All physical theories, from classical Newtonian mechanics to relativistic quantum field theory, entail propositions concerning the geometric structure of spacetime. To give an example, the general theory of relativity entails that spacetime is curved, smooth, and four-dimensional. In this dissertation, I take the structural commitments of our theories seriously and ask: how is such structure instantiated in the physical world? Mathematically, a property like 'being curved' is perfectly well-defined insofar as we know what it means for a mathematical space to (...) be curved. But what could it mean to say that the physical world is curved? Call this the problem of physical geometry. The problem of physical geometry is a plea for foundations--a request for fundamental truth conditions for physical-geometric propositions. My chief claim is that only a substantival theory of spacetime--a theory according to which spacetime is an entity in its own right, existing over and above the material content of the world--can supply the necessary truth conditions. (shrink)

Analytic Philosophy, Volume 62, Issue 3, Page 201-222, September 2021.

Kant’s treatments of incongruent counterparts have been criticized in the recent literature. His 1768 essay has been charged with an ambiguous use of the notion of ‘inner ground’, and his 1770 claim that those differences cannot be apprehended conceptually is thought to be false. The author argues that those two charges rest on an uncharitable reading. ‘Inner ground’ is equivocal only if misread as mapping onto Leibniz notion of quality. Concepts suffice to distinguish counterparts, but are insufficient to specify their (...) spatial forms. Kant’s claims are reasonable and plausible, and have been reaffirmed repeatedly in contemporary discussions of demonstrative identification. (shrink)

A relationist will account for the use of ‘left’ and ‘right’ in terms of relative orientations, and other properties and relations invariant under mirroring. This analysis will apply whenever mirroring is a symmetry, so it certainly applies to classical mechanics; we argue it applies to any physical theory formulated on a manifold: it is in this sense an a priori symmetry. It should apply in particular to parity violating theories in quantum mechanics; mirror symmetry is only broken in such theories (...) as a special symmetry. (shrink)

I explore two views about the relationship between spatial experience and spatial reality: spatial functionalism and spatial presentationalism. Roughly, spatial functionalism claims that the instantiated spatial properties are those playing a certain causal role in producing spatial experience while spatial presentationalism claims that the instantiated spatial properties include those presented in spatial experience. I argue that each view, in its own way, leads to an ontologically inflationary form of primitivism: whereas spatial functionalism leads to primitivism about phenomenal representation, spatial presentationalism (...) leads to primitivism about spatial properties. I conclude by discussing how to adjudicate between spatial functionalism and spatial presentationalism. (shrink)

I propose that we interpret Kant’s argument from incongruent counterparts in the 1768 article ‘Concerning the Ultimate Ground of the Differentiation of Directions in Space’ in light of a theory of dynamic absolute space that he accepted throughout the 1750s and 1760s. This force-based or material conception of space was not an unusual interpretation of the Newtonian notion of absolute space. Nevertheless, commentators have continually argued that Kant’s argument is an utter failure that shifts from the metaphysics of space to (...) its epistemology, because he has no way to connect ‘directionality’ and ‘handedness’ to absolute space. This supposed failure is based on an understanding of absolute space in purely mathematical terms and as an absolute void that lacks any qualitative or dynamic features. If we recognize that Kant held that space had an intrinsic directional asymmetry then his argument successfully connects incongruent counterparts to absolute space. The presence of this notion in Kant’s pre-Critical thought is rarely noted, and its necessity in understanding his incongruence argument is novel. (shrink)

This article argues that time-asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the (...) direction of time are at variance with the claim that orientation of enantiomorphic objects is intrinsic. Second, it is argued that reductive explanations of time-asymmetric processes presuppose that enantiomorphic processes do not have determinate orientation. (shrink)

This article argues that time‐asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the (...) direction of time are at variance with the claim that orientation of enantiomorphic objects is intrinsic. Second, it is argued that reductive explanations of time‐asymmetric processes presuppose that enantiomorphic processes do not have determinate orientation. (shrink)

Historically, a great deal of attention has been addressed to the question of what it would take to test experimentally the metrical structure of spacetime. Arguably, however, consideration of this question has been at the expense of comparable investigations into what it would take to test other structural features of spacetime. In this article, we critique and expand substantially upon an article by Hadley (Hadley in Class Quantum Gravity, 19:4565–4571, 2002), which constitutes one of the best-known paper-length studies of what (...) it would take to test the orientability of spacetime. In so doing, we seek to clarify a number of matters which remain unclear in the wake of Hadley’s article, thereby allowing the literature on this topic to progress. More positively, we also present, compare, and evaluate a number of other potential approaches to testing the orientability of spacetime which have arisen in the recent physics literature. (shrink)

Left and right hands are incongruent counterparts. Yet each replicates the intrinsic properties of the other. This suggests that differing relations to space make the difference. Kant's and Weyl's discussions of the problem are critically discussed. It emerges that spatial relationism fails to explain how its relations may be interpreted. An excursion into visual geometry explains the basis of handedness in the orientable structure of space.

This paper scrutinises the tenability of a strict conceptual distinction between space and matter via the lens of the debate between modified gravity and dark matter. In particular, we consider Berezhiani and Khoury's novel 'superfluid dark matter theory' as a case study. Two families of criteria for being matter and being spacetime, respectively, are extracted from the literature. Evaluation of the new scalar field postulated by SFDM according to these criteria reveals that it is as much matter as anything could (...) possibly be, but alsoꟷbelow the critical temperature for superfluidityꟷas much spacetime as anything could possibly be. A sequel paper examines possible interpretations of SFDM in light of this result, as well as the consequences for our understanding of the modified gravity/ dark matter distinction and the broader spacetime–matter distinction. (shrink)

I consider an argument, due to Geoffrey Lee, that we can know a priori from the left-right asymmetrical character of experience that our brains are left-right asymmetrical. Lee's argument assumes a premise he calls relationism, which I show is well-supported by the best philosophical picture of spacetime. I explain why Lee's relationism is compatible with left-right asymmetrical laws. I then show that the conclusion of Lee's argument is not as strong or surprising as he makes it out to be.

Imagine your mirror‐inverted counterpart on Mirror Earth, a perfect mirror image of Earth. Would her experiences be the same as yours, or would they be phenomenally mirror‐inverted? I argue, first, that her experiences would be phenomenally the same as yours. I then show that this conclusion gives rise to a puzzle, one that I believe pushes us toward some surprising and philosophically significant conclusions about the nature of perception. When you have a typical visual experience as of something to your (...) left, the following three claims seem very plausible: (1) No one could have an experience phenomenally just like yours without thereby having an experience as of something to her left. (2) Your experience is veridical. (3) Your experience doesn't differ from that of your mirror‐inverted counterpart with respect to veridicality. But (1)‐(3) jointly contradict the claim that you and your mirror‐inverted counterpart would have the same experiences. I argue that any viable response to this puzzle will embrace the following disjunction: either there is a degree of independence between perceptual phenomenology and representational content, contrary to popular intentionalist views of perception, or spatial subjectivism is true, where spatial subjectivism is the view that the spatial properties presented in perception are either mind‐dependent or illusory. (shrink)

The phenomenon of broken spacetime symmetry in the quantum theory of infinite systems forces us to adopt an unorthodox ontology. We must abandon the standard conception of the physical meaning of these symmetries, or else deny the attractive “liberal” notion of which physical quantities are significant. A third option, more attractive but less well understood, is to abandon the existing (Halvorson-Clifton) notion of intertranslatability for quantum theories.

In 1768 Immanuel Kant presented an argument showing the necessity of absolute space, i.e. substantivalism in contrast to relationalism, based on the property of handedness. While there is large consensus about the fallacy of Kant’s argument, a more recent debate exists – mainly stimulated by John Earman – about the status of the Kantian argument in view of modern physics and its fundamentally built-in parity violation, which leads to a preferred handedness. According to Earman the relationalist has no means to (...) distinguish one handedness in the cosmos without reference to an absolute structure of space. After recapitulating the historical background of the Newton/Leibniz debate on the ontological status of space as well as the Kantian argument, this paper offers a systematic consideration of arguments about handedness in modern physics. The goal is to show that “Earman’s challenge” can be rejected. (shrink)

In the first part of this paper a relational account of incongruent counterparts is defended against an argument due to Kant. I then consider a more recent attack on such an account, due to John Earman, which alleges that the relationalist cannot account for the lawlike left--right asymmetry manifested in parity-violating phenomena. I review Hoefer's, Huggett's and Saunders' responses to Earman's argument and argue that, while a relationalist account of parity-violating laws is possible, it comes at the cost of non-locality.