Between Logic and Intuition
Essays in Honor of Charles Parsons
Edited by Gila Sher
Edited by Richard Tieszen
Publisher: Cambridge University Press
Print Publication Year: 2000
Online Publication Date:December 2009
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511570681.014
Foundations of a General Theory of Manifolds (Cantor 1883), which I will refer to as the Grundlagen, is Cantor's first work on the general theory of sets. It was a separate printing, with a preface and some footnotes added, of the fifth in a series of six papers under the title of “On infinite linear point manifolds” I want to describe briefly some of the achievements of this great work, but I also want to discuss its connection with the so-called paradoxes in set theory. There seems to be some agreement now that Cantor's own understanding of the theory of transfinite numbers in that monograph did not contain an implicit contradiction, but there is less agreement about exactly why this is so and about the content of the theory itself. For various reasons, both historical and internal, the Grundlagen seems not to have been widely read compared to later works of Cantor, and to have been even less well understood. But even some of the more recent discussions of the work, while recognizing to some degree its unique character, misunderstand it on crucial points and fail to convey its true worth.
Cantor's Pre-Grundlagen Achievements in Set Theory
Cantor's earlier work in set theory contained
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