Contributions of the Wallis-Hobbes Controversy to the Discussions on the Foundations of Infinite Mathematics
DOI:
https://doi.org/10.46553/10.46553/tab.19.2022.p23-36Keywords:
Wallis, Hobbes, infinite mathematics, arithmetic of infinities.Abstract
In this paper we will deal with some aspects of the controversy between Wallis and Hobbes concerning the foundations of infinite mathematics and the use of infinite and infinitely small quantities in mathematics. Thus, after some initial clarification on Wallis’s arithmetic of infinities, we will focus particularly on three main topics of this discussion: the nature of infinitesimals and the validity of their use in mathematics; the infinite number and the supposition of what we will call “the completeness of the series”; and the conception that the “excess” disappears, taking the series to infinity.
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