16 ideas
8208 | In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine] |
8207 | The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [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] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
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] |
8205 | Explaining events just by bodies can't explain two events identical in space-time [Quine] |
8206 | Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |