12 ideas
| 17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17402 | Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri] |
| 17399 | Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev] |
| 17400 | Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri] |
| 17401 | Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev] |