Philosophy of Physics Graduate Lunch Seminar

Abstract: In his 2008 book Scientific Representation: Paradoxes of Perspective, Bas van Fraassen makes the claim that it is impossible to coordinatise a mathematical sphere because of its perfect rotational symmetry. While we broadly endorse his claim, we take it as an opportunity to investigate the act of reference in systems displaying high degrees of symmetry.

As contrast, we first consider what coordinatising a physical sphere entails, invoking indexical arguments made by Maudlin (1993) and Cheng and Read (2022) that parallel van Fraassen's own notion of representation. We then move onto the case of a mathematical sphere, where we consider responses to analogous issues in the philosophy of mathematics and language: starting with Shapiro's position of ante rem structuralism (Shapiro 2008, 2012), we introduce the possibility of arbitrary reference. Accounts of arbitrary reference invoking semantic sovereignty (Breckenridge and Magidor 2012), ideal agents (Carrara and Martino 2024), and arbitrary objects (Fine 1985) are considered and rejected.

We argue a unified account can be found for both the physical and mathematical cases, drawing on the notion of performative reference from Assadian and Sbardolini (2023): reference can be understood as being fixed through a speech act, subject to the conventions of the conversation, and assigned randomly in the case of indeterminacy. For a physical sphere, this is anchored to the act of indexical reference; for the mathematical sphere, we argue that reference (and thus coordinates) remain coherent even if co-reference fails to obtain. Finally, we consider implications for structures in physics, such as the notion of fixed fields in theories of spacetime. 

(Joint work with James Read).

_{Philosophy of Physics Graduate Lunch Seminar Convenors: Paolo Faglia, Gregor Gajic and Rachel Pedersen}