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.


Number Class Choice Sequence Continuity Theorem Legitimate Object Human Intuition 
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Copyright information

© Birkhäuser Verlag AG 2008

Authors and Affiliations

  • Carl Posy
    • 1
  1. 1.Department of PhilosophyThe Hebrew University of JerusalemIsrael

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