"Properly Extensive Quantities" (Abstract)
in Proceedings of the Philosophy of Science Association 2014 Biennial Meeting. Philosophy of Science Vol. 82, No. 5. December, (2015).
This paper introduces and motivates the notion of a "properly extensive" quantity by means of a puzzle about the reliability of certain canonical length measurements. An account of these measurements’ success, I argue, requires a modally robust connection between quantitative structure and mereology which is not mediated by the dynamics and is stronger than the constraints imposed by "mere additivity".
I outline what it means to say that length is not just extensive but properly so, and then briefly sketch an application of proper extensiveness to the project of providing a reductive ground for metric quantitative structure.
Tim Maudlin has influentially argued that Humeanism about laws of nature stands in conflict with quantum mechanics. Specifically Humeanism implies the principle Separability: the complete physical state of a world is determined by the intrinsic physical state of each space-time point. Maudlin argues Separability is violated by the entangled states posited by QM.
We argue that Maudlin only establishes that a stronger principle, which we call Strong Separability, is in tension with QM. Separability is not in tension with QM. Moreover, while the Humean requires Separability to capture the core tenets of her view, there's no Humean-specific motivation for accepting Strong Separability.
We go on to give a Humean account of entangled states which satisfies Separability. The core idea is that certain quantum states depend upon the Humean mosaic in much the same way as the laws do. In fact, we offer a variant of the Best System account on which the systemization procedure that generates the laws also serves to ground these states.
We show how this account works by applying it to the example of Bohmian Mechanics. The 3N-dimensional configuration space, the world particle in it and the wave function on it are part of the best system of the Humean mosaic, which consists of N particles moving in 3-dimensional space. We argue that this account is superior to the Humean account of Bohmian Mechanics defended by Loewer and Albert, which takes the 3N-dimensional space, and its inhabitants, as fundamental.
"How to Be a Substantivalist Without Getting Shifty About It" (Abstract)
in Philosophical Issues 27 (1):223-249. (2017)
According to substantivalism, spacetime points and regions are real entities whose existence is not dependent on matter. In this paper, I motivate and defend a version of substantivalism which takes the totality of spacetime as fundamental, and show how this position avoids certain problem cases, in particular the objection from static Leibniz shifts, and better conforms to how we think about space in physics. I argue that, even though the static Leibniz shifts do not show ordinary substantivalism is committed to in-principle undetectable physical structure ), they do indicate something problematic about the modal profile of space-time and its constituents. While the problem is modal, the solution cannot be solely a matter of revising the substantivalist's modal claims. Rather, I argue, the substantivalist must revise her background ontology of space-time. I show how this can be done by developing substantivalist theory that rejects this picture in favor of an alternative ontology of space-time in the spirit of priority monism.
- Completed or Under Review -
"On Mereology and Metricality" (Abstract)
(Draft available upon request)
I motivate and develops a reductive account of the structure of certain physical quantities in terms of parthood. That is, I argue that quantitative relations like "longer than" or "3.6-times the volume of" can be analyzed in terms of necessary constraints those quantities put on the mereological structure of their instances. I develop this account in detail for spatial volume, and demonstrate how metrical notions, including the rich class of volume ratio relations, can be defined using parthood and the sharing of intrinsic, purely qualitative, properties. This account has numerous advantages. First, it is a genuinely reductive theory of volume's quantitative structure, in that it doesn't require any quantitative notions (such as ordering, summation, or betweenness) to be taken as primitive. Furthermore, the resulting account, I argue, is able to capture the intuition that these quantitative relations are intrinsic to the physical systems they’re called upon to describe and explain.
"Does Physics Motivate a Dynamic Account of Quantity?" (Abstract)
(Draft available upon request)
This paper defends and motivates a "dynamic account" of mass, a theory on which mass’s quantitative structure (specifically, mass ratio relations) is metaphysically dependent on the structure of other quantities (viz. spatiotemporal quantities like length or acceleration) together with the laws of nature. For instance, given F = ma, a dynamic theory of mass grounds the mass ratio "n-times as massive as" in the relative tendency to accelerate at 1/n-times the rate when under an equally strong force.
This account is philosophically fruitful, in that it solves a difficult puzzle in the metaphysics of quantity concerning the possibility of underpopulated worlds. It's also physically well-motivated, in that considerations from the physics—specifically, how the dynamical laws treat these quantities in different possible worlds—strongly suggest that (1) mass is dependent, for its structure, on length and temporal duration, and (2) this dependence obtains only in virtue of the dynamical laws being what they are.
