La production du nombre réel dans l'œuvre de Jean Toussaint Desanti
Başlık çevirisi mevcut değil.
- Tez No: 708877
- Danışmanlar: Belirtilmemiş.
- Tez Türü: Yüksek Lisans
- Konular: Tarih, History
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2020
- Dil: Fransızca
- Üniversite: Université Paris-Est
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 91
Özet
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Özet (Çeviri)
This work is a comment to the research of Jean-Toussaint Desanti which is based on genesis of mathematical concepts. It focuses on the mode of production of real number and the constitution of the real number as object. For Desanti, in the framework of a phenomenological language, a science of idealities concerns mathematical objects representing an ideality, that is to say, beings never offered by their mere presence but by the mediation of the system of properties that allow to dispose of them. In the same way as Desanti, we elaborate concepts in mathematics as concepts hierarchically represented starting with the object-concept that is produced under a categorial-concept which divides itself into two generalized concepts : incomplete and complete concepts. Finally, the latter opens to other generalizations and is delimited by a complete structural concept. With regard to the production of the real number, our aim is to illustrate this classification through works of Russell, Dedekind and Cantor. In this sense, we'll see that concepts occur from an“empty place”and refer to indefinite applicability. As far as the idealities are concerned, they must be defined to exist and objects as natural concepts in the system have no meaning other than their mathematical properties. We try to relate this concept of number to concept of measure by examining Lebesgue's and Borel's definitions of measure and to propose an explanatory and critical reading of Desanti's science of idealites.
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