10 ideas
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
3912 | I must exist in order to be mistaken, so that even if I am mistaken, I can't be wrong about my own existence [Augustine] |
13165 | Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus] |
6683 | The contact of spirit and body is utterly amazing, and incomprehensible [Augustine] |
9569 | The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus] |