34 ideas
| 19740 | A very hungry man cannot choose between equidistant piles of food [Aristotle] |
| 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] |
| 8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
| 18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
| 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] |
| 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] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 398 | Each thing that has a function is for the sake of that function [Aristotle] |
| 394 | An unworn sandal is in vain, but nothing in nature is in vain [Aristotle] |
| 396 | There has to be some goal, and not just movement to infinity [Aristotle] |
| 16102 | Aether moves in circles and is imperishable; the four elements perish, and move in straight lines [Aristotle, by Gill,ML] |
| 17463 | An element is what bodies are analysed into, and won't itself divide into something else [Aristotle] |
| 399 | If the more you raise some earth the faster it moves, why does the whole earth not move? [Aristotle] |
| 18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
| 20918 | Void is a kind of place, so it can't explain place [Aristotle] |
| 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] |
| 402 | The Earth must be spherical, because it casts a convex shadow on the moon [Aristotle] |
| 403 | The earth must be round and of limited size, because moving north or south makes different stars visible [Aristotle] |
| 1498 | Everyone agrees that the world had a beginning, but thinkers disagree over whether it will end [Aristotle] |
| 395 | It seems possible that there exists a limited number of other worlds apart from this one [Aristotle] |
| 20713 | God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B] |