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
Online ISBN:9780511570681
Hardback ISBN:9780521650762
Paperback ISBN:9780521038256
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511570681.014
Subjects: Philosophy of science, Recreational mathematics
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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
pp. i-iv
pp. v-vi
pp. vii-viii
pp. 1-2
Paradox Revisited I: Truth : Read PDF
pp. 3-15
Paradox Revisited II: Sets – A Case of All or None? : Read PDF
pp. 16-26
Truthlike and Truthful Operators : Read PDF
pp. 27-53
pp. 54-78
On Second-Order Logic and Natural Language : Read PDF
pp. 79-99
The Logical Roots of Indeterminacy : Read PDF
pp. 100-123
The Logic of Full Belief : Read PDF
pp. 124-152
pp. 153-154
Immediacy and the Birth of Reference in Kant: The Case for Space : Read PDF
pp. 155-185
Geometry, Construction and Intuition in Kant and his Successors : Read PDF
pp. 186-218
Parsons on Mathematical Intuition and Obviousness : Read PDF
pp. 219-231
Gödel and Quine on Meaning and Mathematics : Read PDF
pp. 232-254
III - NUMBERS, SETS AND CLASSES : Read PDF
pp. 255-256
Must We Believe in Set Theory? : Read PDF
pp. 257-268
Cantor's Grundlagen and the Paradoxes of Set Theory : Read PDF
pp. 269-290
Frege, the Natural Numbers, and Natural Kinds : Read PDF
pp. 291-298
A Theory of Sets and Classes : Read PDF
pp. 299-316
Challenges to Predicative Foundations of Arithmetic : Read PDF
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pp. 339-342
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