10 ideas
| 22820 | Early Romantics sought a plurality of systems, in a quest for freedom [Hösle] |
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| 15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| 9916 | Convention, yes! Arbitrary, no! [Poincaré, by Putnam] |
| 18203 | Avoid non-predicative classifications and definitions [Poincaré] |
| 22819 | In the 18th century history came to be seen as progressive, rather than cyclical [Hösle] |
| 15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |