11 ideas
17824 | The master science is physical objects divided into sets [Maddy] |
15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
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] |
15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
12710 | As well as extension, bodies contain powers [Leibniz] |