•  287
    Infinite Prospects
    Philosophy and Phenomenological Research. forthcoming.
    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 I…Read more
  •  144
    Sleeping Beauty's Evidence
    In Maria Lasonen-Aarnio & Clayton M. Littlejohn (eds.), The Routledge Handbook of the Philosophy of Evidence, Routledge. forthcoming.
    What degrees of belief does Sleeping Beauty's evidence support? That depends.
  •  275
    On the Probability of Plenitude
    Journal of Philosophy 117 (5): 267-292. 2020.
    I examine what the mathematical theory of random structures can teach us about the probability of Plenitude, a thesis closely related to David Lewis's modal realism. Given some natural assumptions, Plenitude is reasonably probable a priori, but in principle it can be (and plausibly it has been) empirically disconfirmed—not by any general qualitative evidence, but rather by our de re evidence.
  •  200
    Non-Archimedean Preferences Over Countable Lotteries
    Journal of Mathematical Economics 88 (May 2020): 180-186. 2020.
    We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.
  •  440
    Possible Patterns
    Oxford Studies in Metaphysics 11. 2018.
    “There are no gaps in logical space,” David Lewis writes, giving voice to sentiment shared by many philosophers. But different natural ways of trying to make this sentiment precise turn out to conflict with one another. One is a *pattern* idea: “Any pattern of instantiation is metaphysically possible.” Another is a *cut and paste* idea: “For any objects in any worlds, there exists a world that contains any number of duplicates of all of those objects.” We use resources from model theory to show …Read more
  •  200
    How Much is at Stake for the Pragmatic Encroacher
    Oxford Studies in Epistemology 6. 2019.
    “Pragmatic encroachers” about knowledge generally advocate two ideas: (1) you can rationally act on what you know; (2) knowledge is harder to achieve when more is at stake. Charity Anderson and John Hawthorne have recently argued that these two ideas may not fit together so well. I extend their argument by working out what “high stakes” would have to mean for the two ideas to line up, using decision theory.
  •  233
    Quality and Quantifiers
    Australasian Journal of Philosophy 96 (3): 562-577. 2018.
    I examine three ‘anti-object’ metaphysical views: nihilism, generalism, and anti-quantificationalism. After setting aside nihilism, I argue that generalists should be anti-quantificationalists. Along the way, I attempt to articulate what a ‘metaphysically perspicuous’ language might even be.
  •  238
    Composition as Abstraction
    Journal of Philosophy 114 (9): 453-470. 2017.
    The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.
  •  429
    The Logic of Opacity
    Philosophy and Phenomenological Research 99 (1): 81-114. 2019.
    We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show that some of…Read more
  •  210
    Temporary Safety Hazards
    Noûs 50 (4): 152-174. 2016.
    The Epistemic Objection says that certain theories of time imply that it is impossible to know which time is absolutely present. Standard presentations of the Epistemic Objection are elliptical—and some of the most natural premises one might fill in to complete the argument end up leading to radical skepticism. But there is a way of filling in the details which avoids this problem, using epistemic safety. The new version has two interesting upshots. First, while Ross Cameron alleges that the Epi…Read more
  •  331
    Actuality for Counterpart Theorists
    Mind 122 (485): 85-134. 2013.
    The counterpart theorist has a problem: there is no obvious way to understand talk about actuality in terms of counterparts. Fara and Williamson have charged that this obstacle cannot be overcome. Here I defend the counterpart theorist by offering systematic interpretations of a quantified modal language that includes an actuality operator. Centrally, I disentangle the counterpart relation from a related notion, a ‘representation relation’. The relation of possible things to the actual things th…Read more
  •  173
    On Where Things Could Be
    Philosophy of Science 81 (1): 60-80. 2014.
    Some philosophers respond to Leibniz’s “shift” argument against absolute space by appealing to antihaecceitism about possible worlds, using David Lewis’s counterpart theory. But separated from Lewis’s distinctive system, it is difficult to understand what this doctrine amounts to or how it bears on the Leibnizian argument. In fact, the best way of making sense of the relevant kind of antihaecceitism concedes the main point of the Leibnizian argument, pressing us to consider alternative spatiotem…Read more
  •  880
    The Structure of Gunk: Adventures in the Ontology of Space
    In Dean Zimmerman (ed.), Oxford Studies in Metaphysics: Volume 4, Oxford University Press. pp. 248. 2008.
    Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response.
  •  510
    Philosophical Studies 172 (5): 1287-1309. 2015.
    How should a group with different opinions (but the same values) make decisions? In a Bayesian setting, the natural question is how to aggregate credences: how to use a single credence function to naturally represent a collection of different credence functions. An extension of the standard Dutch-book arguments that apply to individual decision-makers recommends that group credences should be updated by conditionalization. This imposes a constraint on what aggregation rules can be like. Taking c…Read more
  •  519
    Possible Worlds and the Objective World
    Philosophy and Phenomenological Research 90 (2): 389-422. 2015.
    David Lewis holds that a single possible world can provide more than one way things could be. But what are possible worlds good for if they come apart from ways things could be? We can make sense of this if we go in for a metaphysical understanding of what the world is. The world does not include everything that is the case—only the genuine facts. Understood this way, Lewis's “cheap haecceitism” amounts to a kind of metaphysical anti-haecceitism: it says there aren't any genuine facts about indi…Read more
  •  236
    General Dynamic Triviality Theorems
    Philosophical Review 125 (3): 307-339. 2016.
    Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claim…Read more
  •  191
    Qualitative Grounds
    Philosophical Perspectives 30 (1): 309-348. 2016.
    Suppose that all non-qualitative facts are grounded in qualitative facts. I argue that this view naturally comes with a picture in which trans-world identity is indeterminate. But this in turn leads to either pervasive indeterminacy in the non-qualitative, or else contingency in what facts about modality and possible worlds are determinate.
  •  204
    Indefinite Divisibility
    Inquiry: An Interdisciplinary Journal of Philosophy 59 (3): 239-263. 2016.
    Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the …Read more