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Full Idea
No one shall drive us out of the paradise the Cantor has created for us.
Gist of Idea
No one shall drive us out of the paradise the Cantor has created for us
Source
David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.65
A Reaction
This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities.
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |