Abstract
The foregoing arguments apply not only to mathematics but also to the sciences. Here I review the innovative mathematical representations of time in the work of Galileo, Descartes and Newton, and then turn to the debate over whether time is absolute (to be defined analytically) or relative (to be defined referentially) between Newton and his mouthpiece Clarke, and Leibniz. The detailed examination of Leibniz’s treatment of time is also a re-consideration of the methodology of this book, since it was inspired by Leibniz. How shall we think about the ways in which the two kinds of discourse that record empirical compilation and theoretical analysis may be combined in science? Leibniz calls on the Principle of Sufficient Reason to regulate a science that must be both empirical and rationalist, aiming to correlate precise empirical description with the abstract conception of science more geometrico. He encourages us to work out our sciences through successive stages, moving back and forth between concrete taxonomy and abstract systematization.