the idea that this basic injustice is exacerbated when it forms part of a larger pattern of similar actions that collectively realize a state of cumulative injustice. (shrink)

Dreadful and dreaded outcomes are sometimes brought about via the accumulation of individually trivial effects. Think about inching toward terrible health or toward an environmental disaster. In some such cases, the outcome is seen as unacceptable but is still gradually realized via an extended sequence of moves each of which is trivial in terms of its impact on the health or environment of those involved. Cases of this sort are not only practically challenging, they are theoretically challenging as well. For, (...) they raise puzzling complications concerning the assessment of conduct. In particular, given cases of this sort, we seem forced to conclude that, sometimes, each current doing in an extended sequence of moves can be correctly assessed as permissible (relative to a certain set of concerns) even though the sequence foreseeably leads to an outcome that is unacceptable (relative to that same set of concerns) and even though acceptable outcomes are available. And this seems paradoxical. I argue that this (apparent) puzzle glosses over complications associated with action individuation and units of agency. Reflection on these complications makes it clear that in cases of the sort that have given rise to the puzzle, there is an accurate way of seeing what is being done at various particular moments that clearly brings out the tight connection between a current doing and non-trivial damage that is to be expected (and is indeed bound to occur if the doing is completed without a hitch). (shrink)

It is commonly held that rational preferences must be acyclic. There have, however, been cases that have been put forward as counterexamples to this view. This paper focuses on the following question: If the counterexamples are compelling and rational preferences can be cyclic, what should we conclude about the presumed acyclicity of the “better than” relation? Building on some revisionary suggestions concerning acyclicity and betterness, I make a case for hanging on to the presumption that “better than” is acyclic even (...) if “is rationally preferred to” is not. As I explain, the divergence my view makes room for does not threaten to make “better than” judgments less relevant to choice than judgments about rational preference. To the contrary, it makes them more relevant. Toward the end of the paper, I extend my results to the relation “is morally better than” in light of the possibility that there might be moral preferability cycles. (shrink)

The puzzle of the self-torturer raises intriguing questions concerning rationality, cyclic preferences, and resoluteness. Interestingly, what makes the case puzzling has not been clearly pinpointed. The puzzle, it seems, is that a series of rational choices foreseeably leads the self-torturer to an option that serves his preferences worse than the one with which he started. But this is a very misleading way of casting the puzzle. I pinpoint the real puzzle of the self-torturer and, in the process, reveal a neglected (...) but crucial dimension of instrumental rationality. (shrink)

Larry Temkin challenged what seems to be an analytic truth about comparatives: if A is Φ-er than B and B is Φ-er than C, then, A is Φ-er than C. Ruth Chang denies a related claim: if A is Φ-er than B and C is not Φ-er than B, but is Φ to a certain degree, then A is Φ-er than C. In this paper I advance a context-sensitive semantics of gradability according to which the data uncovered by Temkin and (...) Chang leave both statements intact. (shrink)