A Philosophical Study on the Foundations of Projective Geometry as A Metageometry

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dc.contributor.authorBirlik, Busra asik
dc.contributor.authorEkren, Ugur
dc.date.accessioned2025-10-11T20:47:51Z
dc.date.available2025-10-11T20:47:51Z
dc.date.issued2024
dc.departmentDüzce Üniversitesien_US
dc.description.abstractThroughout history, research on the foundations of mathematics, particularly the debates surrounding Euclid's fifth postulate, has led to the emergence of the concept of metageometry. This paper examines the problems created by Euclid's fifth postulate in a historical and philosophical context, the contributions to the development of non-Euclidean geometries, and how projective geometry was established as a metageometry during this process. The article notes that the first steps of projective geometry began with the Renaissance architect and artist Leon Battista Alberti and were mathematically grounded through the contributions of the French mathematician Girard Desargues. Additionally, the works of mathematicians like Jean Victor Poncelet and Felix Klein facilitated the development of projective geometry and the acceptance of non-Euclidean geometries. The paper evaluates the philosophical background of these developments through Kant's transcendental philosophy and discusses Russell's thoughts and contributions to metageometry. In this context, the article provides a deep analysis of both the historical development and philosophical foundations of projective geometry.en_US
dc.identifier.doi10.29228/beytulhikme.78023
dc.identifier.endpage920en_US
dc.identifier.issn1303-8303
dc.identifier.issue4en_US
dc.identifier.startpage895en_US
dc.identifier.trdizinid1297298en_US
dc.identifier.urihttps://doi.org/10.29228/beytulhikme.78023
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay/1297298
dc.identifier.urihttps://hdl.handle.net/20.500.12684/21615
dc.identifier.volume14en_US
dc.identifier.wosWOS:001398314700001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakTR-Dizinen_US
dc.language.isotren_US
dc.publisherBeytulhikme Felsefe Cevresien_US
dc.relation.ispartofBeytulhikme-An International Journal of Philosophyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.snmzKA_WOS_20250911
dc.subjectMetageometryen_US
dc.subjectprojective geometryen_US
dc.subjectAlbertien_US
dc.subjectDesarguesen_US
dc.subjectKanten_US
dc.subjectRussellen_US
dc.titleA Philosophical Study on the Foundations of Projective Geometry as A Metageometryen_US
dc.typeArticleen_US

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