14 ideas
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] |
12742 | A whole is just its parts, but there are no smallest parts, so only minds and perceptions exist [Leibniz] |
9261 | The 'Ethics' is disappointing, because it fails to try to justify our duties [Prichard] |
9262 | The mistake is to think we can prove what can only be seen directly in moral thinking [Prichard] |
9260 | Virtues won't generate an obligation, so it isn't a basis for morality [Prichard] |
9259 | We feel obligations to overcome our own failings, and these are not relations to other people [Prichard] |
9258 | If pain were instrinsically wrong, it would be immoral to inflict it on ourselves [Prichard] |