Miracles, Counterfactuals, and Relativism in Consequentialist Theories of Right Draft of August 30, 2010 ~please do not cite without permission~ Sean Drysdale Walsh University of Minnesota Duluth [email protected] Abstract Many consequentialists claim that there is always a determinate metaphysical fact about which of our options would maximize utility, even if we do not always know which of those options it is. In this paper I challenge this metaphysical claim with my ‘Miracle Alteration Argument, on which I argue that for standard variants of David Lewis’s theory of counterfactuals, there could be no such metaphysical facts about what maximizes utility among all possible options in deterministic worlds. On Lewis’s theory, the ‘similarity of worlds’ relation is too coarse-grained (imprecise and vague) to allow for such metaphysical facts. While many coarse-grained counterfactuals are determinately true, the counterfactuals needed by many consequentialist theories of right are too fine-grained to be determinately true. Lewis’s own way of precisifying coarse-grained counterfactuals using ‘interest’ is relativistic in a way that is unacceptable for most consequentialists, who wish to avoid ethical relativism. Thus, I argue that many consequentialists face a dilemma: they must either (i) reject the standard Lewisian accounts of counterfactuals, or (ii) reject the standard consequentialist idea that options (e.g., actions, rules, and dispositions) can have maximal (or relatively high) utility as a metaphysically objective matter of fact.

Miracles, Counterfactuals, and Relativism in Consequentialist Theories of Right

1. Introduction The study of counterfactuals is an important part of the study of metaphysics. I believe that the study of counterfactuals is also an important part of the study of ethics. For example, Robert Johnson argues that Rosalind Hursthouse’s Aristotelian theory of right action is problematic since the counterfactual question ‘What would a virtuous agent do in the circumstances?’ lacks a determinate (clear and precise) answer.1 In this paper, I will argue that standard consequentialist theories of right are similarly problematic since the counterfactual question ‘What would the consequences of an alternative possible option be?’ lacks a determinate (clear and precise) answer. I will argue that, if one considers the nature of this counterfactual question for standard consequentialist theories of right (assuming compatibilism and determinism, as many do), many standard consequentialist

See Johnson (2003) and Hursthouse (1999). Consider the counterfactual in Hursthouse’s theory of right, ‘The morally right action is what a virtuous agent (in the Aristotelian sense) acting in character would do in the circumstances,’ given that the circumstances are those in which only a vicious (non-virtuous) person could be. Johnson argues that normal moral agents often (i) are indeed in such circumstances and (ii) can do morally right and wrong things in such circumstance. Johnson argues that because it is necessarily contrary to fact that the truly virtuous person could be in such circumstances, we must reject Hursthouse’s theory of right action. After all, if I am in a circumstance that a virtuous person would have avoided, then asking myself ‘What would the virtuous person do in these circumstances?’ seems absurd, since it is impossible for virtuous people to be in such a circumstance.

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theories of right cannot determine right and wrong in a wide variety of circumstances. This paper is not about an epistemic issue, but rather is about a metaphysical issue. Many consequentialists claim that it is a virtue of their view that there is always a determinate metaphysical fact about which of our options would maximize utility, even if we do not always know which of those options it is. In this paper I challenge this metaphysical claim with my ‘Miracle Alteration Argument,’ on which I argue that on standard variants of David Lewis’s theory of counterfactuals, there could be no such metaphysical facts about what maximizes utility in deterministic worlds. On Lewis’s theory of counterfactuals, I argue, the ‘similarity of worlds’ relation is too coarse-grained (imprecise and vague) to allow for such metaphysical facts. While many coarse-grained counterfactuals are determinately true, the counterfactuals needed by many consequentialist theories of right are too fine-grained to be determinately true. Lewis’s own way of precisifying coarse-grained counterfactuals using ‘interest’ is relativistic in a way that is unacceptable for most consequentialists, who wish to avoid ethical relativism. Thus, I argue that many consequentialists face a dilemma: they must either (i) reject the standard Lewisian accounts of counterfactuals, or (ii) reject the standard consequentialist idea that options (such as actions, rules, dispositions, etc.) can have maximal (or relatively high 3

