11 ideas
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |