Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory (...) to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

Erik Wielenberg [2014] and Mark Murphy [2017], [2018] have defended a series of arguments for the conclusion that creatures are not good intrinsically. In response, I take two steps. First, I introduce a conception of intrinsic value that makes created intrinsic value unproblematic. Second, I respond to their arguments in turn. The first argument is from the sovereignty-aseity intuition and an analysis of intrinsicality that makes derivative good extrinsic. I challenge the analysis. The second comes from a conception of perfection (...) where God exhausts all possibilities for goodness. I challenge this conception. The third comes from the contingency of creation and the internal logic of intrinsic value. I challenge the assumption that connects the two. I then present an argument from reference magnetism that the only conception of God, God's perfections, and religious language that makes it plausible that the sentence "God is intrinsically good and creatures are not" is true involves a strongly univocalist position. A view that is either unstatable or places strong demands on our conception of God, God's perfections and religious language thereby loses plausibility. (shrink)

Molinists hold that there are contingently true counterfactuals about what agents would do if put in specific circumstances, that God knows these prior to creation, and that God uses this knowledge in choosing how to create. In this essay we critique Molinism, arguing that if these theses were true, agents would not be free. Consider Eve’s sinning upon being tempted by a serpent. We argue that if Molinism is true, then there is some set of facts that fully explains both (...) Eve’s action and everything else Eve does that influences that action; and that if this is the case, Eve does not act freely. The first premise of this argument follows from the explanatory relations the Molinist is committed to, and the second premise follows from libertarian intuitions about free will. (shrink)

In his work on the open future, Patrick Todd outlines three models of how to deal with future contingents. These models must answer two questions: one metaphysical, about what facts there are in the world; one semantic, about how to deal with sentences involving ‘will.’ Model 1 has a privileged timeline. Model 2 has an actual future timeline but leaves it indeterminate which timeline that is. Model 3 has no future timeline. All three give will-sentences a modal treatement, as a (...) box over available futures. I will argue that Todd’s second model has problems and should be improved. The first is that it denies what Todd labels as the basic metaphysical intuition behind open-futurism. The second is that indeterminacy about the facts that characterize the actual timeline breaks through into indeterminate identity. I propose a fix to model 2 eliminating its actual future and resolving an issue that arises in applying the neutral semantics Todd endorses to indeterminate sentences. This improved model, I suggest, may even compare favorably to Todd’s preferred model 3. (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)

Jim Sterba’s Is a Good God Logically Possible? looks to resurrect J. L. Mackie’s logical argument from evil. Sterba accepts the general framework that theists seeking to give a theodicy have favored since Leibniz invented the term: the search for some greater good provided or greater evil averted that would justify God in permitting the type and variety of evil we actually observe. However, Sterba introduces a deontic twist, drawing on the Pauline Principle (let us not do evil that good (...) may come) to introduce three deontic side constraints on God’s choice of action. He then splits the possible goods into four categories: first- vs. second-order goods, goods to which we have a right, and goods to which we do not have a right. He argues that his deontic constraints rule out each combination, thereby showing that no God-justifying good is on offer. To defuse the argument, I draw on a pair of ideas from Marilyn McCord Adams: (i) God is outside the bounds of morality, and (ii) God can defeat evils by incorporating them into an incommensurately valuable friendship with each human. Properly appreciated, these show that the new logical argument relies on a false premise that is not easily repaired. (shrink)

Quine taught us the difference between a theory’s ontology and its ideology. Ontology is the things a theory’s quantifiers must range over if it is true, Ideology is the primitive concepts that must be used to state the theory. This allows us to split the theoretical virtue of parsimony into two kinds: ontological parsimony and ideological parsimony. My goal is help illuminate the virtue of ideological parsimony by giving a criterion for ideological innocence—a rule for when additional ideology does not (...) count against parsimony. I propose the expressive power innocence criterion: if the ideology of theory one is expressively equivalent to that of theory two, then neither is ideologically simpler than the other. In its favor I offer the argument from accuracy, showing that any account of a theoretical virtue that is supposed to make theories that have it more likely to be true than theories that do not must respect it. Next I consider its ramifications, eliminating rival views and passing judgment on some arguments from parsimony that can be found in the literature. Finally, I consider two objections. First: I address an objection arising from the possibility of languages with a ‘primitive’ operator that allows us to list a theory’s primitives in the object-language. Second: I address an objection raised by Nelson Goodman against attempts to reckon simplicity by expressive power. Both objections fail. (shrink)

Recent analytic theology has seen a wave of excellent work on the fundamental problem of Christology, the question of how one and the same person can be human full stop and divine full stop. Along the way, new objections have been raised for a venerable family of Christological views, whose distinctive is the employment of qua-devices to dissolve the difficulties stemming from the dual nature doctrine of Chalcedon and its successors. My objective in this article is twofold. First, I propose (...) to lay out a hierarchy of principles that should guide the search for a Christological theory. I then use these principles to illuminate the best qua-theoretic approach to Christology. Finally, I argue that the best qua-theory is at worst on a par with major recent views. (shrink)

Epicurus (in)famously argued that death is not harmful and therefore our standard reactions to it (like deep fear of death and going to great lengths to postpone it) are not rational, inaugurating an ongoing debate about the harm of death. Those who wish to resist this conclusion must identify the harm of death. But not any old harm will do. In order to resist both the claim that death is not harmful and the claim that our standard reactions to it (...) are irrational, we must identify a harm associated with death that rationalizes our standard reactions. We can divide the potential harm properties death might have along two axes: intrinsic/extrinsic and instrumental/final. This gives us four places to search for the harm of death. I argue that it is nowhere to be found. (shrink)

Puzzles can arise in value theory and deontic (permissibility) theory when infinity is involved. These puzzles can arise for ethics, for prudence, or for any normative perspective. For the sake of simplicity, we focus on the ethical versions of these problems. We start by addressing problems that can arise in determining what is permissible, either in a given choice situation when there are an infinite number of options or in infinite sequence of choice situations, each with only finitely many options. (...) There is a common theme here: standard and plausible decision rules, such as the dominance principle or maximising principles, run into conflict with other plausible principles. We then address problems that can arise in determining whether one option is more valuable than another, when the options have infinite, or undefined, value. This includes cases where a single bearer of value has infinite or undefined value, as well as cases where each bearer of value is finite but the total for the collection is infinite or undefined totals. Our focus is on introducing the puzzles, rather than canvassing potential solutions. (shrink)