Suppose that you prefer A to B, B to C, and C to A. Your preferences violate Expected Utility Theory by being cyclic. Money-pump arguments offer a way to show that such violations are irrational. Suppose that you start with A. Then you should be willing to trade A for C and then C for B. But then, once you have B, you are offered a trade back to A for a small cost. Since you prefer A to B, you (...) pay the small sum to trade from B to A. But now you have been turned into a money pump. You are back to the alternative you started with but with less money. This Element shows how each of the axioms of Expected Utility Theory can be defended by money-pump arguments of this kind. The Element also defends money-pump arguments from the standard objections to this kind of approach. This title is also available as Open Access on Cambridge Core. (shrink)

This paper develops transfinite extensions of transitivity and acyclicity in the context of population ethics. They are used to argue that it is better to add good lives, worse to add bad lives, and equally good to add neutral lives, where a life's value is understood as personal value. These conclusions rule out a number of theories of population ethics, feed into an argument for the repugnant conclusion, and allow us to reduce different-number comparisons to same-number ones. Challenges to these (...) arguments are addressed, including the issue of comparing existence and non-existence in terms of personal value, the possibility of minimal quanta of time and life, and the meaningfulness of measuring closeness between outcomes with different population sizes. An asymmetry is uncovered between transfinite cycles of worseness and betterness, supporting a version of the weak procreative asymmetry. Transfinite transitivity principles are also favourably compared to the better-known principles of continuity. (shrink)

Knowledge is good, ignorance is bad. So it seems, anyway. But in this dissertation, I argue that some ignorance is epistemically valuable. Sometimes, we should suspend judgment even though by believing we would achieve knowledge. In this apology for ignorance (ignorance, that is, of a certain kind), I defend the following four theses: 1) Sometimes, we should continue inquiry in ignorance, even though we are in a position to know the answer, in order to achieve more than mere knowledge (e.g. (...) understanding) while minimizing the effects of confirmation bias. 2) It’s false that we should believe every proposition such that we are guaranteed to be right about it (and even such that we are guaranteed to know it) if we believe it. 3) Being in a position to know is the norm of assertion: importantly, this does not require belief or (thereby) knowledge, and so proper assertion can survive speaker-ignorance. 4) It can be permissible and conversationally useful to tell audiences things that it is logically impossible for them to come to know: Proper assertion can survive (necessary) audience-side ignorance. Cumulatively, this project suggests that, properly understood, ignorance has an important role to play in the good epistemic life. (shrink)

Human persons can act with libertarian freedom in heaven according to one prominent view, because they have freely acquired perfect virtue in their pre-heavenly lives such that acting rightly in heaven is volitionally necessary. But since the character of human persons is not perfect at death, how is their character perfected? On the unilateral model, God alone completes the perfection of their character, and, on the cooperative model, God continues to work with them in purgatory to perfect their own character. (...) I argue that although both models can make sense of all human persons enjoying free will in heaven on various assumptions, the cooperative model allows all human persons in heaven to enjoy a greater degree of freedom. This consideration about the degree of heavenly freedom provides a reason for God to implement the cooperative model. (shrink)

What does it mean to be an embodied thinker of abstract concepts? Does embodiment shape the character and quality of our understanding of universals such as 'dog' and 'beauty', and would a non-embodied mind understand such concepts differently? I examine these questions through the lens of Thomas Aquinas’s remarks on the differences between embodied (human) intellects and non-embodied (angelic) intellects. In Aquinas, I argue, the difference between embodied and non-embodied intellection of extramental realities is rooted in the fact that embodied (...) and non-embodied intellects grasp different kinds of universals by means of different kinds of intelligible species (intellectual likenesses), which elicit in them different “modes” of understanding. By spelling out what exactly it means to be an embodied knower, on Aquinas’s account, I argue, we can also shed new light on his mysterious claim that the embodied intellect “turns to phantasms”—the imagination’s likenesses of individuals—in its acts of understanding. (shrink)

