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)

This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

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This volume concerns Rational Agents - humans, players in a game, software or institutions - which must decide the proper next action in an atmosphere of partial information and uncertainty. The book collects formal accounts of Uncertainty, Rationality and Agency, and also of their interaction. It will benefit researchers in artificial systems which must gather information, reason about it and then make a rational decision on which action to take.

One can interpret the No Probabilities for Acts-Principle, namely that any adequate quantitative decision model must in no way contain subjective probabilities for actions in two ways: it can either refer to actions that are performable now and extend into the future or it can refer to actions that are not performable now, but will be in the future. In this paper, I will show that the former is the better interpretation of the principle.

Isaac Levi has long criticized causal decisiontheory on the grounds that it requiresdeliberating agents to make predictions abouttheir own actions. A rational agent cannot, heclaims, see herself as free to choose an actwhile simultaneously making a prediction abouther likelihood of performing it. Levi is wrongon both points. First, nothing in causaldecision theory forces agents to makepredictions about their own acts. Second,Levi's arguments for the ``deliberation crowdsout prediction thesis'' rely on a flawed modelof the measurement of belief. Moreover, theability of agents (...) to adopt beliefs about theirown acts during deliberation is essentialto any plausible account of human agency andfreedom. Though these beliefs play no part inthe rationalization of actions, they arerequired to account for the causalgenesis of behavior. To explain the causes ofactions we must recognize that (a) an agentcannot see herself as entirely free in thematter of A unless she believes herdecision to perform A will cause A,and (b) she cannot come to a deliberatedecision about A unless she adoptsbeliefs about her decisions. FollowingElizabeth Anscombe and David Velleman, I arguethat an agent's beliefs about her own decisionsare self-fulfilling, and that this can beused to explain away the seeming paradoxicalfeatures of act probabilities. (shrink)

When we deliberate about what to do, we appear to be free to decide on different options. Three accounts use ordinary beliefs to explain this apparent freedom—appealing to different types of ‘epistemic freedom’. When an agent has epistemic freedom, her evidence while deliberating does not determine what decision she makes. This ‘epistemic gap’ between her evidence and decision explains why her decision appears free. The varieties of epistemic freedom appealed to might look similar. But there is an important difference. Two (...) rely on an agent's ability to justifiably form beliefs unconstrained by evidence, and identify decisions as beliefs—either beliefs about acts or about decisions. But, when used to explain apparent freedom, these accounts face serious problems: they imply that agents have epistemic freedom over evidence-based beliefs, and rely on a faulty notion of justification. Underlying these troubles, it turns out that these accounts presuppose an unexplained apparent ability to form different beliefs. A third variety of epistemic freedom uses ignorance conditions instead (Levi and Kapitan). We appear free partly because we’re ignorant of what we’ll decide. Ignorance-based accounts avoid the above problems, and remain a promising alternative. (shrink)

Decision-theoretic representation theorems have been developed and appealed to in the service of two important philosophical projects: in attempts to characterise credences in terms of preferences, and in arguments for probabilism. Theorems developed within the formal framework that Savage developed have played an especially prominent role here. I argue that the use of these ‘Savagean’ theorems create significant difficulties for both projects, but particularly the latter. The origin of the problem directly relates to the question of whether we can have (...) credences regarding acts currently under consideration and the consequences which depend on those acts; I argue that such credences are possible. Furthermore, I argue that attempts to use Jeffrey’s non-Savagean theorem in the service of these two projects may not fare much better. (shrink)

Many philosophers (myself included) have been converted to causal decision theory by something like the following line of argument: Evidential decision theory endorses irrational courses of action in a range of examples, and endorses “an irrational policy of managing the news”. These are fatal problems for evidential decision theory. Causal decision theory delivers the right results in the troublesome examples, and does not endorse this kind of irrational news-managing. So we should give up evidential decision theory, and be causal decision (...) theorists instead. Unfortunately, causal decision theory has its own family of problematic examples for which it endorses irrational courses of action, and its own irrational policy that it is committed to endorsing. These are, I think, fatal problems for causal decision theory. I wish that I had another theory to offer in its place. (shrink)