Intuition and infinity: A Kantian theme with echoes in the foundations of mathematics

Kant says patently conflicting things about infinity and our grasp of it. Infinite space is a good case in point. In his solution to the First Antinomy, he denies that we can grasp the spatial universe as infinite, and therefore that this universe can be infinite; while in the Aesthetic he says just the opposite: ‘Space is represented as a given infinite magnitude’ (A25/B39). And he rests these upon consistently opposite grounds. In the Antinomy we are told that we can have no intuitive grasp of an infinite space, and in the Aesthetic he says that our grasp of infinite space is precisely intuitive.
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DOI 10.1017/S135824610800009X
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Critique of Pure Reason.Immanuel Kant & Norman Kemp Smith - 1966 - Philosophy and Phenomenological Research 26 (3):449-451.

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