ERHARD WEIGEL AND HIS INFLUENCE ON LEIBNIZ'S PHILOSOPHY OF MATHEMATICS

In this thesis I argue that Erhard Weigel, professor of mathematics at the University of Jena in the 17th century, had a significant impact on the development of Gottfried Wilhelm Leibniz's philosophy of mathematics. Unlike the generally accepted idea that Weigel's influence lasted only until Leibniz's Parisian stay, it can be proved that they exchanged ideas throughout their lives. In the early years, Weigel influenced Leibniz with his syncretistic interpretation of Hobbes' philosophy and in the revaluation of Euclid's Elements and Aristotle's logic. The analysis of the dissertations written in Jena under Weigel's tutoring show that Leibniz wrote the Hypothesis Physica Nova in the same fashion, following a precise style and focusing on the same topics. This influence led to the revaluation of some universal principles, such as the principle of contradiction and the principle by which the whole is greater than its part, that constitute at a later time Leibniz’s foundation of mathematics. Leibniz’s focus on the concept of homogeneity reveal Weigel’s importance in the following years, especially on the topic of analysis situs and the definition of number. Even more, I argue that Leibniz’s binary arithmetics was developed in the light of Weigel’s mathematical idea of changing the number base, supported by the metaphysical distinction between unity and nothingness. The final outcome of this research is that Leibniz’s philosophy of mathematics could be seen as the rational realization of Weigel’s intuitions, deprived of their dangerous theological consequences.