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.

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

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Authors & Contributors
Moore, Gregory H.
Cantor, Georg
Ferreirós, José
Grattan-Guinness, Ivor
Tapp, Christian
Kertész, Andor
Journals
Historia Mathematica
Proceedings of the ... International Congress of the History of Science
Berichte zur Wissenschaftsgeschichte
Erkenntnis: International Journal of Analytic Philosophy
Synthese
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Publishers
Princeton University Press
Deutsche Akademie der Naturforscher Leopoldina
Teubner
Four Walls Eight Windows
Crítica
Franz Steiner Verlag
Concepts
Set theory
Mathematics
Infinity
Philosophy of mathematics
Logic
Infinitesimals
People
Cantor, Georg Ferdinand Ludwig
Russell, Bertrand Arthur William
Dedekind, Richard
Gödel, Kurt
Hilbert, David
Weierstrass, Karl Theodor
Time Periods
19th century
20th century, early
Medieval
20th century
Places
Germany
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