Katz, Mikhail G. (Author)
Sherry, David M. (Author)
Notices of the American Mathematical Society
Volume: 59, no. 11
Issue: 11
Pages: 1550-1558
We argue that, contrary to Berkeley's view, Leibniz's system for the di erential calculus was robust and free of contradiction. Leibniz articulated a set of coherent heuristic procedures for his calculus. Thus, Leibniz's system incorporated versatile heuristic principles, such as his law of continuity and laws of homogeneity, which were amenable, in the ripeness of time, to implementation as general principles governing the manipulation of modern in nitesimal and in nitely large quantities, such as the transfer principle and the standard part principle. Kanovei [21] and others performed similar reconstructions of Euler's work. We will draw on Leibniz's work, more speci cally his Cum Prodiisset, to argue for the consistency of Leibniz's system for the di erential calculus.1 We will also draw on the work of Leibniz historians Bos, Ferraro, Horváth, Knobloch, and Laugwitz.
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