Galilei, Leibniz, and the scrupulositas of mathematics (Q2738718)

The author compares the views of Galilei and Leibniz with respect to the infinitely large and the infinitely small (indivisibilia). Galilei, influenced by Cusanus, considered actual infinity and the indivisibilia as existing but incomprehensible to the finite human mind, because they surpass the possibilities of our imagination. For Galilei the actually infinitely big and small were non-quantities to which the ordinary rules applicable to quantities cannot be applied without risking contradictions. Unlike Galilei, Leibniz rejected actual infinity. Yet, by introducing ficticious positive quantities, bigger or, respectively, smaller than any quantity given in advance, he succeeded in showing that it is possible to calculate rigorously with infinity and indivisibila.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00023].