Newton’s first two laws of motion are not definitions

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Abstract
Newton’s first two laws of motion are often taken to be a definition of force. It is argued that they are true laws in that they make statements about the nature of the physical world. In particular, the first law can be viewed as asserting the existence of an ensemble of trajectories in a four-dimensional space along which force-free bodies, if they exist, would move. Such an ensemble, together with Newton’s absolute time, constitute the essential ingredients of the underlying geometrical structure of Newtonian space-time. If this view is accepted, it is a relatively simple matter to describe how special and general relativity differ from Newtonian mechanics.

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