12 ideas
2945 | Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer] |
9184 | We can't presume that all interesting concepts can be analysed [Williamson] |
2946 | You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer] |
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] |
9183 | Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson] |
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] |