Productive Ambiguity in Leibniz's Representation of Infinitesimals

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationInfinitesimal Differences: Controversies between Leibniz and his Contemporaries
PublisherWalter de Gruyter GmbH and Co. KG
Pages153-170
Number of pages18
ISBN (Print)9783110202168
DOIs
StatePublished - Nov 3 2008

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Gottfried Wilhelm Leibniz
Calculi
Exposition
Natural World
Mathematics
Metaphysical
Transcendental
Principle of Sufficient Reason
Metaphysics
Continuity
Moral Law
Perfection

All Science Journal Classification (ASJC) codes

  • Arts and Humanities(all)

Cite this

Grosholz, E. R. (2008). Productive Ambiguity in Leibniz's Representation of Infinitesimals. In Infinitesimal Differences: Controversies between Leibniz and his Contemporaries (pp. 153-170). Walter de Gruyter GmbH and Co. KG. https://doi.org/10.1515/9783110211863
Grosholz, Emily Rolfe. / Productive Ambiguity in Leibniz's Representation of Infinitesimals. Infinitesimal Differences: Controversies between Leibniz and his Contemporaries. Walter de Gruyter GmbH and Co. KG, 2008. pp. 153-170
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Grosholz, ER 2008, Productive Ambiguity in Leibniz's Representation of Infinitesimals. in Infinitesimal Differences: Controversies between Leibniz and his Contemporaries. Walter de Gruyter GmbH and Co. KG, pp. 153-170. https://doi.org/10.1515/9783110211863

Productive Ambiguity in Leibniz's Representation of Infinitesimals. / Grosholz, Emily Rolfe.

Infinitesimal Differences: Controversies between Leibniz and his Contemporaries. Walter de Gruyter GmbH and Co. KG, 2008. p. 153-170.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Grosholz ER. Productive Ambiguity in Leibniz's Representation of Infinitesimals. In Infinitesimal Differences: Controversies between Leibniz and his Contemporaries. Walter de Gruyter GmbH and Co. KG. 2008. p. 153-170 https://doi.org/10.1515/9783110211863