56 ideas
| 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] |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| 18216 | Abstractions can form useful counterparts to concrete statements [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] |
| 15435 | If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis] |
| 15451 | I assume there could be natural properties that are not instantiated in our world [Lewis] |
| 8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
| 15433 | Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis] |
| 15436 | Universals are meant to give an account of resemblance [Lewis] |
| 15438 | We can add a primitive natural/unnatural distinction to class nominalism [Lewis] |
| 18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
| 11897 | A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P] |
| 11898 | Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P] |
| 11883 | A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P] |
| 15448 | The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis] |
| 15449 | If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis] |
| 15439 | The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis] |
| 15441 | The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis] |
| 15445 | Butane and Isobutane have the same atoms, but different structures [Lewis] |
| 15434 | Structural universals have a necessary connection to the universals forming its parts [Lewis] |
| 15437 | We can't get rid of structural universals if there are no simple universals [Lewis] |
| 15446 | Composition is not just making new things from old; there are too many counterexamples [Lewis] |
| 15440 | A whole is distinct from its parts, but is not a further addition in ontology [Lewis] |
| 15444 | Different things (a toy house and toy car) can be made of the same parts at different times [Lewis] |
| 11889 | Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P] |
| 11877 | An individual essence is the properties the object could not exist without [Mackie,P] |
| 11882 | No other object can possibly have the same individual essence as some object [Mackie,P] |
| 11886 | There are problems both with individual essences and without them [Mackie,P] |
| 11909 | Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P] |
| 11899 | Why are any sortals essential, and why are only some of them essential? [Mackie,P] |
| 11906 | The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P] |
| 11894 | Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P] |
| 11887 | Transworld identity without individual essences leads to 'bare identities' [Mackie,P] |
| 11890 | De re modality without bare identities or individual essence needs counterparts [Mackie,P] |
| 11892 | Things may only be counterparts under some particular relation [Mackie,P] |
| 11893 | Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P] |
| 11884 | The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 11905 | Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P] |
| 15450 | Maybe abstraction is just mereological subtraction [Lewis] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 15443 | Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis] |
| 11907 | Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P] |
| 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] |