German Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor

When it comes to the relation of modern mathematics and philosophy, most people tend to think of the three major schools of thought—i.e. logicism, formalism, and intuitionism—that emerged as profound researches on the foundations and nature of mathematics in the beginning of the 20th century and hav...

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Autor principal:	Ehsan Karimi Torshizi
Formato:	article
Lenguaje:	EN FA
Publicado:	University of Tabriz 2021
Materias:	pure mathematics german idealism logicism formalism intuitionism riemann dedekind cantor Philosophy (General) B1-5802
Acceso en línea:	https://doaj.org/article/a15ed20c3598462e8d3ebbd002b5a73d
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spelling	oai:doaj.org-article:a15ed20c3598462e8d3ebbd002b5a73d2021-11-29T06:23:05ZGerman Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor2251-79602423-441910.22034/jpiut.2021.47964.2971https://doaj.org/article/a15ed20c3598462e8d3ebbd002b5a73d2021-10-01T00:00:00Zhttps://philosophy.tabrizu.ac.ir/article_13867_d59a1c6f54734335279c452c1867d5ce.pdfhttps://doaj.org/toc/2251-7960https://doaj.org/toc/2423-4419When it comes to the relation of modern mathematics and philosophy, most people tend to think of the three major schools of thought—i.e. logicism, formalism, and intuitionism—that emerged as profound researches on the foundations and nature of mathematics in the beginning of the 20th century and have shaped the dominant discourse of an autonomous discipline of analytic philosophy, generally known under the rubric of “philosophy of mathematics” since then. What has been completely disregarded by these philosophical attitudes, these foundational researches which seek to provide pure mathematics with a philosophically plausible justification by founding it on firm logico-philosophical bases, is that the genuine self-foundation of pure mathematics had been done before, namely during the 19th century, when it was developing into an entirely new and independent discipline as a concomitant of the continuous dissociation of mathematics from the physical world. This self-foundation of the 19th-century pure mathematics, however, was more akin to the German-idealist interpretations of Kant’s transcendental philosophy, than the post-factum, retrospective 20th-century researches on the foundations of mathematics. This article aims to demonstrate this neglected historical fact via delving into the philosophical inclinations of the three major founders of the 19th-century pure mathematics, Riemann, Dedekind and Cantor. Consequently, pure mathematics, with respect to its idealist origins, proves to be a formalization and idealization of certain activities specific to a self-conscious transcendental subjectivity.Ehsan Karimi TorshiziUniversity of Tabrizarticlepure mathematicsgerman idealismlogicismformalismintuitionismriemanndedekindcantorPhilosophy (General)B1-5802ENFAPhilosophical Investigations, Vol 15, Iss 36, Pp 171-188 (2021)
institution	DOAJ
collection	DOAJ
language	EN FA
topic	pure mathematics german idealism logicism formalism intuitionism riemann dedekind cantor Philosophy (General) B1-5802
spellingShingle	pure mathematics german idealism logicism formalism intuitionism riemann dedekind cantor Philosophy (General) B1-5802 Ehsan Karimi Torshizi German Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor
description	When it comes to the relation of modern mathematics and philosophy, most people tend to think of the three major schools of thought—i.e. logicism, formalism, and intuitionism—that emerged as profound researches on the foundations and nature of mathematics in the beginning of the 20th century and have shaped the dominant discourse of an autonomous discipline of analytic philosophy, generally known under the rubric of “philosophy of mathematics” since then. What has been completely disregarded by these philosophical attitudes, these foundational researches which seek to provide pure mathematics with a philosophically plausible justification by founding it on firm logico-philosophical bases, is that the genuine self-foundation of pure mathematics had been done before, namely during the 19th century, when it was developing into an entirely new and independent discipline as a concomitant of the continuous dissociation of mathematics from the physical world. This self-foundation of the 19th-century pure mathematics, however, was more akin to the German-idealist interpretations of Kant’s transcendental philosophy, than the post-factum, retrospective 20th-century researches on the foundations of mathematics. This article aims to demonstrate this neglected historical fact via delving into the philosophical inclinations of the three major founders of the 19th-century pure mathematics, Riemann, Dedekind and Cantor. Consequently, pure mathematics, with respect to its idealist origins, proves to be a formalization and idealization of certain activities specific to a self-conscious transcendental subjectivity.
format	article
author	Ehsan Karimi Torshizi
author_facet	Ehsan Karimi Torshizi
author_sort	Ehsan Karimi Torshizi
title	German Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor
title_short	German Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor
title_full	German Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor
title_fullStr	German Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor
title_full_unstemmed	German Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor
title_sort	german idealism and the origins of pure mathematics: riemann, dedekind, cantor
publisher	University of Tabriz
publishDate	2021
url	https://doaj.org/article/a15ed20c3598462e8d3ebbd002b5a73d
work_keys_str_mv	AT ehsankarimitorshizi germanidealismandtheoriginsofpuremathematicsriemanndedekindcantor
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German Idealism and the Origins of Pure Mathematics: Riemann, Dedekind, Cantor

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