Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units
- Autores
- Esquisabel, Oscar Miguel; Raffo Quintana, Federico
- Año de publicación
- 2017
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this paper, we analyze the arguments that Leibniz develops against the concept of infinite number in his first Parisian text on the mathematics of the infinite, the Accessio ad arithmeticam infinitorum. With this goal, we approach this problem from two angles. The first, rather philosophical or axiomatic, argues against the number of all numbers appealing to a reductio ad absurdum, showing that the acceptance of the infinite number goes against the principle of the whole and the part, which is analytically demonstrated. So, discussing the ideas of Galileo, Leibniz concludes that the infinite number equals 0. Moreover, Leibniz seems to arrive at the same conclusion through his rule for adding the infinite series resulting from the harmonic triangle. Although he acknowledges the conjectural character of this conclusion, he seems to consider it to be a reinforcement of his first argument. Moreover, in reconstructing the justification of the given rule, we try to show that Leibniz does not appeal to the application of infinitesimal quantities, but rather to a treatment of the infinite series in terms of totalities.
Fil: Esquisabel, Oscar Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencias Sociales. Instituto de Estudios Sociales de la Ciencia y la Tecnología; Argentina
Fil: Raffo Quintana, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencias Sociales. Instituto de Estudios Sociales de la Ciencia y la Tecnología; Argentina - Materia
-
Infinite Number
Infinite Series
Infinitesimal Calculus
Mathematical Conjecture - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/73948
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Leibniz in Paris: A Discussion Concerning the Infinite Number of All UnitsEsquisabel, Oscar MiguelRaffo Quintana, FedericoInfinite NumberInfinite SeriesInfinitesimal CalculusMathematical Conjecturehttps://purl.org/becyt/ford/6.3https://purl.org/becyt/ford/6In this paper, we analyze the arguments that Leibniz develops against the concept of infinite number in his first Parisian text on the mathematics of the infinite, the Accessio ad arithmeticam infinitorum. With this goal, we approach this problem from two angles. The first, rather philosophical or axiomatic, argues against the number of all numbers appealing to a reductio ad absurdum, showing that the acceptance of the infinite number goes against the principle of the whole and the part, which is analytically demonstrated. So, discussing the ideas of Galileo, Leibniz concludes that the infinite number equals 0. Moreover, Leibniz seems to arrive at the same conclusion through his rule for adding the infinite series resulting from the harmonic triangle. Although he acknowledges the conjectural character of this conclusion, he seems to consider it to be a reinforcement of his first argument. Moreover, in reconstructing the justification of the given rule, we try to show that Leibniz does not appeal to the application of infinitesimal quantities, but rather to a treatment of the infinite series in terms of totalities.Fil: Esquisabel, Oscar Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencias Sociales. Instituto de Estudios Sociales de la Ciencia y la Tecnología; ArgentinaFil: Raffo Quintana, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencias Sociales. Instituto de Estudios Sociales de la Ciencia y la Tecnología; ArgentinaUniversidade Católica- Faculdade de Filosofia2017-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/73948Esquisabel, Oscar Miguel; Raffo Quintana, Federico; Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units; Universidade Católica- Faculdade de Filosofia; Revista Portuguesa de Filosofia; 73; 3-4; 12-2017; 1319-13420870-5283CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.publicacoesfacfil.pt/product.php?id_product=1047info:eu-repo/semantics/altIdentifier/doi/10.17990/RPF/2017_73_3_1319info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:25:50Zoai:ri.conicet.gov.ar:11336/73948instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:25:50.321CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units |
title |
Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units |
spellingShingle |
Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units Esquisabel, Oscar Miguel Infinite Number Infinite Series Infinitesimal Calculus Mathematical Conjecture |
title_short |
Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units |
title_full |
Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units |
title_fullStr |
Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units |
title_full_unstemmed |
Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units |
title_sort |
Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units |
dc.creator.none.fl_str_mv |
Esquisabel, Oscar Miguel Raffo Quintana, Federico |
author |
Esquisabel, Oscar Miguel |
author_facet |
Esquisabel, Oscar Miguel Raffo Quintana, Federico |
author_role |
author |
author2 |
Raffo Quintana, Federico |
author2_role |
author |
dc.subject.none.fl_str_mv |
Infinite Number Infinite Series Infinitesimal Calculus Mathematical Conjecture |
topic |
Infinite Number Infinite Series Infinitesimal Calculus Mathematical Conjecture |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/6.3 https://purl.org/becyt/ford/6 |
dc.description.none.fl_txt_mv |
In this paper, we analyze the arguments that Leibniz develops against the concept of infinite number in his first Parisian text on the mathematics of the infinite, the Accessio ad arithmeticam infinitorum. With this goal, we approach this problem from two angles. The first, rather philosophical or axiomatic, argues against the number of all numbers appealing to a reductio ad absurdum, showing that the acceptance of the infinite number goes against the principle of the whole and the part, which is analytically demonstrated. So, discussing the ideas of Galileo, Leibniz concludes that the infinite number equals 0. Moreover, Leibniz seems to arrive at the same conclusion through his rule for adding the infinite series resulting from the harmonic triangle. Although he acknowledges the conjectural character of this conclusion, he seems to consider it to be a reinforcement of his first argument. Moreover, in reconstructing the justification of the given rule, we try to show that Leibniz does not appeal to the application of infinitesimal quantities, but rather to a treatment of the infinite series in terms of totalities. Fil: Esquisabel, Oscar Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencias Sociales. Instituto de Estudios Sociales de la Ciencia y la Tecnología; Argentina Fil: Raffo Quintana, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencias Sociales. Instituto de Estudios Sociales de la Ciencia y la Tecnología; Argentina |
description |
In this paper, we analyze the arguments that Leibniz develops against the concept of infinite number in his first Parisian text on the mathematics of the infinite, the Accessio ad arithmeticam infinitorum. With this goal, we approach this problem from two angles. The first, rather philosophical or axiomatic, argues against the number of all numbers appealing to a reductio ad absurdum, showing that the acceptance of the infinite number goes against the principle of the whole and the part, which is analytically demonstrated. So, discussing the ideas of Galileo, Leibniz concludes that the infinite number equals 0. Moreover, Leibniz seems to arrive at the same conclusion through his rule for adding the infinite series resulting from the harmonic triangle. Although he acknowledges the conjectural character of this conclusion, he seems to consider it to be a reinforcement of his first argument. Moreover, in reconstructing the justification of the given rule, we try to show that Leibniz does not appeal to the application of infinitesimal quantities, but rather to a treatment of the infinite series in terms of totalities. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-12 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/73948 Esquisabel, Oscar Miguel; Raffo Quintana, Federico; Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units; Universidade Católica- Faculdade de Filosofia; Revista Portuguesa de Filosofia; 73; 3-4; 12-2017; 1319-1342 0870-5283 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/73948 |
identifier_str_mv |
Esquisabel, Oscar Miguel; Raffo Quintana, Federico; Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units; Universidade Católica- Faculdade de Filosofia; Revista Portuguesa de Filosofia; 73; 3-4; 12-2017; 1319-1342 0870-5283 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.publicacoesfacfil.pt/product.php?id_product=1047 info:eu-repo/semantics/altIdentifier/doi/10.17990/RPF/2017_73_3_1319 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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openAccess |
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Católica- Faculdade de Filosofia |
publisher.none.fl_str_mv |
Universidade Católica- Faculdade de Filosofia |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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