One of the most influential ideas in recent discussions in political philosophy and philosophy of values has been Isaiah Berlin's value pluralism. Given that different ways of living embody different applications of values, it is really difficult to talk about objectivity in the domain of morals. But if we reject the existence of criteria that allow us to judge among different moral proposals, we are led to recognize the prejudiced character of our convictions: their ethnocentric character. In my opinion, this (...) weakens our commitment to those convictions, to the extent that we are not obliged to follow them. At the same time, if that incommensurability is at the root of any interpretation of values, we cannot choose between different ways of understanding pluralism and we cannot evaluate the pluralistic model itself. Saying that some sort of pluralism is good for us if, for us, some sort of pluralism is good, is only proposing an empty tautology. In the end I will argue that we can accept the existence of a sort of moral equilibrium that can allow us to talk of moral progress. (shrink)

I consider the implications of incommensurability for the assumption, in rational choice theory, that a rational agent’s preferences are complete. I argue that, contrary to appearances, the completeness assumption and the existence of incommensurability are compatible. Indeed, reflection on incommensurability suggests that one’s preferences should be complete over even the incommensurable alternatives one faces.

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)

According to a widely accepted philosophical model, agent-regret is practically significant and appropriate when the agent committed a mistake, or she faced a conflict of obligations. I argue that this account misunderstands moral phenomenology because it does not adequately characterize the object of agent-regret. I suggest that the object of agent-regret should be defined in terms of valuable unchosen alternatives supported by reasons. This model captures the phenomenological varieties of regret and explains its practical significance for the agent. My contention (...) is that agent-regret is a mode of valuing: a way in which the agent expresses and confers value. (shrink)

This article discusses the possibility of a rationally justified choice between two options neither of which is better than the other while they are not equally good either (‘3NT’). Joseph Raz regards such options as incomparable and argues that reason cannot guide the choice between them. Ruth Chang, by contrast, tries to show that many cases of putative incomparability are instead cases of parity—a fourth value relation of comparability, in addition to the three standard value relations ‘better than’, ‘worse than’ (...) and ‘equally good as’. It follows, she argues, that many choice situations in which rationally justified choice seems precluded are in fact situations within the reach of practical reason. This article has three aims: (1) it challenges Chang’s argument for the possibility of parity; (2) it demonstrates that, even if parity would exist, its problematic implications for practical reason would not differ from those of Raz’s incomparability; (3) it discusses the underlying cause of hard cases of comparison: the fact that none of the three standard value relations applies (‘3NT’). It will be shown that the problematic implications for the rational justification of the choice are due to 3NT itself, irrespective of whether 3NT is explained as incomparability or parity. (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)

John Broome has argued that incomparability and vagueness cannot coexist in a given betterness order. His argument essentially hinges on an assumption he calls the ‘collapsing principle’. In an earlier article I criticized this principle, but Broome has recently expressed doubts about the cogency of my criticism. Moreover, Cristian Constantinescu has defended Broome’s view from my objection. In this paper, I present further arguments against the collapsing principle, and try to show that Constantinescu’s defence of Broome’s position fails.

Gustafsson and Espinoza have recently argued that the ‘small-improvement argument’, against completeness as a rationality requirement for preference orderings, is defective. They claim that the two main premises of the argument conflict, and hence should not both be accepted. I show that this conflict can be avoided by modifying one of the premises.

Ruth Chang has defended a concept of "parity", implying that two items may be evaluatively comparable even though neither item is better than or equally good as the other. This article takes no stand on whether there actually are cases of parity. Its aim is only to make the hitherto somewhat obscure notion of parity more precise, by defining it in terms of the standard value relations. Given certain plausible assumptions, the suggested definiens is shown to state a necessary and (...) sufficient condition for parity, as this relation is envisaged by Chang. (shrink)

John Broome has argued that alleged cases of value incomparability are really examples of vagueness in the betterness relation. The main premiss of his argument is ‘the collapsing principle’. I argue that this principle is dubious, and that Broome's argument is therefore unconvincing. Correspondence:c1 Erik.Carlson@filosofi.uu.se.

