Introduction

pp. 3-6

in: Vincenzo Risi, Vincenzo De Risi, Leibniz on the parallel postulate and the foundations of geometry, Basel, Birkhäuser, 2016

Abstract

Among the many contributions of Gottfried Wilhelm Leibniz (1646–1716) in mathematics and philosophy, his work on the foundations of geometry is especially relevant. In Leibniz" times, the text of Euclid's Elements still represented the starting point for any advanced mathematical theory, including Leibniz" most celebrated discovery, the Calculus. The Greek treatise, on the other hand, was also the main model for deductive reasoning, and the touchstone of logical analysis and epistemology in general. In the seventeenth and eighteenth centuries, the debate on the Elements was extensive, and philosophers, philologists and mathematicians contributed, with dozens of emended and commented editions of the text, to a better understanding of Euclid's intentions and a deeper insight into the nature of geometry itself. Given Leibniz" great interest in logic, his involvement in foundational discussions about the new infinitesimal techniques, his wide erudition in the history of mathematics, and his didactical preoccupations with scientific education, it comes as no surprise that throughout his entire life he devoted a considerable part of his time to investigating the essence of geometrical reasoning or the system of principles needed to ground the whole of mathematics.