16 ideas
| 3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
| 3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
| 22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 18439 | Because things can share attributes, we cannot individuate attributes clearly [Quine] |
| 18442 | You only know an attribute if you know what things have it [Quine] |
| 18441 | No entity without identity (which requires a principle of individuation) [Quine] |
| 18440 | Identity of physical objects is just being coextensive [Quine] |