6 - Leibniz: not equivalent in practice

Summary

Purpose of this chapter

Leibniz's response to the Principia is one of the most complex intellectual events in the history of science. The homo universalis took a critical attitude towards a number of issues, spanning absolute time and space, the gravitational force, the basic laws of motion, and the role of God in the Universe. In this chapter I will confine myself to Leibniz's reaction to Newton's mathematical methods. Notwithstanding the priority dispute, Leibniz's evaluation of Newton's mathematics was a positive one. As a matter of fact, in their mathematical works Newton and Leibniz shared many techniques and concepts. The algorithms of their calculi (the analytical method of fluxions and the differential and integral calculus) were translatable, and translated, one into the other. Furthermore, contrary to what is generally believed, their ideas on the interpretation of these algorithms were strikingly similar. However, the equivalence between the two breaks down when we move from the abstract level of algorithmic techniques and foundational matters, and we consider the mathematical practices. In fact, as I will show, Newton and Leibniz oriented their research along different lines, since they held different values and different expectations for future research. The idea that I would like to convey is that the two mathematicians shared a common mathematical tool, but used it for different purposes.