This paper presents an argument against the widespread view that ‘hard choices’ are hard because of the incomparability of the alternatives. The argument has two parts. First, I argue that any plausible theory of practical reason must be ‘comparativist’ in form, that is, it must hold that a comparative relation between the alternatives with respect to what matters in the choice determines a justified choice in that situation. If comparativist views of practical reason are correct, however, the incomparabilist view of (...) hard choices should be rejected. Incomparabilism about hard choices leads us to an implausible error theory about the phenomenology of hard choices, threatens an unattractive view of human agency, and leaves us in perplexity about what we are doing when we choose in hard choices. The second part of the argument explores the main competitor to comparativist views of practical reason, noncomparativist view, according tow which a choice is justified so long as it is not worse than any of the alternatives. This view is often assumed by rational choice theorists but has its best philosophical defense in work by Joseph Raz. On Raz’s view, incomparabilism about hard choices avoids the problems faced if comparativism is correct, but it faces different difficulties. I argue that Raz’s noncomparativist view mistakenly assimilates practical reason to more restricted normative domains such as the law. (shrink)

This paper begins with a response to Josh Gert’s challenge that ‘on a par with’ is not a sui generis fourth value relation beyond ‘better than’, ‘worse than’, and ‘equally good’. It then explores two further questions: can parity be modeled by an interval representation of value? And what should one rationally do when faced with items on a par? I argue that an interval representation of value is incompatible with the possibility that items are on a par (a mathematical (...) proof is given in the appendix). I also suggest that there are three senses of ‘rationally permissible’ which, once distinguished, show that parity does distinctive practical work that cannot be done by the usual trichotomy of relations or by incomparability. In this way, we have an additional argument for parity from the workings of practical reason. (shrink)

One of the most common judgments of normative life takes the following form: With respect to some things that matter, one item is better than the other, with respect to other things that matter, the other item is better, but all things considered – that is, taking into account all the things that matter – the one item is better than the other. In this paper, I explore how all-things-considered judgments are possible, assuming that they are. In particular, I examine (...) the question of how the different considerations relevant to an all-things-considered judgment come together in a way that gives each relevant consideration its proper due. I propose an answer which provides a unified account of all-things-considered judgments and highlights a deep connection between value and reason. My suggestion is that ‘all things considered’ is, in effect, a placeholder for a more comprehensive, sometimes nameless, value that includes the things considered as parts, and that this more comprehensive value determines how the things considered normatively relate. (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’.

The central aim of this book is to answer two questions: Are alternatives for choice ever incomparable? and, In what ways can items be compared? The arguments offered suggest that alternatives for choice no matter how different are never incomparable, and that the ways in which items can be compared are richer and more varied than commonly supposed. This work is the first book length treatment of the topics of incomparability, value, and practical reason.

Recently, some of the leading proponents of the view that there is widespread incommensurability among goods have suggested that the incommensurability of some goods is a constitutive feature of the goods themselves. So, for example, a friendship and a million dollars are incommensurable because it is part of what it is to be a friendship that it be incommensurable with money. According to these ‘constitutive incommensurabilists’ incommensurability follows from the very nature of certain goods. In this paper, I examine this (...) idea and argue that constitutive incommensurabilists have mistaken for constitutive incommensurability a particular emphatic kind of comparability. This examination involves an account of ‘higher’ and ‘lower’ goods and an explanation of how goods of different ‘types’ figure in practical conflict. (shrink)

This paper is the introduction to the volume. It gives an argumentative view of the philosophical landscape concerning incommensurability and incomparability. It argues that incomparability, not incommensurability, is the important phenomenon on which philosophers should be focusing and that the arguments for the existence of incomparability are so far not compelling.

And what are the implications for moral and legal decision making? In this book, some of the sharpest minds in philosophy struggle with these questions.

Two competing accounts of value incomparability have been put forward in the recent literature. According to the standard account, developed most famously by Joseph Raz, ‘incomparability’ means determinate failure of the three classic value relations ( better than , worse than , and equally good ): two value-bearers are incomparable with respect to a value V if and only if (i) it is false that x is better than y with respect to V , (ii) it is false that x (...) is worse than y with respect to V and (iii) it is false that x and y are equally good with respect to V . Most philosophers have followed Raz in adopting this account of incomparability. Recently, however, John Broome has advocated an alternative view, on which value incomparability is explained in terms of vagueness or indeterminacy . In this paper I aim to further Broome’s view in two ways. Firstly, I want to supply independent reasons for thinking that the phenomenon of value incomparability is indeed a matter of the indeterminacy inherent in our comparative predicates. Secondly, I attempt to defend Broome’s account by warding off several objections that worry him, due mainly to Erik Carlson and Ruth Chang. (shrink)

