20 ideas
13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
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] |
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] |
15990 | Every individual thing which exists has an essence, which is its internal constitution [Locke] |
15994 | If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |