15 ideas
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 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] |
| 12608 | Concepts are distinguished by roles in judgement, and are thus tied to rationality [Peacocke] |
| 12605 | A sense is individuated by the conditions for reference [Peacocke] |
| 12607 | Fregean concepts have their essence fixed by reference-conditions [Peacocke] |
| 12609 | Concepts have distinctive reasons and norms [Peacocke] |
| 12604 | Any explanation of a concept must involve reference and truth [Peacocke] |
| 12610 | Encountering novel sentences shows conclusively that meaning must be compositional [Peacocke] |