Miracles, Counterfactuals, and Relativism in Consequentialist Theories of Right

and ‘satisficing’) utility as a metaphysically objective matter of fact. If consequentialists wish to retain the standard Lewisian account of counterfactuals, they ought to accept subjective consequentialism, on which what is right or wrong depends on some subjective point of view (e.g., an act is right iff the agent believes it maximizes utility).

2. The Determinacy Standard Mark Timmons says that an adequate moral theory should fulfill the determinacy standard: ‘A moral theory should feature principles that, together with relevant [facts], yield determinate moral verdicts about the morality of actions…’ (Timmons 2002: 14). Many consequentialists put the superiority of their moral theory in terms of its giving a criterion that objectively determines right regardless of what an agent believes or knows, and regardless of the agent’s decision procedures.2 According to the determinacy standard, the moral theory itself is supposed to supply a criterion which, with the nonmoral facts, determines the moral facts regardless of our epistemological limitations.3

For consequentialists that claim the determinacy standard as an advantage consequentialism has over other moral theories, see Sidgwick (1874), Feldman (2006), Pettit in Baron, Pettit, and Slote (1997:133), Parfit (forthcoming: Ch. 9), and Driver (2006: 113-16).

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Cf. Carl Hempel’s Deductive-Nomological Model, which demands that natural laws, plus all the facts, determines the explanandum.

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For example, a divine command theory may be epistemologically inscrutable but nevertheless meet this determinacy standard if, as a matter of fact, there actually is a divine being that makes comprehensive (but inscrutable) judgments about which actions are morally right or wrong. I argue that many consequentialist theories of right fail to meet the determinacy standard in deterministic worlds, much as many divine command theories of right fail the determinacy standard in worlds with no actual divine beings to determine right and wrong.4 A.N. Prior once argued that if we live in a deterministic world (and thus our actions are causally determined), then on classical act utilitarianism every action is trivially right (Prior 2003: 65). On Prior’s view, a determined action has the best consequences of all available actions, since there is but one available action (the causally determined one). Consequentialists might dismiss Prior’s argument by invoking compatibilism, according to which causally determined agents can do otherwise. However, in this paper, I show that given compatibilism Lewis’s account of counterfactuals leads to another serious challenge to utilitarians: various forms of consequentialism (those that require the rank ordering of outcomes for counterfactual alternatives) are

Railton suggests that indeterminacy coming from a pluralistic theory of good is acceptable, but indeterminacy coming from a theory of right is unacceptable (Railton 1992: 731, 735).

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generally unable to determine right at all. Even given all the nonmoral facts, an omnipotent being could not determine the option of maximal utility.

3. The Miracle Alteration Argument Consider a generic, broadly Lewisian account of counterfactuals in terms of closeness of worlds (but not necessarily with Lewis’s ‘mad dog’ modal realism or his counterpart theory).5 Imagine that the actual world is deterministic (as Lewis believes) and I actually decide to stay at home rather than going out for ice cream, but I have the option to go out for ice cream. On a broadly Lewisian view of counterfactuals, a close possible world is maximally similar to the actual world up until (roughly) the time I decide whether or not to go out for some ice cream. So, a close possible world is one which ostensibly is the same up until that point, but instead I go out for ice cream. However, the close possible world cannot be exactly the same up until the exact point that the alternative action begins. That would mean it had the same laws and initial conditions that necessitate that I do the same action and stay home (remember that we are talking about

For a similar account of counterfactuals, see Stalnaker (1968). Often, this possible worlds account of counterfactuals is called the LewisStalnaker account. 5