It is commonly assumed that moral deliberation requires that the alternatives available in a choice situation are evaluatively comparable. This comparability assumption is threatened by claims of incomparability, which is often established by means of the small improvement argument (SIA). In this paper I argue that SIA does not establish incomparability in a stricter sense. The reason is that it fails to distinguish incomparability from a kind of evaluative indeterminacy which may arise due to the vagueness of the evaluative comparatives (...) ‘better than,’ ‘worse than,’ and ‘equally as good as.’. (shrink)

Many contemporary accounts of normative reasons for action accord a single strength value to normative reasons. This paper first uses some examples to argue against such views by showing that they seem to commit us to intransitive or counterintuitive claims about the rough equivalence of the strengths of certain reasons. The paper then explains and defends an alternate account according to which normative reasons for action have two separable dimensions of strength: requiring strength, and justifying strength. Such an account explains (...) our intuitions in the cases that make trouble for single-value views. The justifying/requiring account is compared with two other solutions that have been offered to justify and explain our intuitions about these sorts of cases. These other solutions appeal to the notions of incommensurability of reasons, and to second-order normative entities called `exclusionary permissions'. It is argued that the justifying/requiring distinction provides a superior solution. (shrink)

In this paper, I shall argue that the small-improvement argument, which is the standard objection to completeness, fails since some of the comparisons involved in the argument might be indeterminate. I shall defend this view from two objections due to Ruth Chang, namely the argument from phenomenology and the argument from perplexity. There are some other objections to the small-improvement argument that also hinge on claims about indeterminacy. John Broome argues that alleged cases of value incomparability are merely examples of (...) indeterminacy in the betterness relation. The main premiss of his argument is the much discussed collapsing principle. I shall offer a new counter-example to this principle and argue that Broome’s defence of the principle is not cogent. On the other hand, Nicolas Espinoza argues that the small-improvement argument fails due to the mere possibility of evaluative indeterminacy. I shall argue that his objection is unsuccessful. (shrink)

In order to account for non-traditional preference relations the present paper develops a new, richer framework for preference relations. This new framework provides characterizations of non-traditional preference relations, such as incommensurateness and instability, that may hold when neither preference nor indifference do. The new framework models relations with swaps, which are conceived of as transfers from one alternative state to another. The traditional framework analyses dyadic preference relations in terms of a hypothetical choice between the two compared alternatives. The swap (...) framework extends this approach by analysing dyadic preference relations in terms of two hypothetical choices: the choice between keeping the first of the compared alternatives or swapping it for the second; and the choice between keeping the second alternative or swapping it for the first. (shrink)

The small-improvement argument is usually considered the most powerful argument against comparability, viz the view that for any two alternatives an agent is rationally required either to prefer one of the alternatives to the other or to be indifferent between them. We argue that while there might be reasons to believe each of the premises in the small-improvement argument, there is a conflict between these reasons. As a result, the reasons do not provide support for believing the conjunction of the (...) premises. Without support for the conjunction of the premises, the small-improvement argument for incomparability fails. (shrink)

If A is better than B and B is better than C, then A is better than C, right? Larry Temkin and Stuart Rachels say: No! Betterness is nontransitive, they claim. In this paper, I discuss the central type of argument advanced by Temkin and Rachels for this radical idea, and argue that, given this view very likely has sceptical implications for practical reason, we would do well to identify alternative responses. I propose one such response, which employs the idea (...) that rational agents might regard some options as incommensurate in value, and will reasonably employ a heuristic of status quo maintenance to avoid suboptimal choices from incommensurate goods. (shrink)

What difference does it make to matters of value, for a desire satisfactionist, if a given desire is *absent*, rather than *present*? I argue that it is most plausible to hold that the state in which a given desire is satisfied is, other things being equal, incommensurate with the state in which that desire does not exist at all. In addition to illustrating the internal attractions of the view, I demonstrate that this idea has attractive implications for population ethics. Finally, (...) I show that the view is not subject to John Broome's `greedy neutrality' worry. (shrink)

