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.
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© 2008 Birkhäuser Verlag AG
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Posy, C. (2008). Brouwerian infinity. In: van Atten, M., Boldini, P., Bourdeau, M., Heinzmann, G. (eds) One Hundred Years of Intuitionism (1907–2007). Publications des Archives Henri Poincaré / Publications of the Henri Poincaré Archives. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8653-5_2
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DOI: https://doi.org/10.1007/978-3-7643-8653-5_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8652-8
Online ISBN: 978-3-7643-8653-5
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