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned.Each argument concludes that rationality requires your credences to be probabilities.I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and a corresponding (...) argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. I discuss the extent to which the original arguments can be buttressed.1. Introduction2. The Dutch Book Argument2.1. Saving the Dutch Book argument2.2. ‘The Dutch Book argument merely dramatizes an inconsistency in the attitudes of an agent whose credences violate probability theory’3. Representation Theorem-based Arguments4. The Calibration Argument5. The Gradational Accuracy Argument6. Conclusion. (shrink)

An agent submaximizes with motivation when she aims at the best but chooses a less good option because of a countervailing consideration. An agent satisfices when she rejects the better for the good enough, and does so because the mere good enough gets her what she really wants. Motivated submaximization and satisficing, so construed, are different ways of choosing a suboptimal option, but this difference is easily missed. Putative proponents of satisficing tend to argue only that motivated submaximization can be (...) appropriate while critics of satisficing tend to criticize satisficing, as I construe it. The existing literature, then, leaves satisficing in a very bad state: there are no good arguments for it and there are three unanswered objections to it. This paper clarifies the distinction between motivated submaximization and satisficing and refutes the three most prominent objections to the claim that satisficing can be appropriate. (shrink)

In replying to certain objections to the existence of God, Robert Adams, Bruce Langtry, and Peter van Inwagen assume that God can appropriately choose a suboptimal world, a world less good than some other world God could have chosen. A number of philosophers, such as Michael Slote and Klaas Kraay, claim that these theistic replies are therefore committed to the claim that satisficing can be appropriate. Kraay argues that this commitment is a significant liability. I argue, however, that the relevant (...) defenses of theism are committed to the appropriateness of, not satisficing, but motivated submaximization. When one submaximizes with motivation, one aims at the optimum but accepts the good enough because of a countervailing consideration. When one satisfices, one aims at the good enough and chooses the good enough because it realizes her aim at the good enough. While commitment to the appropriateness of satisficing may be a significant liability, commitment to the appropriateness of motivated submaximization is not. (shrink)

This is the most comprehensive book ever published on philosophical methodology. A team of thirty-eight of the world's leading philosophers present original essays on various aspects of how philosophy should be and is done. The first part is devoted to broad traditions and approaches to philosophical methodology. The entries in the second part address topics in philosophical methodology, such as intuitions, conceptual analysis, and transcendental arguments. The third part of the book is devoted to essays about the interconnections between philosophy (...) and neighbouring fields, including those of mathematics, psychology, literature and film, and neuroscience. (shrink)

A decade ago, Harris Nover and I introduced the Pasadena game, which we argued gives rise to a new paradox in decision theory even more troubling than the St Petersburg paradox. Gwiazda's and Smith's articles in this volume both offer revisionist solutions. I critically engage with both articles. They invite reflections on a number of deep issues in the foundations of decision theory, which I hope to bring out. These issues include: some ways in which orthodox decision theory might be (...) supplemented; the role of simulations of such infinite games; the role of small probabilities, and of idealization, in decision theory; tolerance about practical norms; and alternative ways of understanding decision theory's job description. (shrink)

Three very prominent arguments for atheism are (1) the argument from sub-optimality, (2) the problem of no best world, and (3) the evidential argument from gratuitous evil. To date, it has not sufficiently been appreciated that several important criticisms of these arguments have all relied on a shared strategy. Although the details vary, the core of this strategy is to concede that God either cannot or need not achieve the best outcome in the relevant choice situation, but to insist that (...) God must and can achieve an outcome that is good enough. In short, this strategy invokes divine satisficing in response to these arguments for atheism. (The widespread use of this strategy may have gone unnoticed because the appeal to divine satisficing is usually implicit.) In sections 1–3, the three arguments for atheism will be set out, and it will be shown that the relevant replies all employ this shared strategy. Section 4 will show that those who invoke divine satisficing have failed to establish that this is a coherent notion. Accordingly, these replies to three important arguments for atheism are, at present, incomplete. (shrink)

