Chapter

Shaky foundations

Stig Stenholm

in The Quest for Reality

Published in print June 2011 | ISBN: 9780199603589
Published online September 2011 | e-ISBN: 9780191729270 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199603589.003.0006
Shaky foundations

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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

Chapter.  8433 words. 

Subjects: History of Science and Technology

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