61 ideas
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
| 10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
| 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] |
| 8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
| 18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
| 10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
| 18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
| 9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| 18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
| 18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
| 8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
| 18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
| 4266 | Having beliefs involves recognition, expectation and surprise [Scruton] |
| 4265 | If an animal has beliefs, that implies not only that it can make mistakes, but that it can learn from them [Scruton] |
| 4264 | Perception (which involves an assessment) is a higher state than sensation [Scruton] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 4271 | There is consciousness whenever behaviour must be explained in terms of mental activity [Scruton] |
| 4272 | Our concept of a person is derived from Roman law [Scruton] |
| 4267 | Conditioning may change behaviour without changing the mind [Scruton] |
| 4269 | An emotion is a motive which is also a feeling [Scruton] |
| 4270 | Do we use reason to distinguish people from animals, or use that difference to define reason? [Scruton] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 4284 | All moral life depends ultimately on piety, which is our recognition of our own dependence [Scruton] |
| 4273 | Kant's Moral Law is the rules rational beings would accept when trying to live by agreement [Scruton] |
| 4274 | The modern virtues are courage, prudence, wisdom, temperance, justice, charity and loyalty [Scruton] |
| 4286 | Only just people will drop their own self-interests when faced with an impartial verdict [Scruton] |
| 4283 | Sympathy can undermine the moral order just as much as crime does [Scruton] |
| 4290 | That which can only be done by a callous person, ought not to be done [Scruton] |
| 4285 | As soon as we drop self-interest and judge impartially, we find ourselves agreeing about conflicts [Scruton] |
| 4287 | Utilitarianism merely guides us (by means of sympathy) when the moral law is silent [Scruton] |
| 4282 | Morality is not a sort of calculation, it is what sets the limits to when calculation is appropriate [Scruton] |
| 4281 | Utilitarianism says we can't blame Stalin yet, but such a theory is a sick joke [Scruton] |
| 4280 | Utilitarianism is wrong precisely because it can't distinguish animals from people [Scruton] |
| 4296 | Brutal animal sports are banned because they harm the personality of the watcher [Scruton] |
| 4288 | Many breeds of animals have needs which our own ancestors planted in them [Scruton] |
| 4293 | Introducing a natural means of controlling animal population may not be very compassionate [Scruton] |
| 4295 | We favour our own animals over foreign ones because we see them as fellow citizens [Scruton] |
| 4268 | Animals command our sympathy and moral concern initially because of their intentionality [Scruton] |
| 4291 | Letting your dog kill wild rats, and keeping rats for your dog to kill, are very different [Scruton] |
| 4263 | Many of the stranger forms of life (e.g. worms) interest us only as a species, not as individuals [Scruton] |
| 4276 | An animal has individuality if it is nameable, and advanced animals can respond to their name [Scruton] |
| 4277 | I may avoid stepping on a spider or flower, but fellow-feeling makes me protect a rabbit [Scruton] |
| 4278 | Lucky animals are eaten by large predators, the less lucky starve, and worst is death by small predators [Scruton] |
| 4279 | We can easily remove the risk of suffering from an animal's life, but we shouldn't do it [Scruton] |
| 4289 | Sheep and cattle live comfortable lives, and die an enviably easy death [Scruton] |
| 4292 | Concern for one animal may harm the species, if the individual is part of a bigger problem [Scruton] |
| 4294 | Animals are outside the community of rights, but we still have duties towards them [Scruton] |
| 18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
| 18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
| 18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |