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International Studies in Phenomenology and Philosophy

Book | Chapter

186509

Kant and real numbers

Mark Van Atten

pp. 3-23

Abstract

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.

Publication details

Published in:

Dybjer P, Lindström Sten, Palmgren Erik, Sundholm Göran (2012) Epistemology versus ontology: essays on the philosophy and foundations of mathematics in honour of per Martin-löf. Dordrecht, Springer.

Pages: 3-23

DOI: 10.1007/978-94-007-4435-6_1

Full citation:

Van Atten Mark (2012) „Kant and real numbers“, In: P. Dybjer, S. Lindström, E. Palmgren & G. Sundholm (eds.), Epistemology versus ontology, Dordrecht, Springer, 3–23.