Recent work in the philosophy of religion has resurrected Leibniz’s idea that there is a best possible world, perhaps ours. In particular, Klaas Kraay’s [2010] construction of a theistic multiverse and Nevin Climenhaga’s [2018] argument from infinite value theory are novel defenses of a best possible world. I do not think that there is a best world, and show how both Kraay and Climenhaga may be resisted. First, I argue that Kraay’s construction of a theistic multiverse can be resisted from (...) plausible assumptions about set theory. Next, I argue against the value-theoretic assumptions that underlie Climenhaga’s argument and show how to give an infinite value theory where there is no best world. (shrink)

Decision-making under normative uncertainty requires an agent to aggregate the assessments of options given by rival normative theories into a single assessment that tells her what to do in light of her uncertainty. But what if the assessments of rival theories differ not just in their content but in their structure -- e.g., some are merely ordinal while others are cardinal? This paper describes and evaluates three general approaches to this "problem of structural diversity": structural enrichment, structural depletion, and multi-stage (...) aggregation. All three approaches have notable drawbacks, but I tentatively defend multi-stage aggregation as least bad of the three. (shrink)

Theories that use expected utility maximization to evaluate acts have difficulty handling cases with infinitely many utility contributions. In this paper I present and motivate a way of modifying such theories to deal with these cases, employing what I call “direct difference taking”. This proposal has a number of desirable features: it’s natural and well-motivated, it satisfies natural dominance intuitions, and it yields plausible prescriptions in a wide range of cases. I then compare my account to the most plausible alternative, (...) a proposal offered by Arntzenius (2014). I argue that while Arntzenius’s proposal has many attractive features, it runs into a number of problems which direct difference taking avoids. (shrink)

Standard decision theory has trouble handling cases involving acts without finite expected values. This paper has two aims. First, building on earlier work by Colyvan (2008), Easwaran (2014), and Lauwers and Vallentyne (2016), it develops a proposal for dealing with such cases, Difference Minimizing Theory. Difference Minimizing Theory provides satisfactory verdicts in a broader range of cases than its predecessors. And it vindicates two highly plausible principles of standard decision theory, Stochastic Equivalence and Stochastic Dominance. The second aim is to (...) assess some recent arguments against Stochastic Equivalence and Stochastic Dominance. If successful, these arguments refute Difference Minimizing Theory. This paper contends that these arguments are not successful. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.

Many think that Pascal’s Wager is a hopeless failure. A primary reason for this is because a number of challenging objections have been raised to the wager, including the “many gods” objection and the “mixed strategy” objection. We argue that both objections are formal, but not substantive, problems for the wager, and that they both fail for the same reason. We then respond to additional objections to the wager. We show how a version of Pascalian reasoning succeeds, giving us a (...) reason to pay special attention to the infinite consequences of our actions. (shrink)

J.L. Schellenberg argues that divine hiddenness provides an argument for the conclusion that God does not exist, for if God existed he would not allow non-resistant non-belief to occur, but non-resistant non-belief does occur, so God does not exist. In this paper, I argue that the stakes involved in theistic considerations put pressure on Schellenberg’s premise that non-resistant non-belief occurs. First, I specify conditions for someone’s being a resistant non-believer. Then, I argue that many people fulfill these conditions because, given (...) some plausible assumptions, there is a very good pragmatic reason to be a theist rather than an atheist. I assume it is more likely that theists go to heaven than atheists, and I argue there is a non-zero probability that one can receive infinite utility and a method of comparing outcomes with infinite utilities in which the probability of each outcome affects the final expected values. Then, I show how this argument entails there is no good reason to think that there are very many non-resistant non-believers. (shrink)