35 ideas
| 11103 | We aren't stuck with our native conceptual scheme; we can gradually change it [Quine] |
| 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] |
| 11092 | A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine] |
| 11093 | We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine] |
| 11101 | General terms don't commit us ontologically, but singular terms with substitution do [Quine] |
| 18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
| 11096 | Discourse generally departmentalizes itself to some degree [Quine] |
| 8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
| 11099 | Understanding 'is square' is knowing when to apply it, not knowing some object [Quine] |
| 11094 | 'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine] |
| 11097 | Red is the largest red thing in the universe [Quine] |
| 18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
| 17595 | To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine] |
| 11095 | We should just identify any items which are indiscernible within a given discourse [Quine] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 11104 | Concepts are language [Quine] |
| 11102 | Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 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] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 6610 | I believe because it is absurd [Tertullian] |