The Dissertation

Dirk van Dalen
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Dirk van Dalen: Utrecht University, Department of Philosophy

Chapter Chapter 3 in L.E.J. Brouwer – Topologist, Intuitionist, Philosopher, 2013, pp 77-117 from Springer

Abstract: Abstract Brouwer’s Thesis is a somewhat ambiguous book, it contains a purely mathematical part, dealing with ‘Hilbert 5’, i.e. the elimination of differentiability conditions in the theory of Lie groups, and a number of geometrical investigations. But the larger part was the presentation of a personal approach to the foundations of mathematics together with well-argued criticism of contemporary schools. The chapter makes extensive use of archive material, that allows us to follow how Brouwer’s ideas evolved. It contains the fundamental material on Brouwer’s ur-intuition, the genesis of the natural numbers and the continuum. Furthermore Brouwer’s views and first steps in intuitionistic logic are discussed. The dissertation and the archive material shows that Brouwer’s philosophical principles went beyond just mathematics.

Keywords: Number Class; Mathematical System; Continuum Problem; Continuum Hypothesis; Outer World (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-1-4471-4616-2_3

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