Abstract
In this essay, I argue that Leibniz believed that mathematics is best investigated by means of a variety of modes of representation, often stemming from a variety of traditions of research, like our investigations of the natural world and of the moral law. I expound this belief with respect to two of his great metaphysical principles, the Principle of Perfection and the Principle of Continuity, both versions of the Principle of Sufficient Reason; the tension between the latter and the Principle of Contradiction is what keeps Leibniz's metaphysics from triviality. I then illustrate my exposition with two case studies from Leibniz's mathematical research, his development of the infinitesimal calculus, and his investigations of transcendental curves.
Original language | English (US) |
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Title of host publication | Infinitesimal Differences |
Subtitle of host publication | Controversies between Leibniz and his Contemporaries |
Publisher | Walter de Gruyter GmbH and Co. KG |
Pages | 153-170 |
Number of pages | 18 |
ISBN (Print) | 9783110202168 |
DOIs | |
State | Published - Nov 3 2008 |
All Science Journal Classification (ASJC) codes
- General Arts and Humanities