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a deterministic world). At least one of four things must be different on the standard account of counterfactuals: (a) The laws must be different, or (b) The initial conditions (e.g., at the Big Bang) must be different, or (c) A miracle is inserted at some time before the alternative action, or (d) Some combination of a-c obtains.6

For the purposes of this paper, I am agnostic about which of these must obtain for the difference to obtain. Let me make an important point about the determinacy of counterfactuals in light of the laws of nature. One thing that must obtain, on a standard view of counterfactuals, is that the laws of nature support certain counterfactuals. These ‘nomic counterfactuals’ are determinate in virtue of the laws of the actual world, but are coarsegrained. So, for examples, coarse-grained counterfactuals like ‘If I had lit the match and put the flame to the fuel, it would have burned’ are true in standard contexts in which the circumstances are nomically adequate for the burning of fuel. Given the right context, some such coarse-grained counterfactuals are determinately true. However, I will argue that these determinate counterfactuals are too coarse-grained to

The miracle account may actually be (d), a combination of the first three accounts, since miracles are exceptions to the laws (and thus the laws must be different in close miracle worlds) and the laws themselves are part of the initial conditions (and thus the initial conditions must be different in close miracle worlds).

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ground the more fine-grained counterfactuals required by many versions of consequentialism. Because these nomic counterfactuals that support natural laws are coarse-grained and vague, their truth does not, in themselves, determine the many fine-grained facts which determine the precise close possible world in which they obtain. There are many close possible worlds in which I light the fuel in such circumstances. Some ‘fuel burning’ worlds are more distant that others, but (as Lewis argues) there is no reason to think there will be a uniquely closest world. I will argue that if there is not a uniquely closest world, then there is not a single fact of the matter about what the consequences would be for such an alternative action. So I will not be arguing that all counterfactuals are indeterminate, but I will be arguing that those relevant to many consequentialists are. Consider Lewis’s miracle account for alternative, counterfactual action for my ice cream case. Of such close possible worlds, Lewis says: The deterministic laws of w0 [the actual world] are violated at w1 [a close nonactual possible world] in some simple, localized, inconspicuous way. A tiny miracle takes place. Perhaps a few extra neurons fire in some corner of [the agent’s] brain. (Lewis 1979: 468)

On Lewis’s view, in certain contexts and under certain circumstances, the following coarse-grained ‘ice cream counterfactual’ is true: ‘If I had decided to get ice cream at an ice cream store, I would have procured 8

Miracles, Counterfactuals, and Relativism in Consequentialist Theories of Right

ice cream at a local ice cream store.’ The closer alternative worlds in which I get ice cream are very similar to the actual world prior to the small miracle, but may diverge more substantially after that point. Similarly, in worlds in which Nixon starts a nuclear holocaust, the closest worlds may diverge significantly from the actual world, but only after the miracle (Lewis 1979: 468). Here is a key point for what I call my ‘Miracle Alteration Argument’: there must be multiple ways and places in time and space to put any number of small miracles that alter my behavior and determine that I go out for ice cream. Each alternative miracle represents an alternative possible world, so there are many miracle worlds in which I go out for ice cream. These alternate ways of inserting various miracles for the same coarse-grained ‘ice cream counterfactual’ could affect how I go to the ice cream store, which of my favorite ice cream stores I choose, which of my favorite ice cream flavors I choose, how I react to eating my ice cream, how others react to my getting ice cream, etc.7 For example, do I turn a little left, or right, or stay still (and for how long) when I am at the ice cream parlor? Each of the multiple miraculous, slight rearrangements of my neurons may

To be properly nomic, some argue that the compatibilist counterfactuals of my alternative actions generally should leave my character and dispositions largely intact, but this nevertheless is coarsegrained and gives a lot of leeway. For an account of how character and dispositions are involved in compatibilist counterfactuals, see Clarke (2008).

