Article ID: CBB001211734

Leibniz's Laws of Continuity and Homogeneity (2012)

unapi

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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Authors & Contributors
Arthur, Richard T. W.
Bair, Jacques
Ely, Robert
Raffo Quintana, Federico
Kuhlemann, Karl
Esquisabel, Oscar M.
Concepts
Calculus
Philosophy of mathematics
Mathematics
Infinitesimals
Philosophy of science
Continuity
Time Periods
17th century
18th century
19th century
Enlightenment
20th century, early
Places
Europe
Germany
France
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