Katz and Sherry’s [Pt.4.1] “Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond,” 4.1 ‘Critique of Nieuwentijt’, summary

summary by Corry Shores
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Mikhail G. Katz  and David Sherry

“Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond”

4. Cum Prodiisset

 

4.1 Critique of Nieuwentijt

Brief Summary:

Leibniz begins Cum Prodiisset by criticizing Niewentijt’s position that the product of two infinitesimals is zero.

Summary

Niewentijt “defended a conception of infinitesimal according to which the product of two infinitesimals is always zero.” [KS 577] In his Cum Prodiisset, Leibniz begins by criticizing this argument. Regarding Niewentijt’s positions, “Leibniz rejects nilsquare and nilcube infinitesimals, which are altogether incompatible with his approach to differential calculus, as we will see in Sect. 4.6.” [577]

Bibliography:

Katz, M.; Sherry, D. Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond. Erkenntnis 78 (2013), no. 3, 571-625. See http://dx.doi.org/10.1007/s10670-012-9370-y, http://www.ams.org/mathscinet-getitem?mr=3053644, and http://arxiv.org/abs/1205.0174

The above bibliography material taken from the following source, a page by Mikhail Katz, which links to many other recent publications on infinitesimals.

http://u.cs.biu.ac.il/~katzmik/infinitesimals.html