Ferreirós, José
(2004)
The Motives behind Cantor’s Set Theory – Physical,
Biological, and Philosophical Questions.
Science in Context, 17 (1).
pp. 49-83.
Abstract
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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