Contributions of the Wallis-Hobbes Controversy to the Discussions on the Foundations of Infinite Mathematics

Authors

  • Federico Raffo Quintana Pontificia Universidad Católica Argentina ; Consejo Nacional de Investigaciones Científicas y Técnicas

DOI:

https://doi.org/10.46553/10.46553/tab.19.2022.p23-36

Keywords:

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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Author Biography

Federico Raffo Quintana, Pontificia Universidad Católica Argentina ; Consejo Nacional de Investigaciones Científicas y Técnicas

Federico Raffo Quintana es doctor en Filosofía por la Universidad Nacional de La Plata. Con anterioridad obtuvo los títulos de Profesor y Licenciado en Filosofía por la UCA. Su ámbito principal de investigación es la concepción del infinito de Leibniz, en especial en el contexto de sus exámenes sobre el problema de la composición del continuo y de su desarrollo en cuestiones de matemática infinita, temas sobre los que ha publicado libros y artículos especializados. Es investigador asistente del CONICET y con anterioridad se ha desempeñado como becario doctoral y posdoctoral en dicho Consejo. Además, se desempeña como Profesor Titular de Taller de lectura filosófica I y II y como Profesor Adjunto de Epistemología en la carrera de Filosofía, UCA.

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Published

04/22/2022

How to Cite

Raffo Quintana, F. (2022). Contributions of the Wallis-Hobbes Controversy to the Discussions on the Foundations of Infinite Mathematics. Tábano, (19), 23–36. https://doi.org/10.46553/10.46553/tab.19.2022.p23-36

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