Leibniz and Zeno’s Paradoxes

It is widely believed that prior to the work of Cauchy in the first half of the nineteenth century it was impossible to resolve Zeno’s Dichotomy and Achilles Paradoxes because there was no satisfactory treatment of convergent infinite series; and that prior to the provision of a satisfactory analysis of the real number system and its connections with the calculus by Dedekind, Weierstrass et al., there was no satisfactory treatment of Zeno’s Arrow Paradox. Both these claims, I maintain, are utterly false. In this talk, I aim to convince you not only that Gottfried Leibniz formulated logically impeccable foundations for the mathematics of the infinite already in the 17th century; but that there are good grounds for believing that these foundations are adequate for a resolution of Zeno’s paradoxes of the Dichotomy and Achilles (and if I still have the time to show this, of the Arrow Paradox too).

Speakers

Ric Arthur, McMaster University