Kant and real numbers
pp. 3-23
in: P. Dybjer, Sten Lindström, Erik Palmgren, Göran Sundholm (eds), Epistemology versus ontology, Berlin, Springer, 2012Abstract
Kant held that under the concept of √2 falls a geometrical magnitude, but not a number. In particular, he explicitly distinguished this root from potentially infinite converging sequences of rationals. Like Kant, Brouwer based his foundations of mathematics on the a priori intuition of time, but unlike Kant, Brouwer did identify this root with a potentially infinite sequence. In this paper I discuss the systematical reasons why in Kant"s philosophy this identification is impossible.