According to one prominent view of rationality, for the choice of alternative to be justified, it must be at least as good as other alternatives. Michael Jensen has recently invoked this view to argue that managers should act exclusively to maximize the long-run market value of economic enterprises. According to Jensen, alternative accounts of managerial responsibility, such as stakeholder theory, are to be rejected because they lack a single measure to compare alternatives as better or worse. Against Jensen’s account, this (...) paper argues that choosing the alternative that is at least as good as other alternatives need not preclude managers from respecting considerations in addition to long-run market value. The paper argues that such considerations may be incorporated into managerial decision-making by introducing constraints and priorities into the process of maximizing long-run market value and by allowing for “clumpy” values. (shrink)

The incomparability of two items is thought to pose a problem for making justified choices and for consequentialist theories that rely on comparing states of the world to judge the goodness of a particular course of action. In response, it has been argued that items thought incomparable by one of the three standard relations, ‘better than’, ‘worse than’ and ‘equally good’, are instead comparable by some fourth relation, such as ‘roughly equal’ or ‘on a par’. Against such accounts, this article (...) argues that values in virtue of which comparisons are made can be ‘clumpy’ and that in comparisons involving clumpy values, we have no reason to accept ‘roughly equal’ or ‘on a par’ as distinct from ‘equally good’. The article supports the possibility of incomparability by arguing for an interpretation of incomparability as an instance of incommensurability. (shrink)

Some theories of practical reasons incorporate a lexical priority structure, according to which some practical reasons have infinitely greater weight than others. This includes absolute deontological theories and axiological theories that take some goods to be categorically superior to others. These theories face problems involving cases in which there is a non-extreme probability that a given reason applies. In view of such cases, lexical-priority theories are in danger of becoming irrelevant to decision-making, becoming absurdly demanding, or generating paradoxical cases in (...) which each of a pair of actions is permissible yet the pair is impermissible. (shrink)

Several prominent ethical philosophers have attempted to demonstrate that there exist instances or types of value that are of crucial moral significance but which cannot legitimately be compared with one another. Bernard Williams and Michael Stocker, for example, argue that it can sometimes be rational to regret having chosen the all-things-considered better of two alternatives, and that this sense of regret entails that the goodness of the worse option is not made up for by and is therefore incommensurable with that (...) of the better. Joseph Raz and others have made similar points. In this paper, I propose a theory of value that is monistic in that it countenances just one sort of morally crucial value, but pluralistic in that several distinct properties bearer this value. I then explain how this view avoids incommensurable values without doing violence to the core intuitions that seemed to necessitate them, and how it fits into a larger conception of morality, right conduct, and moral psychology. (shrink)

According to a standard picture, for any two comparable objects and a basis for comparison, either one is greater than the other or they are equal with respect to the basis. This picture has been called the Trichotomy Thesis, and although it is intuitive and plausible, it has been called into question by such philosophers as Derek Parfit, James Griffin, Joseph Raz, and Ruth Chang. Chang’s discussion is particularly rich, for she proposes and provides a detailed account of a possible (...) fourth relation that, she argues, provides a satisfying explanation of hard cases of comparison. In this paper, I will examine a version of the main argument against the Trichotomy Thesis and attempt to show that it is unsound. (shrink)

By analyzing cases in which we must choose between options whose values are not precisely comparable, this paper presents the case for the existence of a previously unrecognized class of practical reasons – reasons that arise from how the value of an option compares to the values of the alternatives. Several implications of these comparative value-based reasons are discussed – including the context-dependence of one option’s being ‘rationally preferable to’ an alternative, and the fact that, even when the values of (...) an agent’s alternatives fail to be precisely comparable, practical reason will always be able to determine that the choice of at least one option is justified. (shrink)

Anselmian theism holds that there necessarily exists a being, God, who is essentially unsurpassable in power, knowledge, goodness, and wisdom. This being is also understood to be the creator and sustainer of all that is. In contemporary analytic philosophy of religion, this role is generally understood as follows: God surveys the array of possible worlds, and in his wisdom selects exactly one for actualization, based on its axiological properties. In this paper, I discuss an under-appreciated challenge for this account of (...) the Anselmian God’s selection of a world. In particular, I urge that there are failures of comparability between various possible worlds, and I argue that, given certain assumptions, these failures threaten the rationality of God’s choice of a world. To the extent that rationality is deemed necessary for unsurpassability, this result also challenges the core Anselmian notion that God is an unsurpassable being. (shrink)

I defend a form of moral relativism that draws upon value pluralism and incommensurability.