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affect my future actions and the actions of others (and other features of the physical world around me). There are multiple times and places where multiple types of small miracles that could be inserted into my brain, and these different things can affect longer-term outcomes of the alternative action. Note that I can assume that it is determinate what one’s alternative options are. So, for example, it might be determinate that I indeed have the option to walk to the ice cream store. It might be determinate that I could walk with or without crutches. However, what is not determinate is exactly how a miracle is inserted to realize each within a determinate set of options. And for each precise way this alternative action and its consequences could go due to a miracle, there is a possible world. Certainly some worlds are more distant that others, but there is no reason to think there will be a uniquely closest world. Lewis rejects the idea that there is a uniquely closest world (Lewis 1973: 12, 91-95). But if there is no uniquely closest world, then there is not a single metaphysical fact of the matter about what the consequences would be for my getting the ice cream. Many different but plausible miracles could lead to different outcomes. Lewis’s miracle account is too coarse-grained about similarity of worlds for there to be one utility for each alternative option (each alternative action, alternative rule, alternative disposition, etc.). I agree with Lewis’s insistence that context cannot resolve the indeterminacy for these counterfactuals, and that the answers to these 10

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questions about similarity of worlds are not precisely determined by the laws of physics or initial conditions (Lewis 1973: 12, 91-95). Moreover, it is arguable that chaos theory is nomic in our world (i.e., the butterfly effect obtains, in which small differences in initial conditions lead to significant differences in long-term outcomes). So, to maintain this chaotic, law-like character across worlds, generally such butterfly effects obtain for close possible worlds. However, if such butterfly effects obtain, then slight differences in the miracles can generate significant differences in utility outcomes for each alternative. A variant of my Miracle Alteration Argument can be applied even if we reject the miracles account of counterfactuals and instead advocate for (i) slightly altering the natural laws for nearby possible worlds or (ii) slightly altering the initial conditions. If we can change the initial conditions or the laws of nature slightly to have a maximally similar world to the actual world up until the necessary time of divergence for the alternative act to occur, such changes can certainly be done in a variety of ways that mimic the variety of ways small miracles can be inserted. There can be a variety of such close possible worlds that represent a variety of outcomes for an alternative action that differ in the initial conditions or laws of nature. As with miracle alteration, it is not the case that one way of altering the laws or initial conditions (in a way that leads to the same alternative action with a maximally similar prior history) is more likely (and close to the actual world) than others. 11

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A consequentialist might reply that the laws, empirical facts, or a priori truths demands that these miracles be represented by objective, precise probabilities for their outcomes for a particular option that is spread across all the various close worlds. So, they might argue, while there is no one utility for an alternative option, there is a precise distribution of probabilities for the utilities that may obtain. I disagree, and would argue that the probabilities themselves are vague and coarse-grained. Does one small miracle, placed in a certain way among the neurons of the brain, have some precise, fine-grained probability compared to other miracles placed in other ways? Certainly some outlandish miracle may be less probable in coarse-grained ways, but not precisely less probable (say, exactly 83.2364% less probable than some other). Some miracles (or altered laws or initial conditions) might be slightly more or less probable than others, but there is no compelling reason to believe this probability is precise or determinate. However, to calculate expected utility as a function of objective probabilities (rather than subjective probabilities, which may be determinate simply because an agent believes they are) across a wide range of outcomes and miracles for one alternative option, we would need more precise probabilities than ‘Miracle1 seems a bit more probable than Miracle2.’ Coarse-grained (vague and imprecise) probabilities are hardly precise enough to rank order a wide array of potential outcomes across a wide

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array of alternative actions. Lewis advocates for the vagueness of probabilities when he says: Recognizing the inevitable vagueness of comparative salience [concerning similarity of worlds], we see that we almost never will simply have a tie. What we will have is indeterminacy between many reasonable ways to resolve the vagueness. (Lewis 1973: 116)

Thus, a metaphysically objective (non-subjective8) form of expected utility for an alternative possible option (as a function of these indeterminate, vague, and imprecise probabilities) is metaphysically indeterminate as well.9 Consider another reply to my Miracle Alteration Argument. A consequentialist might reply that even though a number of different permutations of miracles (initial conditions or laws) would enable one

Although this is directly an argument against objective, actual utility theories, my argument also puts pressure on subjective, expected utility theories. For example, why should we take a subjective theory seriously when it is about something which does not exist? Similarly, why should we take a subjective divine command theory seriously if no divine being exists and thus an objective divine command theory could not obtain for the actual world?

