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

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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, differe...

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Autores principales: Esquisabel, Oscar M., Raffo Quintana, Federico
Formato: Artículo
Lenguaje:Inglés
Publicado: Springer 2021
Materias:
FILOSOFIA DE LAS MATEMATICAS
FILOSOFIA MODERNA
Leibniz, Gottfried Wilhelm, 1646-1716
MATEMATICAS
FICCION
Acceso en línea:https://repositorio.uca.edu.ar/handle/123456789/12339
Aporte de:
Repositorio Institucional de la Universidad Católica Argentina (UCA) de Universidad Católica Argentina
id I33-R139-123456789-12339
record_format dspace
spelling I33-R139-123456789-123392025-04-30T01:03:46Z Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work Esquisabel, Oscar M. Raffo Quintana, Federico FILOSOFIA DE LAS MATEMATICAS FILOSOFIA MODERNA Leibniz, Gottfried Wilhelm, 1646-1716 MATEMATICAS FICCION 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. 2021-09-20T19:00:15Z 2021-09-20T19:00:15Z 2021 Artículo Esquisabel, O. M., Raffo Quintana, F. Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work [en línea]. Posprint del artículo publicado en Archive for History of Exact Sciences, 2021. doi:10.1007/s00407-021-00277-0. Disponible en: https://repositorio.uca.edu.ar/handle/123456789/12339 0003-9519 (impreso) 1432-0657 (online) https://repositorio.uca.edu.ar/handle/123456789/12339 10.1007/s00407-021-00277-0 eng La Ciencia General de Leibniz como fundamentación de las ciencias: lógica, ontología y filosofía natural Acceso abierto. 12 meses de embargo http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer Posprint del artículo publicado en Archive for History of Exact Sciences, 2021. doi:10.1007/s00407-021-00277-0
institution Universidad Católica Argentina
institution_str I-33
repository_str R-139
collection Repositorio Institucional de la Universidad Católica Argentina (UCA)
language Inglés
topic FILOSOFIA DE LAS MATEMATICAS
FILOSOFIA MODERNA
Leibniz, Gottfried Wilhelm, 1646-1716
MATEMATICAS
FICCION
spellingShingle FILOSOFIA DE LAS MATEMATICAS
FILOSOFIA MODERNA
Leibniz, Gottfried Wilhelm, 1646-1716
MATEMATICAS
FICCION
Esquisabel, Oscar M.
Raffo Quintana, Federico
Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work
topic_facet FILOSOFIA DE LAS MATEMATICAS
FILOSOFIA MODERNA
Leibniz, Gottfried Wilhelm, 1646-1716
MATEMATICAS
FICCION
description 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.
format Artículo
author Esquisabel, Oscar M.
Raffo Quintana, Federico
author_facet Esquisabel, Oscar M.
Raffo Quintana, Federico
author_sort Esquisabel, Oscar M.
title Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work
title_short Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work
title_full Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work
title_fullStr Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work
title_full_unstemmed Fiction, possibility and impossibility : three kinds of mathematical fictions in Leibniz’s work
title_sort fiction, possibility and impossibility : three kinds of mathematical fictions in leibniz’s work
publisher Springer
publishDate 2021
url https://repositorio.uca.edu.ar/handle/123456789/12339
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