Brouwerian infinity

Carl J. Posy

pp. 21-36

in: Pascal Boldini, Michel Bourdeau, Gerhard Heinzmann (eds), One hundred years of intuitionism (1907–2007), Berlin, Springer, 2008

Abstract

Brouwer believed that we humans build the objects of mathematics, and thus he held that those objects are things that we finite beings can intuitively grasp. This was a problem, for mathematics is inherently infinitary (by his time infinite processes, Cantorian higher infinities and a thoroughly infinitary conception of the continuum were already at center stage), but infinite entities and infinite processes exceed our finite grasp. This dilemma — to balance infinity and human intuition — defined Brouwer's intuitionistic career.

Cited authors

Brouwer Luitzen Egbertus Jan