13 ideas
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
| 15645 | Nominal essence are the observable properties of things [Eagle] |
| 15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
| 7876 | Even if we identify pain with neural events, we can't explain why those neurons cause that feeling [Levine, by Papineau] |
| 7877 | Only phenomenal states have an explanatory gap; water is fully explained by H2O [Levine, by Papineau] |
| 7878 | Materialism won't explain phenomenal properties, because the latter aren't seen in causal roles [Papineau on Levine] |
| 15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |