On the independence problem of Newton's first law

Abstract

Newton's laws of motion pose an apparent problem, sometimes referred to as "the independence problem": the first law seems to be a simple consequence of the second law, raising the question of why it was included as a separate law. Numerous answers to this question have been proposed in the literature. The main contribution of this paper is a novel answer which we call "the formal explanation." Unlike previous accounts it relies on mathematical formalism and argues that the definitions of Euclidean geometry necessitate the inclusion of the first law. We provide evidence in support of this claim. A second contribution is a comprehensive review of previously suggested explanations, which so far have often been treated in a fragmented manner, and a discussion of the plausibility of the various answers.