Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work

• Autores: Esquisabel, Oscar M.; Raffo Quintana, Federico
• Año de publicación: 2021
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Posprint del artículo publicado en Archive for History of Exact Sciences, 2021. doi:10.1007/s00407-021-00277-0
• Materia: FILOSOFIA DE LAS MATEMATICAS; FILOSOFIA MODERNA; Leibniz, Gottfried Wilhelm, 1646-1716; MATEMATICAS; FICCION
• Institución: Pontificia Universidad Católica Argentina

Fil: Esquisabel, Oscar M. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Esquisabel, Oscar M. Universidad Nacional de Quilmes. Centro de Estudios de Filosofía e Historia de la Ciencia; Argentina
Fil: Esquisabel, Oscar M. Pontificia Universidad Católica Argentina; Argentina
Fil: Raffo Quintana, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Raffo Quintana, Federico. Pontificia Universidad Católica Argentina. Facultad de Filosofía y Letras; Argentina
This paper is concerned with the status of mathematical fictions in Leibniz’s work and especially with infinitary quantities as fictions. Thus, it is maintained that mathematical fictions constitute a kind of symbolic notion that implies various degrees of impossibility. With this framework, different kinds of notions of possibility and impossibility are proposed, reviewing the usual interpretation of both modal concepts, which appeals to the consistency property. Thus, three concepts of the possibility/impossibility pair are distinguished; they give rise, in turn, to three concepts of mathematical fictions. Moreover, such a distinction is the base for the claim that infinitesimal quantities, as mathematical fictions, do not imply an absolute impossibility, resulting from self-contradiction, but a relative impossibility, founded on irrepresentability and on the fact that it does not conform to architectonic principles. In conclusion, this “soft” impossibility of infinitesimals yields them, in Leibniz view, a presumptive or “conjectural” status.