17 ideas
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
| 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] |
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
| 21275 | Unlike a stone, the parts of a watch are obviously assembled in order to show the time [Paley] |
| 21276 | From the obvious purpose and structure of a watch we must infer that it was designed [Paley] |
| 21277 | Even an imperfect machine can exhibit obvious design [Paley] |
| 21278 | All the signs of design found in a watch are also found in nature [Paley] |
| 21357 | No organ shows purpose more obviously than the eyelid [Paley] |