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The Quest for RealityBohr and Wittgenstein - two complementary views$
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Stig Stenholm

Print publication date: 2011

Print ISBN-13: 9780199603589

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199603589.001.0001

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Shaky foundations

Shaky foundations

Chapter:
(p.164) 6 Shaky foundations
Source:
The Quest for Reality
Author(s):

Stig Stenholm

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199603589.003.0006

Here this chapter summarizes the effort to reach absolute certainty in mathematics. This endeavor ended in failure, because no absolute truths can be found even in formal systems. The underdetermination of all such systems is taken to imply that not even the best theory can reach an absolute truth, In view of this, Wittgenstein devotes a lot of discussion to the very activity of doing mathematics: What can we know and what can we do even without a solid foundation? If the world of mathematics is posited, what life can live and develop in this world?

Keywords:   foundations, mathematics, determination, Russel, Frege, Gödel, Turing

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