more on this theme | more from this thinker
Full Idea
The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements.
Gist of Idea
The master science is physical objects divided into sets
Source
Penelope Maddy (Sets and Numbers [1981], II)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.347
A Reaction
This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects.
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 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] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |