From Humean Laws to a Neo-Kantian Spacetime: A Dynamics-First View of Topology

TL;DR

This paper advocates a dynamics-first approach to spacetime topology, supported by new topological redescriptions, aligning with Neo-Kantian views that spacetime's structure is not metaphysically fundamental but epistemologically useful.

Contribution

It introduces a novel dynamics-first perspective on spacetime topology, supported by the ISE Method for flexible topological redescriptions, extending the analogy between laws and geometric structures.

Findings

The ISE Method enables switching between different spacetime topologies.

A theory's topological structure can be identified via a Best Systems Analysis.

Supports a Neo-Kantian view that spacetime topology is not metaphysically fundamental.

Abstract

Do the spacetime manifolds which feature in our best scientific theories reflect anything metaphysically weighty in the world (e.g., any fundamental substances or relations)? Should we extend our notions of space and time beyond the epistemological roles they play in helping us codify the dynamical behavior of matter? Kant famously answered ``No'' to both of these questions, contra Newton and Leibniz. This paper introduces novel technical and philosophical support for such a (Neo-)Kantian perspective on the metaphysics of space and time. To begin, I will make an explicit analogy between broadly Humean views of laws (e.g., Lewis, Demarest, etc.) and dynamics-first views of geometry (e.g., Brown). I will then continue this line of analogous views beyond the metaphysics of laws debate and the dynamical vs geometric spacetime debate by extending it into the context of spacetime topology. Namely, I will put forward a dynamics-first view of topology (in answer to Norton's problem of pre-geometry). This dynamics-first view of topology is supported by some powerful new techniques for topological redescription which I have recently developed in Grimmer (2023a) and Grimmer (2023b), namely the ISE Method. These new techniques allow us to remove and replace the topological underpinnings of our spacetime theories just as easily as we can switch between different coordinate systems. For instance, a theory set on a M\"obius strip might be redescribed as being set on the Euclidean plane and vice versa. Indeed, as Grimmer (2023b) has proved, the ISE Method gives us access to effectively every possible spacetime framing of a given theory's kinematical and dynamical content. Given this overabundance of candidate spacetime framings, it is then conceivable that one can pick out a theory's topological structure via something analogous to a Best Systems Analysis.