19 ideas
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
| 10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
| 9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
| 10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
| 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] |
| 10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
| 10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
| 10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
| 10004 | Our minds are at their best when reasoning about objects [Hofweber] |
| 16764 | The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus] |