12 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] |
21982 | I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L] |
14365 | Scientific understanding is always the grasping of a correct explanation [Strevens] |
14368 | We may 'understand that' the cat is on the mat, but not at all 'understand why' it is there [Strevens] |
14369 | Understanding is a precondition, comes in degrees, is active, and holistic - unlike explanation [Strevens] |