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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/73948
Acceder
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network_name_str CONICET Digital (CONICET)
spelling 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/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv 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
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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