37 ideas
| 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] |
| 10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
| 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] |
| 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] |
| 22673 | Wherever there is a small community, the association of the people is natural [Tocqueville] |
| 22676 | The people are just individuals, and only present themselves as united to foreigners [Tocqueville] |
| 22679 | Vast empires are bad for well-being and freedom, though they may promote glory [Tocqueville] |
| 22680 | People would be much happier and freer in small nations [Tocqueville] |
| 22675 | In American judges rule according to the Constitution, not the law [Tocqueville] |
| 22677 | A monarchical family is always deeply concerned with the interests of the state [Tocqueville] |
| 22683 | Despots like to see their own regulations ignored, by themselves and their agents [Tocqueville] |
| 22669 | Aristocracy is constituted by inherited landed property [Tocqueville] |
| 22674 | In Europe it is thought that local government is best handled centrally [Tocqueville] |
| 22678 | An election, and its lead up time, are always a national crisis [Tocqueville] |
| 22682 | Universal suffrage is no guarantee of wise choices [Tocqueville] |
| 22670 | Slavery undermines the morals and energy of a society [Tocqueville] |
| 22681 | The liberty of the press is more valuable for what it prevents than what it promotes [Tocqueville] |
| 22672 | It is admirable to elevate the humble to the level of the great, but the opposite is depraved [Tocqueville] |
| 22671 | Equality can only be established by equal rights for all (or no rights for anyone) [Tocqueville] |
| 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] |