Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs

The present work aims at providing an account of mathematical explanation in two different areas: scientific explanation and within mathematics. The research is addressed from two different perspectives: the one arising from an ontological concern about mathematical entities, and the other originati...

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Detalles Bibliográficos
Autor: Rivas de Castro, Navia
Tipo de recurso: tesis doctoral
Fecha de publicación:2020
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/24582
Acceso en línea:http://hdl.handle.net/10347/24582
Access Level:acceso abierto
Palabra clave:Materias::Investigación::72 Filosofía::7205 Filosofía de la ciencia::720503 Filosofía de las matemáticas
Materias::Investigación::72 Filosofía::7201 Filosofía del conocimiento::720102 Epistemología
Materias::Investigación::72 Filosofía::7203 Filosofía general::720303 Metafísica, ontología
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spelling Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical ProofsRivas de Castro, NaviaMaterias::Investigación::72 Filosofía::7205 Filosofía de la ciencia::720503 Filosofía de las matemáticasMaterias::Investigación::72 Filosofía::7201 Filosofía del conocimiento::720102 EpistemologíaMaterias::Investigación::72 Filosofía::7203 Filosofía general::720303 Metafísica, ontologíaThe present work aims at providing an account of mathematical explanation in two different areas: scientific explanation and within mathematics. The research is addressed from two different perspectives: the one arising from an ontological concern about mathematical entities, and the other originating from a methodological choice: to study our chosen problems (mathematical explanation in science and in mathematics itself) in mathematical practice, that is to say, looking at the way mathematicians understand and perform their work in these diverse areas, including a case study for the context of intra-mathematical explanation. The central target is the analysis of the role that mathematical explanation plays in science and its relevance to the success or failure of scientific theories. The ontological question of whether the explanatory role of abstract objects, mathematical objects in particular, is enough to postulate their existence will be one of the issues to be addressed. Moreover, the possibility of a unified theory of explanation which can accommodate both external and internal mathematical explanation will also be considered. In order to go deeper into these issues, the research includes: (1) an analysis how the question of what is involved in internal mathematical explanation has been addressed in the literature, an analysis of the role of mathematical proof and the reasons why it makes sense to search for more explanatory proofs of already known results, and (2) an analysis of the relation between the use of mathematics in scientific explanation and the ontological commitment that arises from these explanatory tools in science. Part of the present work consists of an analysis of the explanatory role of mathematics through the study of cases reflecting this role. Case studies is one of the main sources of data in order to clarify the role mathematical entities play, among other methodological resources.Martínez Vidal, ConchaLeng, MaryUniversidade de Santiago de Compostela. Escola de Doutoramento Internacional (EDIUS)20202020-01-0120202020-01-01doctoral thesishttp://purl.org/coar/resource_type/c_db06info:eu-repo/semantics/doctoralThesisapplication/pdfhttp://hdl.handle.net/10347/24582reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/245822026-06-15T12:47:27Z
dc.title.none.fl_str_mv Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs
title Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs
spellingShingle Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs
Rivas de Castro, Navia
Materias::Investigación::72 Filosofía::7205 Filosofía de la ciencia::720503 Filosofía de las matemáticas
Materias::Investigación::72 Filosofía::7201 Filosofía del conocimiento::720102 Epistemología
Materias::Investigación::72 Filosofía::7203 Filosofía general::720303 Metafísica, ontología
title_short Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs
title_full Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs
title_fullStr Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs
title_full_unstemmed Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs
title_sort Mathematical Explanation and Ontology: An Analysis of Applied Mathematics and Mathematical Proofs
dc.creator.none.fl_str_mv Rivas de Castro, Navia
author Rivas de Castro, Navia
author_facet Rivas de Castro, Navia
author_role author
dc.contributor.none.fl_str_mv Martínez Vidal, Concha
Leng, Mary
Universidade de Santiago de Compostela. Escola de Doutoramento Internacional (EDIUS)
dc.subject.none.fl_str_mv Materias::Investigación::72 Filosofía::7205 Filosofía de la ciencia::720503 Filosofía de las matemáticas
Materias::Investigación::72 Filosofía::7201 Filosofía del conocimiento::720102 Epistemología
Materias::Investigación::72 Filosofía::7203 Filosofía general::720303 Metafísica, ontología
topic Materias::Investigación::72 Filosofía::7205 Filosofía de la ciencia::720503 Filosofía de las matemáticas
Materias::Investigación::72 Filosofía::7201 Filosofía del conocimiento::720102 Epistemología
Materias::Investigación::72 Filosofía::7203 Filosofía general::720303 Metafísica, ontología
description The present work aims at providing an account of mathematical explanation in two different areas: scientific explanation and within mathematics. The research is addressed from two different perspectives: the one arising from an ontological concern about mathematical entities, and the other originating from a methodological choice: to study our chosen problems (mathematical explanation in science and in mathematics itself) in mathematical practice, that is to say, looking at the way mathematicians understand and perform their work in these diverse areas, including a case study for the context of intra-mathematical explanation. The central target is the analysis of the role that mathematical explanation plays in science and its relevance to the success or failure of scientific theories. The ontological question of whether the explanatory role of abstract objects, mathematical objects in particular, is enough to postulate their existence will be one of the issues to be addressed. Moreover, the possibility of a unified theory of explanation which can accommodate both external and internal mathematical explanation will also be considered. In order to go deeper into these issues, the research includes: (1) an analysis how the question of what is involved in internal mathematical explanation has been addressed in the literature, an analysis of the role of mathematical proof and the reasons why it makes sense to search for more explanatory proofs of already known results, and (2) an analysis of the relation between the use of mathematics in scientific explanation and the ontological commitment that arises from these explanatory tools in science. Part of the present work consists of an analysis of the explanatory role of mathematics through the study of cases reflecting this role. Case studies is one of the main sources of data in order to clarify the role mathematical entities play, among other methodological resources.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
2020
2020-01-01
dc.type.none.fl_str_mv doctoral thesis
http://purl.org/coar/resource_type/c_db06
dc.type.openaire.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
dc.identifier.none.fl_str_mv http://hdl.handle.net/10347/24582
url http://hdl.handle.net/10347/24582
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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