In this article I try to elucidate the concept of human dignity by taking a closer look at the features of a paradigmatic torture situation. After identifying the salient aspects of torture, I discuss various accounts for the moral wrongness of such acts and argue that what makes torture a violation of human dignity is the perverted moral relationship between torturer and victim. This idea is subsequently being substantiated and defended against important objections. In the final part of the chapter (...) I give a (qualified) defense of the methodology employed in the previous sections. (shrink)

Some philosophers believe that two objects of value can be ‘roughly equal’, or ‘on a par’, or belong to the same ‘clump’ of value in a sense that is fundamentally different from that in which some objects are ‘better than’, ‘worse than’, or ‘equally as good as’ others. This article shows that if two objects are on a par, or belong to the same clump, then an agent accepting a few plausible premises can be exploited in a money-pump. The central (...) premise of the argument is that value is choice-guiding. If one object is more valuable than another, then it is not permitted to choose the less valuable object; and if two objects are equally valuable it is permitted to choose either of them; and if two objects are on a par or belong to the same clump it is also permitted to choose either of them. (shrink)

This article seeks to contribute to the discussion on the nature of choice in virtue theory. If several different actions are available to the virtuous agent, they are also likely to vary in their degree of virtue, at least in some situations. Yet, it is widely agreed that once an action is recognised as virtuous there is no higher level of virtue. In this paper we discuss how the virtue theorist could accommodate both these seemingly conflicting ideas. We discuss this (...) issue from a modern Aristotelian perspective, as opposed to a purely exegetic one. We propose a way of resolving what seems to be a major clash between two central features of virtue ethics. Our proposal is based on the notion of parity, a concept which recently has received considerable attention in the literature on axiology. Briefly put, two alternatives are on a par (or are ‘roughly equal’) if they are comparable, although it is not the case that one is better than the other, nor that they are equally good. The advantages of applying the concept of parity to our problem are twofold. Firstly, it sheds new light on the account of choice in virtue theory. Secondly, some of the criticisms that have been mounted against the possibility of parity can be countered by considering the notion of choice from a virtue theory perspective. (shrink)

On the Total Principle, the best state of affairs (ceteris paribus) is the one with the greatest net sum of welfare value. Parfit rejects this principle, because he believes that it implies the Repugnant Conclusion, the conclusion that for any large population of people, all with lives well worth living, there will be some much larger population whose existence would be better, even though its members all have lives that are only barely worth living. Recently, however, a number of philosophers (...) have suggested that the Total Principle does not imply the Repugnant Conclusion provided that a certain axiological view (namely, the ‘Discontinuity View’) is correct. Nevertheless, as I point out, there are three different versions of the Repugnant Conclusion, and it appears that the Total Principle will imply two of the three even if the Discontinuity View is correct. I then go on to argue that one of the two remaining versions turns out not to be repugnant after all. Second, I argue that the last remaining version is not, as it turns out, implied by the Total Principle. Thus, my arguments show that the Total Principle has no repugnant implications. (shrink)

This paper uses a formal analysis of the relation of ‘parity’ to make sense of a well-known solution to Parfit’s ‘mere addition paradox’. This solution is sometimes dismissed as a recourse to ‘incomparability’. In this analysis, however, the solution is consistent with comparability, as well as transitivity of ‘better than’. The analysis is related to Blackorby, Bossert and Donaldson’s ‘incomplete critical-level generalised utilitarianism’ (ICLGU). ICLGU is inspired by Parfit’s work and can be related to the analysis of parity, though the (...) distinctive ‘mark’ of parity suggests that the boundaries of a set of critical levels is not exact. One has to allow for vagueness to make an account based on parity plausible. These accounts are then contrasted with Broome’s view which also involves vagueness. (shrink)

The vagueness view holds that when evaluative comparisons are hard, there is indeterminacy about which comparative relation holds. It is sceptical about whether there are any incommensurate items (in some domain). The sceptical element of John Broome’s version of this view rests on a controversial principle. Robert Sugden advances a similar view which does not depend on this principle. Sugden’s argument fails as a vagueness view because it assumes rather than shows that there are no incommensurate items (in some domain). (...) Nonetheless, I argue that an interpretation of his argument constitutes a defensible vagueness view which is supported by intuition about examples. On this interpretation Sugden’s view can be mapped onto Broome’s application of a supervaluationist view of vagueness. It is also (on this reading) a close relative of James Griffin’s ‘rough equality’ view when this is interpreted in terms of vagueness. On an alternative interpretation Sugden’s view is not sceptical about incommensurateness. On this interpretation he does not defend a vagueness view and is ‘sceptical’ about the contribution of the philosophical literature to our understanding of rational choice. (shrink)

