The genesis of mathematical objects, following Weyl and Brouwer

Dirk van Dalen

pp. 77-85

in: Causality, meaningful complexity and embodied cognition, Berlin, Springer, 2010

Abstract

Almost a century ago, Brouwer launched his first intuitionistic programme for mathematics. He did so in his dissertation of 1907, where he formulated the basic act of creation of mathematical objects, known as the ur-intuition of mathematics. Mathematics, in Brouwer's view, was an intellectual activity of men (of the subject), independent of language and logic. The objects of mathematics come first in the process of human cognition, and description and systematization (in particular logic) follow later. The formulation of the ur-intuition is somewhat hermetic, but in view of its fundamental role, let us reproduce it here.

Cited authors

Weyl Hermann

Brouwer Luitzen Egbertus Jan