Chapter

The Continuum

Mathieu Marion

in Wittgenstein, Finitism, and the Foundations of Mathematics

Published in print August 2008 | ISBN: 9780199550470
Published online September 2011 | e-ISBN: 9780191701559 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199550470.003.0007
The Continuum

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Ludwig Wittgenstein wrote or spoke extensively on the nature of the continuum during the years 1929-–33. This is hardly surprising, since this topic was at the centre of the Grundlagenstreit: classical mathematicians felt that their beautiful Cantorian construction of the continuum was threatened by L. E. J. Brouwer's bolshevism. There are several methods in classical mathematics for introducing real numbers. Wittgenstein's comments were limited to the two principal ones, the introduction of the set of reals via Cauchy sequences of rationals and the method of Dedekind cuts. Wittgenstein's remarks on these are, again, of an elementary nature and of little interest to logicians today, but for people, they are definitely worth a closer look because they show much coherence in his commitment to finitism.

Keywords: Ludwig Wittgenstein; continuum; classical mathematics; L. E. J. Brouwer; Cauchy sequences; diagonal method; Dedekind cuts

Chapter.  8098 words. 

Subjects: History of Western Philosophy ; Philosophy of Mathematics and Logic

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