James Griffin (1986, 1997, 2000) and Ruth Chang (1997) have argued that alternatives (and values) can be comparable when it is neither true that one is better than the other, nor true that they are exactly equal in value. The relation which holds between them has gone under various names: the alternatives are ‘roughly equal in value’ (Griffin) or ‘on a par’ (Chang). In this paper, I give a formal analysis of this relation. This analysis allows us to distinguish between (...) two slightly different notions of ‘at least as good as’. It is argued that the distinction between these notions is important for discussions of rationality, as is the distinction between ‘rough equality’ or ‘parity’ and incomparability. (shrink)

In Rabinowicz (2008), I considered how value relations can best be analysed in terms of fitting pro-attitudes. In the formal model of that paper, fitting pro-attitudes are represented by the class of permissible preference orderings on a domain of items that are being compared. As it turns out, this approach opens up for a multiplicity of different types of value relationships, along with the standard relations of , , and . Unfortunately, the approach is vulnerable to a number of objections. (...) I believe these objections can be avoided if one re-interprets the underlying notion of preference: instead of treating preference as a attitude directed towards a pair of items, we can think of it as a difference of degree between attitudes of favouring. Each such monadic attitude has just one item as its object. Given this re-interpretation, permissible preferences can be modelled by the class of permissible assignments of degrees of favouring to items in the domain. From this construction, we can then recover the old modelling in terms of the class of permissible preference orderings, but the previous objections to that model no longer apply. (shrink)

This paper casts doubts on John Broome's view that vagueness in value comparisons crowds out incommensurability in value. It shows how vagueness can be imposed on a formal model of value relations that has room for different types of incommensurability. The model implements some basic insights of the 'fitting attitudes' analysis of value.

Abstract: The paper provides a general account of value relations. It takes its departure in a special type of value relation, parity, which according to Ruth Chang is a form of evaluative comparability that differs from the three standard forms of comparability: betterness, worseness and equal goodness. Recently, Joshua Gert has suggested that the notion of parity can be accounted for if value comparisons are interpreted as normative assessments of preference. While Gert's basic idea is attractive, the way he develops (...) it is flawed: His modeling of values by intervals of permissible preference strengths is inadequate. Instead, I provide an alternative modeling in terms of intersections of rationally permissible preference orderings. This yields a general taxonomy of all binary value relations. The paper concludes with some implications of this approach for rational choice. (shrink)

It is widely held that the possibility of value-incomparability between alternatives poses a serious threat to comparativism. Some comparativists have proposed to avoid this problem by supplementing the three traditional value relations with a fourth value relation, variously identified as "roughly equal" or "on a par", which is supposed to hold between alternatives that are incomparable by the three traditional value relations. However, in a recent article in this journal, Nien-he Hsieh has proposed that the comparisons thought to require rough (...) equality or parity could instead be understood in terms of the concept of "clumpiness". Against this suggestion, Martin Peterson has argued that the concept of clumpiness allows agents to be exploited in money-pumps, and thus that there is no way of linking clumpiness to rational choice. This would remove the central appeal of the concept. In this note, I show that Peterson’s argument fails to establish that the concept of clumpiness allows agents to be exploited in money-pumps. (shrink)

In his original semantics for counterfactuals, David Lewis presupposed that the ordering of worlds relevant to the evaluation of a counterfactual admitted no incomparability between worlds. He later came to abandon this assumption. But the approach to incomparability he endorsed makes counterintuitive predictions about a class of examples circumscribed in this paper. The same underlying problem is present in the theories of modals and conditionals developed by Bas van Fraassen, Frank Veltman, and Angelika Kratzer. I show how to reformulate all (...) these theories in terms of lower bounds on partial preorders, conceived of as maximal antichains, and I show that treating lower bounds as cutsets does strictly better at capturing our intuitions about the semantics of modals, counterfactuals, and deontic conditionals. (shrink)