8 ideas
18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
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] |
15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
6011 | There is a remote first god (the Good), and a second god who organises the material world [Numenius, by O'Meara] |