Leibniz, Philosopher Mathematician and Mathematical Philosopher

Abstract

Like no other philosopher in his time, Leibniz was concerned to develop a metaphysics which could provide an intellectually rigorous account of the success of the mathematical sciences in harnessing and explaining the natural world. Part of the motivation for this concern was his recognition that disciplines such as optics, pneumatics, and mechanics contributed substantially to the improvement of the human condition, this being on his view the ultimate aim of all philosophical endeavour. This paper considers how Leibniz’s drive to explain the successful application of mathematics impacted already on the architectonics of his earlier philosophical system and how in his later metaphysics he sought to incorporate aspects of his method of infinitesimal analysis. It points, in particular, to the crucial and in many ways parallel role played by the concepts of negligible and sensible error in justifying the employment of infinitesimal techniques on the one side and in explaining differences between the mathematical and natural worlds on the other side. Furthermore, it describes, how neither mathematical certainty nor philosophical rigor is compromised when using infinite procedures. Conversely, the paper shows that for Leibniz nature conforms to mathematically definable rules in such a way as a hyperbola approaches its asymptote.