15 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] |
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] |
17499 | Theoretical models can represent, by mapping onto the data-models [Portides] |
17498 | In the 'received view' models are formal; the 'semantic view' emphasises representation [Portides, by PG] |
17501 | Representational success in models depends on success of their explanations [Portides] |
17502 | The best model of the atomic nucleus is the one which explains the most results [Portides] |
17496 | 'Model' belongs in a family of concepts, with representation, idealisation and abstraction [Portides] |
17497 | Models are theory-driven, or phenomenological (more empirical and specific) [Portides] |
17500 | General theories may be too abstract to actually explain the mechanisms [Portides] |
8478 | Dewey argued long before Wittgenstein that there could not seriously be a private language [Dewey, by Orenstein] |