We pose and resolve several vexing decision theoretic puzzles. Some are variants of existing puzzles, such as 'Trumped' (Arntzenius and McCarthy 1997), 'Rouble trouble' (Arntzenius and Barrett 1999), 'The airtight Dutch book' (McGee 1999), and 'The two envelopes puzzle' (Broome 1995). Others are new. A unified resolution of the puzzles shows that Dutch book arguments have no force in infinite cases. It thereby provides evidence that reasonable utility functions may be unbounded and that reasonable credence functions need not be countably (...) additive. The resolution also shows that when infinitely many decisions are involved, the difference between making the decisions simultaneously and making them sequentially can be the difference between riches and ruin. Finally, the resolution reveals a new way in which the ability to make binding commitments can save perfectly rational agents from sure losses. (shrink)

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and (...) a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. (shrink)

In this paper it is shown that the most rational of all creatures, Homo Oeconomicus, can be enticed to freely engage in an activity that is guaranteed to lead to his ruin. It is furthermore shown that this is possible if and only if utility functions are unbounded. The paper thus develops an argument in favour of bounded utility functions.

The so-called optimising conception of rationality includes (amongst other things) the following two claims: (i) that it is irrational to choose an option if you know there is a better one, and (ii) there are no situations in which an agent, through no practical fault of her own, cannot avoid acting irrationally. As part of his ongoing attempt to explain why we need to go beyond the optimising conception, Michael Slote discusses a number of examples in which it seems that (...) (i) and (ii) are inconsistent. According to Slote, these situations seem to involve the existence of rational supererogation (a denial of (i)), or rational dilemmas (a denial of (ii)). The purpose of this paper is to examine Slote''s arguments for these claims, and to propose an alternative solution to the problem he presents. (shrink)

Practical reasoning aims at deciding what actions to perform in light of the goals a rational agent possesses. This has been a topic of interest in both philosophy and artificial intelligence, but these two disciplines have produced very different models of practical reasoning. The purpose of this paper is to examine each model in light of the other and produce a unified model adequate for the purposes of both disciplines and superior to the standard models employed by either.The philosophical (decision-theoretic) (...) model directs activity by evaluating acts one at a time in terms of their expected utilities. It is argued that, except in certain special cases, this constitutes an inadequate theory of practical reasoning leading to intuitively incorrect action prescriptions. Acts must be viewed as parts of plans, and plans evaluated as coherent units rather than piecemenal in terms of the acts comprising them. Rationality dictates choosing acts by first choosing the plans prescribing them. Plans, in turn, are compared by looking at their expected values. However, because plans can be embedded in one another, we cannot select plans just by maximizing expected values. Instead, we must employ a more complex criterion here named coextendability. (shrink)

Suppose you have an infinite past. If you had banked the spare dollar you have always had, then the interest would have made you rich by now. Your procrastination is inexcusable. But what should you have done? At any time at which you invest the dollar you would regret not investing it earlier. Satisficers can solve prospective puzzles involving infinite choice but cannot solve this retrospective puzzle about regret. A moral version of the puzzle suggests that there can be inevitable (...) moral failure. It does so without appeal to moral luck, moral dilemmas or original sin. (shrink)

Moving from simple to increasingly sophisticated candidate cases, I argue against the idea that there can be cases in which, due to no fault of the agent or to any ambiguity regarding how things will go depending on which option is selected, all the options available to an agent are rationally impermissible. Whether there are cases that fit this bill—qualifying as what I will label no-fault-or-ambiguity rational dilemmas—depends on the characteristics of conclusive reasons. My reasoning leads me to the view (...) that a key feature of conclusive reasons is that they capture or ground overall assessments that are relationally significant. I then argue that, while this view does not itself conflict with the most sophisticated candidate cases of purported dilemmas of the relevant sort, following the spirit of the view does lead to a conclusion that blocks counting even these cases as ones in which there is a conclusive reason against every available option. My conclusion is that there is no solid basis for the view that there are cases of no-fault-or-ambiguity rational dilemmas. (shrink)