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McCall points out that ‘Lewis accepts this inherent [metaphysical] vagueness’ of similarity of worlds (1984: 463). McCall also says: ‘In logically possible branches on which Napoleon wins at Waterloo almost anything goes, and it seems no more unlikely that he should die on St. Helena than that he should die at Fontainebleau’ (1984: 477). While I do not think anything goes, since I suspect it would be even a bit less likely that Waterloo-winning Napoleon would die in Siberia or the United States, I do think that it is not less probable in any metaphysically precise way.

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to perform an alternative action, the consequences for the alternative option may be overdetermined. A set of initial conditions may overdetermine a single outcome despite such variations in miracles (Lewis 1979: 473-474). My reply is that some outcomes at the level of short-term, coarsegrained descriptions may be overdetermined, but the long-term, finegrained utility outcomes generally will not be overdetermined as a matter of law (due to the nomic nature of chaos). So, for example, consider the alternative action in which I go out for ice cream rather than stay at home. The indeterminacy of my getting either one of my two favorite flavors of ice cream or going to one of my two favorite ice cream parlors, at a coarse-grained level of description, will probably not significantly alter the utility outcome in the short-term. I suspect, in this context, the short-term consequences for my getting ice cream in the ‘chocolate flavor world’ and the ‘vanilla flavor world’ typically will be roughly the same. However, chaos theorist rightly point out that little differences in initial conditions regularly have dramatic differences in long-term outcomes. My future counterfactual choices of chocolate or vanilla, or Baskin Robbins or Cold Stone Creamery, for example, may affect my choices and others choices in the future. It might affect what career I pursue, or who I associate with in the future. For example, at Baskin Robbins I might have met a future spouse, with whom I would have had some (albeit indeterminate) particular children. 14

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A consequentialist might reply here that all the alternatives I am speaking about (e.g., whom I marry, or what career I have) also have roughly the same long-term outcomes. However, my reply is that (i) what progeny comes from the option can indeed make for significantly different outcomes, and (ii) the consequentialist generally wants precise metaphysical facts about things like which of my career or marriage options maximize utility, and there seems to be no reason to think that it is possible to precisely rank order one option over the other. Others might reply to the Miracle Alteration Argument and argue that each deterministic alternative possible world represents an alternative option for an agent, and since each possible world represents a precise utility for that option, then we have a precise utility for each option. I suspect Lewis would agree with me that the alternative options agents have are not this precise and fine-grained. So, while I do have the option to go out for ice cream (a coarse-grained option), I do not have the option to go out for ice cream in a particular possible world in which all the consequences are causally determined in a very particular way with a particular utility. Options for alternative actions are coarse-grained, imprecise, and vague. Agents generally lack the option to make their alternative actions come from a specific miracle. But different miracles can lead to different outcomes in deterministic worlds. Since the options are

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coarse-grained and vague, their outcomes are coarse-grained and vague as well.10 The counterfactuals for such options are coarse-grained in a way similar to that of the counterfactuals needed to support natural laws. Coarse-grained counterfactuals like ‘If I had lit the match and put the flame to the fuel, it would have burned’ are true, but there are many, many close possible worlds in which I light the match and it burns. The outcomes for that burning will vary widely across all those worlds, even given the specific context and situation in which it occurs.

