Article ID: CBB000500123

The Motives behind Cantor's Set Theory -- Physical, Biological, and Philosophical Questions (2004)

unapi

Ferreirós, José (Author)


Science in Context
Volume: 17
Pages: 49-83


Publication Date: 2004
Edition Details: Volume Title: New Questions and Approaches in the History of Mathematics, Part II: Modern Mathematics
Language: English

The celebrated creation of transfinite set theory by Georg Cantor has been studied in detail by historians of mathematics. However, it has generally been overlooked that his research program cannot be adequately explained as an outgrowth of the mainstream mathematics of his day. We review the main extra-mathematical motivations behind Cantor's very novel research, giving particular attention to a key contribution, the Grundlagen (Foundations of a general theory of sets) of 1883, where those motives are articulated in some detail. Evidence from other publications and correspondence is pulled out to provide clarification and a detailed interpretation of those ideas and their impact upon Cantor's research. Throughout the paper, a special effort is made to place Cantor's scientific undertakings within the context of developments in German science and philosophy at the time (philosophers such as Trendelenburg and Lotze, scientists like Weber, Riemann, Vogt, Haeckel), and to reflect on the German intellectual atmosphere during the nineteenth century.

...More
Included in

Article Corry, Leo (2004) Introduction: The History of Modern Mathematics---Writing and Rewriting. Science in Context (p. 1). unapi

Citation URI
https://data.isiscb.org/isis/citation/CBB000500123/

Similar Citations

Article Moore, Gregory H.; (2008)
The Emergence of Open Sets, Closed Sets, and Limit Points in Analysis and Topology (/isis/citation/CBB000950203/)

Book Cantor, Georg; Ferreirós, José; (2006)
Fundamentos para una teoría general de conjuntos: Escritos y correspondencia selecta (/isis/citation/CBB000930382/)

Article Cobos Bueno, José M.; (2004)
Maimónides y la paradoja de Burali-Forti (/isis/citation/CBB000650510/)

Article Deisera, Oliver; (2010)
On the Development of the Notion of a Cardinal Number (/isis/citation/CBB001210973/)

Article Moore, Matthew E.; (2002)
A Cantorian Argument Against Infinitesimals (/isis/citation/CBB000300363/)

Article Błaszczyk, Piotr; Katz, Mikhail G.; Sherry, David; (2013)
Ten Misconceptions from the History of Analysis and Their Debunking (/isis/citation/CBB001252715/)

Book Aczel, Amir D.; (2000)
The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity (/isis/citation/CBB000470016/)

Article Peckhaus, Volker; Kahle, Reinhard; (2002)
Hilbert's Paradox (/isis/citation/CBB000200284/)

Article Moore, Gregory H.; Garciadiego, Alejandro; (1981)
Burali-Forti's paradox: A reappraisal of its origins (/isis/citation/CBB000013259/)

Book Kertész, Andor; (1983)
Georg Cantor, 1845-1918: Schöpfer der Mengenlehre. Bearbeitet von Manfred Stern (/isis/citation/CBB000008801/)

Article Bussotti, Paolo; Tapp, Christian; (2009)
The Influence of Spinoza's Concept of Infinity on Cantor's Set Theory (/isis/citation/CBB000931166/)

Article Medvedev, F. A.; (1984)
Über die Abstrakten Mengenlehre von Cantor und Dedekind (/isis/citation/CBB000015927/)

Article Jané, Ignacio; (1995)
The role of the absolute infinite in Cantor's conception of set (/isis/citation/CBB000070611/)

Article Murata, Tamotsu; (1974 (pub. 1975))
L'évolution des principes philosophico-mathématiques de la théorie des ensembles chez Georg Cantor (/isis/citation/CBB000002807/)

Article Medvedev, F.A.; (1985)
Kantorovskaia teoriia mnozhestv i telogiia. (Cantor's theory of sets and theology.) (/isis/citation/CBB000035290/)

Article Ferreirós, José; (1995)
“What fermented in me for years”: Cantor's discovery of transfinite numbers (/isis/citation/CBB000061644/)

Authors & Contributors
Tapp, Christian
Moore, Gregory H.
Medvedev, F. A.
Grattan-Guinness, Ivor
Ferreirós, José
Sherry, David M.
Concepts
Set theory
Mathematics
Infinity
Infinitesimals
Mathematical analysis
Philosophy of mathematics
Time Periods
19th century
20th century, early
Medieval
20th century
Places
Germany
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment