Jacopo Giraldo

This paper explores a number of measure-theoretic notions of spatial extension. It surveys variants of the notion based on Lebesgue measure, and develops one based on Hausdorff measure instead. The Hausdorff-based notion of spatial extension, I argue, secures a measure of spatial extension for all spatial regions, determines extension independently of the dimension of the ambient space, including non-integer ones, and, remarkably, can be defined for any metric space, not just Euclidean ones. Insofar as these are taken to be desiderata for an account of spatial extension—a matter I leave for another occasion—the Hausdorff-based notion proves useful and metaphysically significant, as shown also by its bearing on existing debates over receptacles, extended simples, and persistence. However, the paper should not be read as an argument for preferring one notion over the others, but simply as a contribution to the rapidly growing debate on spatial extension.

Computer simulations (CSs) are widely adopted in science, although their characteristics and purposes can significantly vary depending on the scientific context. In this paper, we focus on CSs in astrophysics and we consider the paradigmatic case of the BepiColombo-MORE relativity experiment. By presenting three different case studies in which the same set of CSs is adopted, we argue that CSs allow us to make inferential claims by serving three distinct roles: (i) providing higher-order knowledge, (ii) orienting knowledge, (iii) disclosing knowledge. We discuss this three-fold taxonomy, drawing the similarities and the differences with respect to the literature in philosophy of astrophysics. We point out that the proposed classification is not intended as a general and exhaustive categorization for any astrophysical problem; rather, it highlights that the roles of CSs should be addressed on a case-by-case basis, given the strong context-sensitivity of the problem. Additionally, we emphasize that the three proposed roles can be performed by the same set of CSs, depending on the context and scientific goals. While the set of CSs underpinning each case study remains the same, it enables distinct epistemic claims based on the specific case.