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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
4.3 Souverain Principe
Brief Summary:
Another of Leibniz’s formulations of his law of continuity is: “the rules of the finite succeed in the infinite, and conversely.”
Summary
As a basic principle, all things are governed by reason [[the world is not irrational but operates in accordance with rational law-like regularities]]. For this reason, the “the rules of the finite succeed in the infinite, and conversely.” (KS 579). This is another formulation of the law of continuity.
[[Perhaps Leibniz is noting that both the infinitely small and the finite coincide in the world, but it cannot be that the some parts of the world are governed by some laws, and other parts by other laws, especially when considering that the infinitely small parts reside compositionally within finite bodies.]]
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.
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