Full Description
This monograph presents an interpretive essay on the foundations of Leibniz's calculus, accompanied by key texts in English translation. The essay examines Leibniz's evolving views on infinitesimals and infinite numbers, tracing their development from his early metaphysical ideas to his mature justifications of the calculus.
Leibniz first proposed treating infinitesimals as fictions in the 1670s, in line with the mathematical practices of his time, where abstract concepts could be used in calculations without implying their existence. By 1676, he rejected their status as quantities, yet continued to refine his arguments on this topic into the 1690s.
The essay concludes with an analysis of Leibniz's defense of his calculus in the early 18th century, showing how his later works naturally extended from earlier insights. This monograph will be a valuable resource for scholars and students of Leibniz and the history of science.
Contents
- Part I Interpretive Essay.- Chapter 1. Introduction.- Chapter 2. On the Metaphysics of the Continuum (1669-1676).- Chapter 3. Mathematical Fictions.- Chapter 4. De Quadratura Arithmetica (DQA).- Chapter 5. Infinitesimals and Existence after 1676.- Chapter 6. Leibniz's Mature Justifications of the Calculus.- Chapter 7. Conclusion.- Part II A selection of translations of key texts.- Chapter 8: Texts for chapter 2, On the Metaphysics of the Continuum (1669-1676).- Chapter 9: Texts for chapter 3, Mathematical Fictions.- Chapter 10: Texts for chapter 4, De Quadratura Arithmetica (DQA).- Chapter 11: Texts for chapter 5, Infinitesimals and Existence after 1676.- Chapter 12: Texts for chapter 6, Leibniz's Mature Justifications of the Calculus.