We examine a distinctive kind of problem for decision theory, involving what we call discontinuity at infinity. Roughly, it arises when an infinite sequence of choices, each apparently sanctioned by plausible principles, converges to a ‘limit choice’ whose utility is much lower than the limit approached by the utilities of the choices in the sequence. We give examples of this phenomenon, focusing on Arntzenius et al.’s Satan’s apple, and give a general characterization of it. In these examples, repeated dominance reasoning (...) (a paradigm of rationality) apparently gives rise to a situation closely analogous to having intransitive preferences (a paradigm of irrationality). Indeed, the agents in these examples are vulnerable to a money pump set-up despite having preferences that exhibit no obvious defect of rationality. We explore several putative solutions to such problems, particularly those that appeal to binding and to deliberative dynamics. We consider the prospects for these solutions, concluding that if they fail, the examples show that money pump arguments are invalid. (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)

In a recent article (Kraay 2013), I argued that some prominent responses to two important arguments for atheism invoke divine satisficing – and that the coherence and propriety of this notion have not been established. Chris Tucker (2016) agrees with my evaluation of divine satisficing, but disagrees with my exegesis of these responses. He argues that they should be understood as invoking motivated submaximization instead. After reviewing the dialectical situation to date, I assess whether motivated submaximization can be deployed in (...) such a way as to defeat these argument for atheism. I argue that it’s far from clear that it can. (shrink)

Theories of rationality advance principles that differ in topic, scope, and assumptions. A typical version of the principle of utility maximization formulates a standard rather than a procedure for decisions, evaluates decisions comprehensively, and relies on idealizations. I generalize the principle by removing some idealizations and making adjustments for their absence. The generalizations accommodate agents who have incomplete probability and utility assignments and are imperfectly rational. They also accommodate decision problems with unstable comparisons of options.

In some decision problems adoption of an option furnishes evidence about the option's consequences. Rational decisions take account of that evidence, although it makes an option's adoption changes the option's expected utility.

There has been considerable debate regarding the relative merits of two theses about moral obligation known as actualism and possibilism. Both theses seek to give expression to the general idea that one ought to do the best one can. According to actualism, one’s obligations turn on what would happen if one chose some course of action, whereas, according to possibilism, they turn on what could happen if one chose some course of action. There are two strands to the debate: the (...) substantive verdicts that the two theses render in particular cases, and the accounts that they yield of the conceptual structure of moral obligation. Possibilism is conceptually appealing, whereas actualism is not, but the latter may seem to render superior substantive verdicts. In this paper, it is argued that, by turning from the objectivist’s emphasis on what is actually best to the prospectivist’s emphasis on what one’s evidence indicates is best, possibilists can provide an account of moral obligation that is both conceptually and substantively attractive. (shrink)

A general format is introduced for deriving preferences over states of affairs from preferences over a set of contextually complete alternatives. Formal results are given both for this general format and for a specific instance of it that is a plausible explication of ceteris paribus preference.

This paper uses the idea of a proxy, which figures in discussions of bounded rationality, to construct an argument for a revisionary conclusion about ideal instrumental rationality. I consider how subjective responses can figure as proxies in heuristics and develop the following argument: (1) Proxies, even if relatively easy to recognize, can sometimes be messy, prompting incomplete or cyclic preferences. (2) From the point of view of ideal instrumental rationality, it is permissible for an agent to be concerned with a (...) proxy rather than with what it is a proxy for. And so, (3) although it is standardly assumed, as part of the prevailing conception of ideal instrumental rationality, that rational preferences are complete and acyclic, neither incomplete preferences nor cyclic preferences can be dismissed as invariably irrational from the point of view of ideal instrumental rationality. (shrink)