35 ideas
23367 | Even pointing a finger should only be done for a reason [Epictetus] |
192 | Only one thing can be contrary to something [Plato] |
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] |
190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
20185 | The most important things in life are wisdom and knowledge [Plato] |
20184 | The only real evil is loss of knowledge [Plato] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
191 | Everything resembles everything else up to a point [Plato] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
203 | Courage is knowing what should or shouldn't be feared [Plato] |
202 | No one willingly and knowingly embraces evil [Plato] |
193 | Some things are good even though they are not beneficial to men [Plato] |
197 | Some pleasures are not good, and some pains are not evil [Plato] |
200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
188 | Socrates did not believe that virtue could be taught [Plato] |
204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
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] |