44 ideas
| 23853 | Truth is not a object we love - it is the radiant manifestation of reality [Weil] |
| 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] |
| 23855 | Creation produced a network or web of determinations [Weil] |
| 15201 | That Queen Anne is dead is a 'general fact', not a fact about Queen Anne [Prior,AN] |
| 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] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 23848 | The aesthete's treatment of beauty as amusement is sacreligious; beauty should nourish [Weil] |
| 23854 | Beauty is the proof of what is good [Weil] |
| 23837 | Respect is our only obligation, which can only be expressed through deeds, not words [Weil] |
| 23844 | The most important human need is to have multiple roots [Weil] |
| 23838 | The need for order stands above all others, and is understood via the other needs [Weil] |
| 23836 | Obligations only bind individuals, not collectives [Weil] |
| 23840 | A citizen should be able to understand the whole of society [Weil] |
| 23843 | Even the poorest should feel collective ownership, and participation in grand display [Weil] |
| 23846 | Culture is an instrument for creating an ongoing succession of teachers [Weil] |
| 23839 | A lifelong head of society should only be a symbol, not a ruler [Weil] |
| 23842 | Party politics in a democracy can't avoid an anti-democratic party [Weil] |
| 23847 | Socialism tends to make a proletariat of the whole population [Weil] |
| 23845 | The capitalists neglect the people and the nation, and even their own interests [Weil] |
| 23841 | By making money the sole human measure, inequality has become universal [Weil] |
| 23835 | People have duties, and only have rights because of the obligations of others to them [Weil] |
| 23852 | To punish people we must ourselves be innocent - but that undermines the desire to punish [Weil] |
| 23850 | The soldier-civilian distinction should be abolished; every citizen is committed to a war [Weil] |
| 23851 | Education is essentially motivation [Weil] |
| 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] |
| 22899 | 'Thank goodness that's over' is not like 'thank goodness that happened on Friday' [Prior,AN] |
| 23849 | Religion should quietly suffuse all human life with its light [Weil] |