11 ideas
17824 | The master science is physical objects divided into sets [Maddy] |
14181 | Validity is where either the situation or the interpretation blocks true premises and false conclusion [Etchemendy, by Read] |
14180 | Etchemendy says fix the situation and vary the interpretation, or fix interpretations with varying situations [Etchemendy, by Read] |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
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] |