Maxwell's Derivation of the Velocity Distribution: An Example of A Priori Discovery in Science?
Abstract: I examine James Clerk Maxwell's apparently a priori discovery of the Maxwell-Boltzmann distribution. The form of Maxwell's reasoning is made explicit, and the reasons for its success discussed. I argue that, though the reasoning that led Maxwell to the distribution was in fact a posteriori, it is an example of a kind of a posteriori reasoning that (a) is able to draw very strong conclusions from apparently rather weak premises, (b) plays an essential role in some very important branches of science, and (c) has been almost entirely neglected by philosophers of science.
This long paper has four major parts. The first part argues, by way of a close reading of the original paper, that Maxwell's reasoning takes into account physical symmetries. The second part describes a rule for inferring probabilities from symmetries that, I assert, Maxwell used to infer the velocity distribution. The third part explains why this rule is reliable for a large class of complex systems. The fourth part investigates the application of the rule outside the ambit of statistical physics, in particular, to biological systems.