15 ideas
10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
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] |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
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] |
10885 | Computer proofs don't provide explanations [Horsten] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
15797 | All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer] |
15800 | All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer] |
15798 | Kinds are arrangements of dispositions [Fetzer] |
15799 | Lawlike sentences are general attributions of disposition to all members of some class [Fetzer] |