Aditya Jha
University of Canterbury and MIT
A debate has been raging in the philosophy literature over whether some physical facts have a purely mathematical, as opposed to a causal, explanation. Among the various accounts of mathematical explanations — given by Baker, Baron and Lange — Lange’s (2013; 2016) account of DMEs is distinguished by the necessity that the DMEs obtain with, regardless of the contingent causal laws in operation. The explanatory facts in a DME explain either by their modal necessity or by being understood in the why question’s context as constitutive of the physical task or arrangement at issue. We argue that the account of DMEs is fallacious because the antecedent of the conditional of a DME may conceal various contingent causal phenomena, and therefore, the resulting explanation cannot be a genuine instance of a mathematical explanation of a physical phenomenon — it is a causal explanation in disguise.
We illustrate the problem with contingency being packed into the antecedent of DMEs by exposing Lange’s inconsistent stand on contingencies being tucked into the conditionals in many of the examples discussed in his work — Because without Cause (OUP, 2016). We mainly discuss the purported DMEs for the existence of Gaussian distributions related to gas diffusion and the potential existence of antipodal temperature and pressure patterns on the earth. We show that although contingency is tucked into the conditional of both of these explanations, Lange’s account is inconsistent in characterising one as a causal explanation and the other one as a DME. This is because, as we demonstrate, various physical assumptions that make a mathematical explanation work, such as the continuity of temperature and pressure (in the case of the antipodal temperature and pressure patterns) are contingent matters, and Lange’s purported DMEs suppress these contingencies into the associated conditionals. We also refute a narrowing down of these conditionals as it only makes the causal role played by contingent facts in the explanation obvious.
Chair: Sanggu Lee
Time: September 8th, 10:40-11:10
Location: HS E.002
SOPhiA 2026 