39 ideas
| 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] |
| 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] |
| 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] |
| 20184 | The only real evil is loss of knowledge [Plato] |
| 20185 | The most important things in life are wisdom and 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] |
| 22098 | Socrates neglects the gap between knowing what is good and doing good [Kierkegaard, by Carlisle] |
| 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] |
| 200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
| 197 | Some pleasures are not good, and some pains are not evil [Plato] |
| 204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
| 188 | Socrates did not believe that virtue could be taught [Plato] |
| 189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
| 22096 | Anxiety is not a passing mood, but a response to human freedom [Kierkegaard, by Carlisle] |
| 22097 | The ultimate in life is learning to be anxious in the right way [Kierkegaard] |
| 21909 | Ultimate knowledge is being anxious in the right way [Kierkegaard] |
| 20758 | Anxiety is staring into the yawning abyss of freedom [Kierkegaard] |
| 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] |