30 ideas
9271 | Human knowledge may not produce well-being; the examined life may not be worth living [Gray] |
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] |
8978 | Events are made of other things, and are not fundamental to ontology [Bennett] |
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] |
9275 | Knowledge does not need minds or nervous systems; it is found in all living things [Gray] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
9276 | The will hardly ever does anything; most of our life just happens to us [Gray] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
9278 | Nowadays we identify the free life with the good life [Gray] |
10364 | Facts are about the world, not in it, so they can't cause anything [Bennett] |
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] |
9280 | Over forty percent of the Earth's living tissue is human [Gray] |
9272 | Without Christianity we lose the idea that human history has a meaning [Gray] |
9279 | What was our original sin, and how could Christ's suffering redeem it? [Gray] |