14 ideas
| 21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| 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] |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| 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] |