Constructing a Cartesian Dynamics with “Fixed” Reference Frames: The “Kinematics of Mechanisms” Theory

Abstract

Continuing our analysis of the Cartesian response to the De gravitatione argument, this chapter will investigate the possibility of avoiding the consequences of Newton’s allegations by undermining one of the key premises in its construction: that a matter-filled universe cannot allow unchanging spatial positions. In short, if some sort of fixed reference point can be located in the Cartesian plenum, then a method of tracking a moving body’s velocity over time can be established (thus dispelling Newton’s anti-relationalist worries). Unlike the procedure adopted in chapters 6 and 8, where we employed the dynamics-based “rest” force or Huygens’ notion of a center-of-mass frame to reconstruct a Cartesian dynamics founded upon the collision rules, that is, by using these methods to pick out the privileged frames needed to conserve quantity of motion, this chapter will not appeal to Descartes’ specific predictions on the outcomes of bodily collision in order to thwart Newton’s argument. Our exclusive concern will be to develop a theory of space and time that will allow a Cartesian to meaningfully conserve quantity of motion, and which does not attempt to utilize any of the collision rules as the basis of this reconstruction. Without the need to maintain the precise predictions of the collision rules (as Huygens’ had attempted), it will no longer be necessary to adopt methods that only temporarily preserve quantity of motion from the perspective of a local collision frame. On the formulation of Cartesian dynamics presented in this chapter, we will attempt to posit reference frames that conserve Descartes’ quantity of motion for extended regions of the plenum and for extended temporal periods.