On the Classical Laws of Motion

A number of logical objections may be raised against the classical laws of motion as they are formulated by Newton and as they are usually presented in textbooks of physics. These objections, which center about the conceptions of mass and force, were first clearly presented by Mach and Poincaré among others. Although these objections are widely known, there appear to be few attempts to present the classical laws in a logically unobjectionable manner and in such a way as to bring out the essential significance of the force and mass concepts. It is the purpose of the following paper to suggest a reformulation of the basic laws of motion. After a short introduction (Sec. 1) the objections to Newton's presentation of the laws of motion are reviewed (Sec. 2). In Sec. 3, the classical laws are given a new formulation.