4. Ethical Relativism in Consequentialist Theories of Right Things get even worse for many consequentialists and utilitarians. Lewis says that counterfactuals generally ought to be precisified from among the ‘many reasonable ways to resolve the vagueness’ by using interest (Lewis 1973: 116). According to Lewis, similarity of worlds is a vague notion, since there is no objective matter of fact about which worlds are more similar than others, and context is often not enough to make a counterfactual determinate (Lewis 1973: 91-95). To precisify (to some extent) coarse-grained counterfactuals given this indeterminacy of similarity, Lewis proposes that we use our interest to decide.

I believe it is arguable that alternative options are coarse-grained and indeterminate regardless of counterfactual semantics, but this is an argument for another paper.

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But one can immediately see how bad this would be for the classical objective consequentialist, who wants an objective theory of right that does not depend for its substance on subjective interests.11 However, if we take Lewis’s account of counterfactuals seriously, we should take such consequentialism to require using subjective (individual or group) interests in just this way. This makes classical act utilitarianism, for example, relativistic, since this makes the rank ordering of the utilities of possible actions relative to interest, and thus makes what is right and wrong relative to interest. It is important to see that this interest, when it is not fixed by the context of the situation, is entirely up to personal preference. Some context will help precisify counterfactuals. For example, if I ask Bert ‘What would have happened if Caesar had led the U.S. in the Vietnam War?’, Bert may respond ‘Are you thinking of the Caesar who uses the latest weapons, or the Ceasar who uses the weapons with which he actually grew up?’12 I can make the context more specific by saying ‘I was thinking about what he would do with the modern weapons available today.’

I am following Feldman’s (2006) distinction between ‘objective consequentialists’ who are interested in actual utility, and ‘subjective consequentialists’ who are interested in a subjective form of expected utility. I call into question the notion of ‘actual utility’ that Feldman employs.

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See Quine (1960), p. 222.

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However, it is not reasonable to ask what the exact physical states of the world will be if Caesar were alive today, and it is just that state which dictates the long-term consequences for the counterfactual question ‘What would happen if Caesar fought a war today?’ If Bert kept incessantly asking questions to precisify the counterfactuals concerning the long-term outcome, at some point I (or anyone) would cease to be able to answer the questions to clarify the context. At that point, Lewis suggests that one introduce arbitrary personal preferences (interest) to dictate some of the ways the counterfactual goes, but even this will not precisify enough to determine the entire initial condition and laws that point to exactly one close possible world. Even by adding such relativism, as Lewis suggests we should, some indeterminacy remains. Objective consequentialism is supposed to give an alternative to ethical relativism by arguing that there are objective metaphysical facts about what the optimal consequences are among alternative options. However, standard forms of objective consequentialism require ethical relativism on Lewis’s account of counterfactuals, since interest is required for the precisification of counterfactuals.13

Lewis’ ‘interests’ are coarse-grained as well, and often will not by themselves determine the exact closest possible world for a coarsegrained counterfactual.

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5. Conclusion Many consequentialists assert the superiority of their moral theory in terms of its giving a criterion that objectively determines right without the need for relativistic, subjective judgment. In this paper, however, I have argued that consequentialism cannot have such a criterion of right, if we presume Lewisian compatibilism. I have argued that various consequentialist theories of right are indeterminate since the rank ordering of the outcomes of possible options are indeterminate. Without a determinate rank ordering among the outcomes of alternative options, many objective consequentialists cannot determine right action. There are a multitude of deterministic possible worlds which are (at least roughly) identical to the actual world up until they must diverge for some counterfactual alternative action to occur. These worlds diverge, for example, in the utility of the outcomes for that alternative action. Empirical facts and a priori principles do not determine which of these alternative worlds resembles our world more closely. Lewis suggests that one’s interest ought to precisify this to some extent. However, if interest is needed to help determine utility for counterfactual actions, then utilitarianism is relativistic. Thus, the standard utilitarian theory of right itself is indeterminate, and possibly relativistic. Not only are precise, fine-grained alternative options not nomically required for agents to have legitimate alternatives, but also 19

