Research

Infinite Value

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We can find infinite values in a number of ways. Perhaps by aggregating infinitely large collections of goods. Perhaps in the expectations of games with infinite state spaces. Perhaps because some goods are so much better than others that no finite number could bridge the gulf. Regardless of how infinite value arises, it provide a serious challenge to decision theories and formal value theories. The standard (Cantorian) mathematics of infinity make a hash of decision rules like expected utility maximization and aggregation techniques such as addition and averaging. We can see this in puzzles like Pascal’s Wager, the St. Petersburg Game, the Pasadena Game, and the Sphere of Suffering. 

My goal in this project is to explore the viability of alternative conceptions of infinity as models of infinite value. Most notably, this has involved appeals to John Conway’s Surreal Mathematics. In surreal arithmetic, some of the more problematic aspects of Cantor’s cardinal and ordinal arithmetic, such as the tendency of infinite numbers to ‘absorb’ smaller numbers and failures of commutativity in finite sums disappear. Eddy Chen and I have laid the foundations of a surreal-valued decision theory in our 2020 PPR paper Surreal Decisions. In it, we show how to give a decision theory with surreal utilities in finite state spaces and analyze Pascal’s Wager. In continuing work, we are developing a surrealized approach to decision problems involving infinite state spaces using formalism based on Mark Colyvan’s Relative Expectations, and plan to expand our work into surreal probability theory. 

God and Value

My work on infinite value theories supplements my work on the relationship between God and value or morality. In my 2018 God Meets Satan’s Apple (Phil Studies), I argue for two theses, assuming that there is no best of all possible worlds: (i) combining plausible moral/rational norms and the standard commitments of theism results in a paradox, and (ii) the best theistic resolution of the paradox is to exempt God from the norms of morality/rationality. In my Forthcoming (AJP) paper In Defense of No Best World, I respond to recent arguments that there is a best possible world, perhaps ours. 

I have a couple of developing papers in this area. My in-progress In Defense of Created Intrinsic Value takes on recent arguments that no created thing can be intrinsically valuable. There are two lines of argument in support of this view. One, from Erik Wielenberg and Mark Murphy claims that because of the structure of grounds that theists must embrace, everything is dependent on God for its value properties, and so no created thing’s value properties can be intrinsic. In response, I note that this line of argument extends to all intrinsic properties and show how a hyperintensional definition of intrinsically gets around the problem. Another, embraced by a number of writers, argues that since God’s value must be unsurpassable and without measure, nothing distinct from God should add value to the universe. I draw on the surreal value theory laid out in In Defense of No Best World to parry this line of thought.

Further work in progress with Eddy Chen takes up the question, recently posed by Dean Zimmerman and Jason Turner: if Everett’s many-worlds interpretation of Quantum Mechanics is true, does the problem of evil become immeasurably worse? Plausibly it does, since on the Everettian view every possible history consistent without laws and boundary conditions is, in some sense, actual. This includes histories filled with pointless suffering. However, we argue that if Everett is to be empirically adequate than something like David Wallace’s decision-theoretic account of probability in Everett must be true, and if Wallace’s strategy is successful then the structure of value in an Everettian universe leaves the act of creating an Everettian universe with expected value equal to the act of creating a single universe with the same wave function. This leaves the problem of evil no worse in an Everettian world than in a single universe. 

Theoretical Virtue

My work on theoretical virtue starts with my writing sample, Ideological Innocence. Recall from Quine that we divide theoretical commitment into two types: ontology, the things that must exist if a theory is to be true, and ideology, the primitive concepts or notions used in stating a theory. This allows us to divide the theoretical virtue of parsimony into two kinds: ontological parsimony and ideological parsimony. I argue for a partial analysis of ideological parsimony: if two ideologies are expressively equivalent, then neither is more parsimonious than the other. In its favor I offer the argument from accuracy, showing that any analysis of ideological parsimony as an epistemic virtue - a property of theories that makes them ceteris paribus more likely to be true - must respect my criterion.

I am currently trying to get Ideological Innocence published. My next planned step in this project is to tackle the problem of aggregating theoretical virtues. Suppose we find three theoretical virtues that tend to indicate truth. If different theories have them in different degrees, how do we reckon the best candidate? This problem has parallels in social choice theory with Arrow-style impossibility theorems, and my future work on theoretical virtue will be devoted to finding out how to navigate these difficult results. 

Normative Disharmony

It is standard to talk about different sources of normativity. Epistemic rationality is aimed at truth, or knowledge, or understanding. The norms of epistemic rationality concern gaining this goal in the best way. Individual practical rationality is aimed at achieving the individuals goals, whatever they may, in the best way. Social practical rationality is aimed at achieving the groups goals, whatever they may be, in the best way. Moral rationality is aimed at doing what is right. All of these norms come in at least two flavors: structural/wide-scope norms tell us the abstract ‘shape’ our reasoning should take, like deductive consistency or expected-utility maximization, and substantive/narrow-scope norms, like expert-deference principles or codes of conduct, that tell us what the true, good, or valuable things or actions in fact are. Sometimes, these norms appear to conflict. I defend the view that these conflicts are not subject to rational reconciliation.

One example. My in-progress paper Countable Sure-Thing vs. the Axiological Principal Principle explores a conflict between a structural norm of individual practical rationality and a substantive norm of individual practical rationality. Isaacs and Russell’s countable sure-thing principle is designed to shield agents from certain kinds of dutch books that arise in infinitely situations like the St. Petersburg Game, and is an extension of the finite sure-thing principle standard to expected utility theory. The axiological principal principle, inspired by David Lewis’s chance-credence-connecting principal principle, instructs agents to desire or value things in accordance with their objective goodness. These principles come into conflict in cases where there exist an infinitely-ascending series of goods, each of which improves on its predecessors without limit. For example, suppose an agent comes to possess a bottle of EverBetter Wine, a bottle of wine whose flavor and quality improves every day. The axiological principal principle tells her to prefer drinking the wine tomorrow to drinking it today, all else equal. The countable sure-thing principle tells her that this preference is unreasonable. But how can this dispute be resolved? We may choose one principle or the other, but I argue that any meta-principle we try to introduce to settle the dispute will not succeed. It, too, will have some constitutive goal, one that differs from the goals of the countable sure thing principle and the axiological principal principle. There is no neutral ground.  

Persons

My work on persons touches on both metaphysics and value theory. In Death’s Shadow Lightened, I defend Epicureanism about death. Epicureans say that death is not a great harm to the one who dies. I categorize the harms that death might inflict into four categories: extrinsic instrumental harms, intrinsic instrumental harms, extrinsic final harms, and intrinsic final harms. I then show that, looking in each category, we do not find a harm suitable to play the role of the harm of death. 

In Presentist Counterpart Theory, I extend Ted Sider’s ‘stage theory’ (or exdurantism) to presentist views of time, that is, views of temporal ontology according to which only present things exist. I argue that this counterpart theory can solve problems stemming from intrinsic change and transtemporal reference that presentists do not otherwise have easy ways to escape. Extending the counterpart theory to presentist ontologies renders it more plausible, which in turn opens up a range of interesting theoretical options for accounts of personal identity.

These streams will cross in future work. I favor a heavily social view of personal identity, where facts about value and practical reason wield heavy influence over facts about who exists in the future. A counterpart theory of persistence gives a plausible explanation for why this is, giving a clear route for facts about value and practical reason to explain more ‘metaphysical’ facts about persistence: namely, by being among the important determinants of the counterpart relation in common contexts.