Xavier Piccone
Colorado State University
In this paper I propose one approach to answering the question of how apparently intractable infinite systems help us understand the finite natural world. To do this I focus on the role of thermodynamic limit taking operations in statistical mechanics that explain critical behavior in fluids. I argue that the prevalence of these “misrepresentations” or infinite idealizations, though disrupting standard views of the epistemic role of mathematics in science, does not force us to abandon the intuition that our best mathematical explanations, and the understandings they furnish, are true of the world in an important sense.
In §2 I lay out the problem of modelling critical phase transitions (PT) and introduce the renormalization group (RG) explanations used to solve it. §2.1 presents the standard mapping account of applied mathematics, illustrates how RG complicates it, and fleshes out three desiderata for a more comprehensive approach. In §3 I offer such an account, mathematical aspect realism, drawing on both the later Wittgenstein’s philosophy of mathematics and recent developments in the literature on idealization and scientific understanding. Before concluding I consider, in §4, the objection that RG qua mathematical operation adds no unique epistemic value.
Chair: Edoardo Fazzini
Time: 05 September, 10:00 – 10:30
Location: SR 1.005
SOPhiA 2026 