Ferreirós, José (Author)
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.
...MoreArticle Corry, Leo (2004) Introduction: The History of Modern Mathematics---Writing and Rewriting. Science in Context (p. 1).
Article
Cobos Bueno, José M.;
(2004)
Maimónides y la paradoja de Burali-Forti
(/isis/citation/CBB000650510/)
Book
Grattan-Guinness, I.;
(2000)
The Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor through Russell to Gödel
(/isis/citation/CBB000111675/)
Article
Deisera, Oliver;
(2010)
On the Development of the Notion of a Cardinal Number
(/isis/citation/CBB001210973/)
Book
Cantor, Georg;
Ferreirós, José;
(2006)
Fundamentos para una teoría general de conjuntos: Escritos y correspondencia selecta
(/isis/citation/CBB000930382/)
Article
Moore, Gregory H.;
(2008)
The Emergence of Open Sets, Closed Sets, and Limit Points in Analysis and Topology
(/isis/citation/CBB000950203/)
Book
Tapp, Christian;
(2005)
Kardinalität und Kardinäle: Wissenschaftshistorische Aufarbeitung der Korrespondenz zwischen Georg Cantor und katholischen Theologen seiner Zeit
(/isis/citation/CBB001021540/)
Book
Grattan-Guiness, I.;
(2000)
Search for Mathematical Roots, 1870-1940: Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel
(/isis/citation/CBB000102346/)
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/)
Book
Cantor, Georg;
(1984)
Über unendliche, lineare Punktmannigfaltigkeiten: Arbeiten zur Mengenlehre aus den Jahren 1872-1884. Hrsg. und kommentiert von Asser, G.
(/isis/citation/CBB000029121/)
Article
Nagaoka, Ryosuke;
(1974 (pub. 1975))
The earlier development of set theory by Cantor
(/isis/citation/CBB000022480/)
Article
Dauben, Joseph W.;
(1974 (pub. 1975))
“Hypotheses non fingo”: Georg Cantor's set theory and his philosophy of the infinite
(/isis/citation/CBB000022406/)
Article
Murata, Tamotsu;
(1974 (pub. 1975))
L'évolution des principes philosophico-mathématiques de la théorie des ensembles chez Georg Cantor
(/isis/citation/CBB000002807/)
Article
Meyer, Heiner;
(1983)
Über einige naturphilosophische Diskussionen im Zusammenhang mit der Begründung der Mengentheorie durch Georg Cantor
(/isis/citation/CBB000016341/)
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/)
Be the first to comment!