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Topic: Matheology § 291
Replies: 28   Last Post: Jun 19, 2013 5:29 PM

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mueckenh@rz.fh-augsburg.de

Posts: 15,737
Registered: 1/29/05
Matheology § 291
Posted: Jun 16, 2013 4:46 PM
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Matheology § 291


Only someone who (like the intuitionist) denies that the concepts and axioms of classical set theory have any meaning (or any well-defined meaning) could be satisfied with such a solution {{undecidability of the continuum hypothesis}}, not someone who believes them to describe some well-determined reality. For this reality Cantor's conjecture must be either true or false, and its undecidability from the axioms known today can only mean that these axioms do not contain a complete description of this reality; [...] not one plausible proposition is known which would imply the continuum hypothesis. Therefore one may on good reason suspect that the role of the continuum problem in set theory will be this, that it will finally lead to the discovery of new axioms which will make it possible to disprove Cantor's conjecture.
[Kurt Godel: "What is Cantor's Continuum Problem?", The American Mathematical Monthly, 54,9 (1947) p. 520, 524]
http://www.personal.psu.edu/ecb5/Courses/M475W/Readings/Week06-IntoTheTwentiethCentury-10-8/Supplementary/What%20is%20Cantor's%20Continuum%20Problem,%20by%20Kurt%20Godel.pdf

Regards, WM




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