Kant and real numbers

Mark van Atten (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

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.

Mots clés: philosophy of science

Domaines: Histoire, Philosophie et Sociologie des sciences; Philosophie

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⟩