15 ideas
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 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] |
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| 18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
| 16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
| 10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
| 10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
| 10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |