15 ideas
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 9216 | Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 9214 | Unsupported testimony may still be believable [Fine,K] |
| 9215 | Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K] |