"Is there Anything More to Mass Additivity than Dynamics?" (Abstract)
(Draft available upon request)
I argue that the additivity of mass (i.e. the property according to which a composite object's mass is the "sum" of its parts') is metaphysically dependent on dynamical laws governing massive bodies. In particular, taking additivity to be independent of dynamics commits you to widespread unexplained correlations between the mass properties of composites and the dynamic behavior of massive bodies. The second half of the paper extends this explanatory worry, arguing that the very same considerations apply to aspects of mass’s quantitative structure. This gives rise to a new and powerful worry for certain popular theories about the fundamental structure of physical quantities—most notably the accounts defended by Mundy ("The Metaphysics of Quantity", 1987) and Eddon ("Fundamental Properties of Fundamental Properties", 2013).
- Works in Progress -
"There's Nothing in the Rulebook that Says a Dog Can't Play Basketball; Two Ways the Laws of Nature Might Govern" (Abstract)
This paper considers two ways we might make sense of the claim that the laws "govern" the physical world. On the "pushy" conception, governing laws are responsible for "producing" or "bringing about" the temporal evolution of the physical state. On the "constraining" conception, laws govern by putting limits on the possible evolution of the physical state. I consider how well each conception deals with the objections commonly raised against governing accounts of laws, and discuss how these conceptions of governing make a difference to our account of lawhood and of the role of laws in the physical world. For instance, only the constraining conception of law understands those aberrant physical scenarios for which Newtonian particle mechanics fails to have a unique solution—cases like "space-invaders" or the Norton dome—as cases of indeterminism in the theory; fewer constraints mean more possible evolutions. On the pushy conception, unless there are probabilistic laws that govern stochastically, the lack of a unique solution means that the dynamical laws are unable to evolve the physical state.
"Extension, Zero magnitudes, and the Problem of Quantitative Resemblance" (Abstract)
My "Properly Extensive Quantities" (2015) introduces the notion of a "properly extensive" quantity (like length, volume, or temporal duration), and distinguish them from "merely additive quantities" (like mass and charge), which are extensive but not properly so. It is sometimes said of mass (or of extensive quantities in general) that it is the "measure" of a physical system’s "extent". In this paper, I argue that properly extensive quantities are better suited to "measure of the extent" of a physical system than the broader category of "extensive" quantities. Two important issues in the metaphysics of quantity depend, I argue, on which quantities are "measures of extent": The first concerns quantitative resemblance. It’s generally thought that the notion of "exact similarity", understood in terms of shared natural properties, cannot account for a 3m rod being more similar a 2m rod than it is to a 45m rod (since none of them share any natural length properties except "has a length"). I argue, however, that we can give an elegant theory of quantitative resemblance, in the case of properly extensive quantities, in terms of exact similarity, but only if these quantities are the measure of a system’s "extent". This account depends on the second issue, which concerns so-called "zero magnitudes". Should we interpret the terms '0m' (zero meters of length) or '0kg' as denoting a lack of length/mass? Or, are they merely another way of having length/mass, on par with any of that quantity’s other magnitudes? The notion of extent, I argue, offers a clear answer: zero extent is a lack, while other zero magnitudes are not.
"There's no Speed of Light, So What the Heck did Michelson Measure?" (Abstract)
This paper concerns the tension between two claims that, I maintain, are both plausibly true. The first is that A. A. Michelson measured the speed of light in the late 1800s and arrived at a value that was very close to accurate. The second is that, strictly speaking, there is no such thing as the speed of light in special relativity. The first part of the paper is devoted to defending the second of these claims, which is remarkably controversial even among working physicists and philosophers of physics. Once this claim is established, the second half of the paper resolves this tension. Specifically, I explain that the value arrived at by Michelson and others does correspond to an objective feature of the physical world, but that this feature is not a speed. Rather, it has to do with an a posteriori relationship between our independently-chosen spatial and temporal units.
"Pushy Governing Laws and Nomological Modality"
- Papers Not Yet in Progress -
"Are Physical Constants Quantities?"
"Constitutive Properties and Epistemic Accessibility: What Artworks Hide from Us"
"Understanding Physical Lorentz Contraction"