Inconsistency in Classical Electrodynamics

I show that the standard approach to modeling phenomena involving microscopic classical electrodynamics is mathematically inconsistent. I argue that there is no conceptually unproblematic and consistent theory covering the same phenomena to which this inconsistent theory can be thought of as an approximation; and I propose a set of conditions for the acceptability of inconsistent theories. 1. Introduction. Among the different criteria for evaluating scientific theories proposed by philosophers, internal consistency appears to be privileged. A highly successful theory may be more or less accurate or may be more or less simple, but according to what appears to be a widely held view, internal consistency is not similarly up for negotiation: Internal consistency is a necessary condition for a theory to be even minimally successful, for an inconsistent set of principles threatens to be trivial in that any sentence whatever can be derived from it. In this paper I want to discuss some central features of classical electrodynamics with the aim of raising some doubts about this view. The main approach to modeling classical electromagnetic phenomena involving charged particles relies on a set of internally inconsistent assumptions. Yet despite the inconsistency this theory is strikingly successful. What is more, there does not appear to be an otherwise at least equally as successful yet fully consistent alternative theory that the standard approach could be taken to approximate. There are a number of conclusions that I wish to draw from my case study. First and foremost, the traditional view according to which con