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)

Traditional theistic arguments conclude that God exists. Pragmatic theistic arguments, by contrast, conclude that you ought to believe in God. The two most famous pragmatic theistic arguments are put forth by Blaise Pascal (1662) and William James (1896). Pragmatic arguments for theism can be summarized as follows: believing in God has significant benefits, and these benefits aren’t available for the unbeliever. Thus, you should believe in, or ‘wager on’, God. This article distinguishes between various kinds of theistic wagers, including finite (...) vs. infinite wagers, premortem vs. postmortem wagers, and doxastic vs. acceptance wagers. Then, we’ll turn to the epistemic-pragmatic distinction, and discusses the nuances of James’ argument, and how views like epistemic permissivism and epistemic consequentialism provide unique “hybrid” wagers. Finally, we’ll cover outstanding objections and responses. (shrink)

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (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)

This article argues that we should be prudentially and morally biased toward earlier events: other things equal, we should prefer for good events to occur earlier and disprefer for bad events to occur earlier. The argument contends that we should accord at least some credence—if only a small one—to a theoretical package featuring the growing block theory of time and that that package generates a presumptive bias toward earlier events. Rival theoretical packages are considered. Under reasonable allocations of credence to (...) them, the presumptive bias escapes defeat. The argument has several corollaries: other things equal, we should be biased toward the past over the future, the further past over the nearer past, and the nearer future over the further future. (shrink)

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

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)

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 :31–58, 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)

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)

I examine the relationship between taking Pascal’s wager, faith, and hope. First, I argue that many who take Pascal’s wager have genuine faith that God exists. The person of faith and the wagerer have several things in common, including a commitment to God and positive cognitive and conative attitudes toward God’s existence. If one’s credences in theism are too low to have faith, I argue that the wagerer can still hope that God exists, another commitment-justifying theological virtue. I conclude with (...) two upshots of the argument, including how it provides responses to common objections to Pascal’s wager. (shrink)

Epistemic permissivism is the thesis that the evidence can rationally permit more than one attitude toward a proposition. Pascal’s wager is the idea that one ought to believe in God for practical reasons, because of what one can gain if theism is true and what one has to lose if theism is false. In this paper, I argue that if epistemic permissivism is true, then the defender of Pascal’s wager has powerful responses to two prominent objections. First, I argue that (...) if permissivism is true, then permissivism is true about theistic belief. Second, I show how epistemic permissivism about theistic belief dispels two objections to Pascal’s wager: the objection that wagering is impossible, and the objection that wagering is epistemically impermissible. (shrink)

Epistemic consequentialism is the view that epistemic goodness is more fundamental than epistemic rightness. This paper examines the relationship between epistemic consequentialism and theistic belief. I argue that, in an epistemic consequentialist framework, there is an epistemic reason to believe in God. Imagine having an unlimited amount of time to ask an omniscient being anything you wanted. The potential epistemic benefits would be enormous. Considerations like these point to an epistemic version of Pascal’s wager. I compare and contrast the epistemic (...) wager with the traditional wager, and argue that the epistemic wager has several notable advantages. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (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)

First, I introduce the concept of a “non-agential subject,” where a non-agential subject exists within an organism and has phenomenally conscious experiences in a morally significant way, but is not morally responsible for the organism's voluntary actions. Second, I argue that it's a live possibility that typical adult humans contain non-agential subjects. Finally, I argue that, if there are non-agential subjects, this has important and surprising implications for a variety of ethical issues. Accordingly, ethicists should pay more attention to whether (...) there are non-agential subjects and what their implications for ethics would be. (shrink)

It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the same (...) agents and some agents are better off in the first world than they are in the second and no agents are worse off than they are in the second, then the first world is better than the second. I show that if we accept four axioms – the Pareto principle, transitivity, an axiom stating that populations of worlds can be permuted, and the claim that if the ‘at least as good as’ relation holds between two worlds then it holds between qualitative duplicates of this world pair – then we must conclude that there is ubiquitous incomparability between infinite worlds. I show that this is true even if the populations of infinite worlds are disjoint or overlapping, and that we cannot use any qualitative properties of world pairs to rank these worlds. Finally, I argue that this incomparability result generates puzzles for both consequentialist and non-consequentialist theories of objective and subjective permissibility. (shrink)

This chapter presents several arguments related to Parfit's notion of evaluative imprecision and his imprecisionist lexical view of population ethics. After sketching Parfit's view, it argues that, contrary to Parfit, imprecision and lexicality are both compatible with thinking about goodness in terms of positions on a scale of value. Then, by examining the role that imprecision is meant to play in defusing spectrum argument, it suggests that imprecision should be identified with vagueness. Next, it argues that there is space for (...) robust moral realists to think of evaluative vagueness as a semantic phenomenon, illustrating this view with a version of conceptual role semantics on which the precisifications of betterness are correctness conditions for the precisifications of preference. Finally, it gives a probability-based argument against the imprecisionist lexical view. (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.