30 ideas
| 16951 | It was realised that possible worlds covered all modal logics, if they had a structure [Dummett] |
| 16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
| 16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
| 16960 | If possibilitiy is relative, that might make accessibility non-transitive, and T the correct system [Dummett] |
| 16958 | In S4 the actual world has a special place [Dummett] |
| 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] |
| 4444 | One moderate nominalist view says that properties and relations exist, but they are particulars [Armstrong] |
| 4445 | If properties and relations are particulars, there is still the problem of how to classify and group them [Armstrong] |
| 4448 | Should we decide which universals exist a priori (through words), or a posteriori (through science)? [Armstrong] |
| 4446 | It is claimed that some universals are not exemplified by any particular, so must exist separately [Armstrong] |
| 4440 | 'Resemblance Nominalism' finds that in practice the construction of resemblance classes is hard [Armstrong] |
| 4439 | 'Resemblance Nominalism' says properties are resemblances between classes of particulars [Armstrong] |
| 4431 | 'Predicate Nominalism' says that a 'universal' property is just a predicate applied to lots of things [Armstrong] |
| 4433 | Concept and predicate nominalism miss out some predicates, and may be viciously regressive [Armstrong] |
| 4432 | 'Concept Nominalism' says a 'universal' property is just a mental concept applied to lots of things [Armstrong] |
| 4436 | 'Class Nominalism' may explain properties if we stick to 'natural' sets, and ignore random ones [Armstrong] |
| 4434 | 'Class Nominalism' says that properties or kinds are merely membership of a set (e.g. of white things) [Armstrong] |
| 4435 | 'Class Nominalism' cannot explain co-extensive properties, or sets with random members [Armstrong] |
| 4437 | 'Mereological Nominalism' sees whiteness as a huge white object consisting of all the white things [Armstrong] |
| 4438 | 'Mereological Nominalism' may work for whiteness, but it doesn't seem to work for squareness [Armstrong] |
| 16957 | Possible worlds aren't how the world might be, but how a world might be, given some possibility [Dummett] |
| 16959 | If possible worlds have no structure (S5) they are equal, and it is hard to deny them reality [Dummett] |
| 16956 | To explain generosity in a person, you must understand a generous action [Dummett] |
| 16954 | Generalised talk of 'natural kinds' is unfortunate, as they vary too much [Dummett] |