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imprecise, coarse-grained alternatives are nomically required. Chaos is nomic, and with some plausible premises, chaos nomically requires that each (course-grain individuated) alternative action has a wide variety of potential outcomes. Chaos theory says that given little differences in initial conditions (in worlds like our own), there will very likely be substantially different longer-term outcomes. There are a number of plausible, slightly different ways to insert miracles, change the laws, or change the initial conditions in order to accommodate the counterfactual for an alternative action. Each permutation can have a different outcome, and a different utility. Which permutation is closest and most similar is indeterminate and vague. Lewis says not only that context will not generate precision for the similarity relations among these counterfactual worlds (Lewis 1973: 13, 91-95, 116), but also that there will be no precise probability that is simply even between the similarity of two possible worlds to the actual world. There are no compelling reasons to believe in such determinacy (e.g., no reason such as ‘The laws of nature require determinacy, and this so does consequentialism’) and there are many reasons to believe in the indeterminacy (e.g., Lewis might accept my Miracle Alteration Argument). As a final note, this metaphysical imprecision is not a problem for rational choice among counterfactual alternatives. Decision theorists have been writing for years about epistemic vagueness and imprecision in rational choice. I see no reason why much of the 20

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literature on epistemic indeterminacy and rational choice cannot be applied to cases of metaphysical indeterminacy among alternatives as well. There is a substantial literature on ‘imprecise probability,’ which discusses the rationality of decisions when relevant information is unobtainable, conflicting, or vague and the relevant probabilities and alternatives are unrankable.14

See Arló-Costa and Helzner (2010), Gärdenfors and Sahlin (1988: Part 4), and Levi (2000). 14

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References Arló-Costa, H., and J. Helzner. 2010. Ambiguity aversion: the explanatory power of indeterminate probabilities. Synthese 172: 37–55. Baron, M., P. Pettit, and M. Slote. 1997. Three Methods of Ethics. Oxford: Blackwell. Clarke, R. 2008. Dispositions, abilities to act, and free will: the new dispositionalism. Mind 118: 323-51. Driver, J. 2006. Virtue theory (a debate with Rosalind Hursthouse). In Contemporary Debates In Moral Philosophy. ed. J. Dreier, 113-123. Cambridge: Blackwell Publishing. Feldman, F. 2006. Actual utility, the objection from impracticality, and the move to expected utility. Philosophical Studies 129: 49-79. Gärdenfors, P. and N. Sahlin. 1988. Decision, Probability, and Utility. Cambridge University Press. Hursthouse, R. 1999. On Virtue Ethics. Oxford: Oxford University Press. Johnson, R. 2003. Virtue and right. Ethics 113.4: 810-834. Levi, I. 2000. Imprecise and indeterminate probabilities. Risk, Decision and Policy 5: 111-122 Lewis, D. 1973. Counterfactuals. Oxford: Blackwell. Lewis, D. 1979. Counterfactual dependence and time’s arrow. Noûs 13: 455-476. McCall, S. 1984. Counterfactuals based on real possible worlds. Noûs 18: 463-477. Parfit, D. forthcoming. On What Matters. Oxford: Oxford University Press. Prior, A. 2003. Papers on Time and Tense. 2nd ed. New York: Oxford University Press. Quine, W. V. O. 1960. Word and Object. Cambridge: MIT Press. Railton, P. 1992. Pluralism, determinacy, and dilemma. Ethics 102: 720741. Sidgwick, H. 1874. The Methods of Ethics. London: Macmillan. Stalnaker, R. 1968. A theory of conditionals. In Studies in Logical Theory American Philosophical Quarterly Monograph Series 2, ed. N. Rescher, 98-112. Oxford: Blackwell. Timmons, M. 2002. Moral Theory: An Introduction. New York: Rowman and Littlefield.

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