Kant and real numbers

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.
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Mark van Atten. Kant and real numbers. Peter Dybjer, Sten Lindström, Erik Palmgren, Göran Sundholm. Epistemology versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf, 27, Springer, pp.203-213, 2012, Logic, Epistemology, and the Unity of Science, 978-94-007-4434-9. ⟨10.1007/978-94-007-4435-6_10⟩. ⟨halshs-00775352⟩

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