A famous mathematical theorem says that the sum of an infinite series of numbers can depend on the order in which those numbers occur. Suppose we interpret the numbers in such a series as representing instances of some physical quantity, such as the weights of a collection of items. The mathematics seems to lead to the result that the weight of a collection of items can depend on the order in which those items are weighed. But that is very hard to believe! A puzzle then arises: How do we interpret the metaphysical significance of this mathematical theorem? I first argue that prior solutions to the puzzle lead to implausible consequences. Then I develop my own solution, where the basic idea is that the weight of a collection of items is equal to the limit of the weights of its finite subcollections contained within ever-expanding regions of space. I show how my solution is intuitively plausible and philosophically motivated, how it reveals an underexplored line of metaphysical inquiry about quantities and locations, and how it elucidates some classic puzzles concerning supertasks.

According to orthodoxy, our best physical theories strongly support Eternalism over Presentism. Our goal is to argue against this consensus, by arguing that a certain overlooked aspect of our best physical theories strongly supports Presentism over Eternalism.

In this paper I propose a new solution to the problem of change: situationalism. According to this view, parts of reality fundamentally disagree about what is the case and reality as a whole is unsettled (i.e. metaphysically indeterminate). When something changes, parts of the world irreconcilably disagree about what properties it has. From this irreconcilable disagreement, indeterminacy arises. I develop this picture using situations, which are parts of possible worlds; this gives it the name situationalism. It allows a B-theory endurance view on which there is genuine incompatibility when things change. There are costs to the view, which are explored, but it is a novel approach which offers a distinct explanation of what happens when things exist through change. (PDF forthcoming)

Congratulations to Harjit Singh Bhogal for winning the 2018 Sanders Metaphysics Prize! Dr. Bhogal is Assistant Professor of Philosophy at the University Maryland, College Park. Dr. Bhogal works primarily in metaphysics and the philosophy of science. This year’s competition included 45 submissions from scholars across the globe. After careful consideration, the five judges – Elizabeth Barnes, Karen Bennett, Ross Cameron, Jonathan Schaffer, and Dean Zimmerman – eventually settled on Harjit’s paper as their top choice. The runner-ups for the prize were Dan Korman’s (University of California, Santa Barbara) essay “A Puzzle about Places” and Mahrad Almotahari’s (University of Illinois at Chicago) essay “A Little Puzzle about a Piece and a Puddle.” Abstract: Humeanism about laws of nature — the view that the laws reduce to the Humean mosaic — is a popular view, but currently existing versions face powerful objections. The non-supervenience objection, the non-fundamentality objection and the explanatory circularity objection have all been thought to cause problems for Humeanism. However, these objections share a guiding thought — they are all based on the idea that there is a certain kind of divergence between the practice of science and the metaphysical picture suggested by Humeanism. I suggest that the Humean can respond to these objections not by rejecting this divergence, but by arguing that is appropriate. In particular the Humean can, in the spirit of Loewer (2012), distinguish between scientific and metaphysical explanation — this is motivated by differing aims of explanation in science and metaphysics. And they can further leverage this into distinctions between scientific and metaphysical fundamentality and scientific and metaphysical possibility. We can use these distinctions to respond to the objections that the Humean faces.

The judges (Karen Bennett, Ted Sider, Laurie Paul, Ross Cameron, and Jason Turner) had their work cut out for them. In the end, four essays were offered publication in Oxford Studies in Metaphysics or given invitations to revise-and-resubmit — more than usual for this competition, indicating the strength of the field. The first runner-up for the prize was Jonathan Simon, a post-doctoral associate and research fellow at NYU. His essay, “Fragmenting the Waves”, will also be published in the next volume of Oxford Studies in Metaphysics. Scott Dixon is an Assistant Professor of Philosophy at Ashoka University. His primary research interest is in metaphysics, particularly in grounding. He also has interests in logic (especially plural logic and infinitary logic) and the philosophy of mathematics. Abstract: Fine (2000) argues, pace Russell, that relations have neither directions nor converses. He considers two ways to conceive of these new “neutral” relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former. Gilmore (2013) argues for a generalization of positionalism, slot theory–the view that a relation is n-adic if and only if there are n slots in it, and, roughly, that each slot may be occupied by at most one entity. Slot theory bears the full brunt of Fine’s (2000) symmetric completions and conflicting adicities problems. I develop an alternative view, plural slot theory, which avoids these problems, key elements of which are first considered by Yi (1999). Like the slot theorist, the plural slot theorist posits entities in properties and relations that can be occupied. But unlike the slot theorist, the plural slot theorist denies that at most one entity can occupy any one of them. As a result, she must also deny that the adicity of a relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the plural slot theorist is able to avoid Fine’s problems, resulting in a stronger theory about the internal structure of properties and relations. Plural slot theory also avoids a serious drawback of anti-positionalism.

The fact that physical laws often admit certain kinds of space-time symmetries is often thought to be problematic for substantivalism – the view that space-time is as real as the objects it contains. The most prominent alternative, relationism, avoids these problems but at the cost of giving abstract objects (rather than space-time points) a pivotal role in the fundamental metaphysics. This incurs related problems, I shall argue, concerning the relation of the physical to the mathematical. In this paper I will present a version of substantivalism that respect Leibnizian theses about space-time symmetries, and argue that it is superior to both relationism and the more orthodox form of substantivalism.

The Problem of Iterated Ground is to explain what grounds truths about ground: if Γ grounds φ, what grounds that Γ grounds φ? This paper develops a novel solution to this problem. The basic idea is to connect ground to explanatory arguments. By developing a rigorous account of explanatory arguments we can equip operators for factive and non-factive ground with natural introduction and elimination rules. A satisfactory account of iterated ground falls directly out of the resulting logic: non- factive grounding claims, if true, are zero-grounded in the sense of Fine.

I propose a teleological account of dispositions. Details aside, the view is that to have a disposition is to be in a state with a certain telos. I argue that such an account of dispositions provides exactly what those working on dispositions have been searching for: (i) a robust explanation of the sense in which dispositions are directed at their manifestations, and (ii) an interesting and counterexample free connection between dispositions and conditionals.

Analyticity theorists, as I will call them, endorse the doctrine of analyticity in ontology: if some truth P analytically entails the existence of certain things, then a theory that contains P but does not claim that those things exist is no more ontologically parsimonious than a theory that also claims that they exist. Suppose, for instance, that the existence of a table in a certain location is analytically entailed by the existence and features of certain particles in that location. The doctrine implies that the table’s existence requires nothing more of the world than that those particles exist and bear the features in question. Analyticity theorists have alleged that this idea may be used to defend controversial existence claims against a battery of objections. I argue that this style of defence fails, because the doctrine faces counter-examples. An existence claim may be analytically entailed by some truth and still report a substantial further fact. These counter-examples suggest a picture according to which the theoretical utility of analyticity in the investigation of extra-linguistic reality is virtually nil.

Gilmore’s winning essay, “Time Travel, Coinciding Objects, and Persistence,” is also published in Oxford Studies in Metaphysics, Vol. 3 (2007), pp. 177 – 198.