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dc.contributor.author
Esquisabel, Oscar Miguel

dc.contributor.author
Raffo Quintana, Federico

dc.date.available
2022-08-11T13:19:38Z
dc.date.issued
2021-04
dc.identifier.citation
Esquisabel, Oscar Miguel; Raffo Quintana, Federico; Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work; Springer; Archive for History of Exact Sciences; 75; 6; 4-2021; 613-647
dc.identifier.issn
0003-9519
dc.identifier.uri
http://hdl.handle.net/11336/165158
dc.description.abstract
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 architectural principles. In conclusion, this “soft” impossibility of infinitesimals yields them, in Leibniz view, a presumptive or “conjectural” status.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer

dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
FICTIONS
dc.subject
INFINITESIMALS
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INFINITARY QUANTITIES
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POSSIBILITY
dc.subject.classification
Filosofía, Historia y Filosofía de la Ciencia y la Tecnología

dc.subject.classification
Filosofía, Ética y Religión

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HUMANIDADES

dc.title
Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-08-11T13:05:31Z
dc.journal.volume
75
dc.journal.number
6
dc.journal.pagination
613-647
dc.journal.pais
Alemania

dc.description.fil
Fil: Esquisabel, Oscar Miguel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencias Sociales. Instituto de Estudios sobre la Ciencia y la Tecnología. Centro de Estudios de Filosofía e Historia de la Ciencia; Argentina
dc.description.fil
Fil: Raffo Quintana, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires"; Argentina
dc.journal.title
Archive for History of Exact Sciences

dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/10.1007/s00407-021-00277-0
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00407-021-00277-0
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