13 ideas
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] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
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] |
21846 | Bergson was a rallying point, because he emphasised becomings and multiplicities [Bergson, by Deleuze] |
21854 | Bergson showed that memory is not after the event, but coexists with it [Bergson, by Deleuze] |