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Full Idea
The goal of my theory is to establish once and for all the certitude of mathematical methods.
Gist of Idea
I aim to establish certainty for mathematical methods
Source
David Hilbert (On the Infinite [1925], p.184)
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.184
A Reaction
This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems.
| 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] |