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Full Idea
The semantic value of a determiner (an adjective) is a function from semantic values to nouns to semantic values of full noun phrases.
Gist of Idea
An adjective contributes semantically to a noun phrase
Source
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §3.1)
Book Ref
-: 'Philosophical Review 114' [Phil Review 2005], p.187
A Reaction
This kind of states the obvious (assuming one has a compositional view of sentences), but his point is that you can't just eliminate adjectival uses of numbers by analysing them away, as if they didn't do anything.
| 9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
| 10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
| 10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
| 10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
| 10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
| 10004 | Our minds are at their best when reasoning about objects [Hofweber] |
| 10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
| 10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
| 10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
| 10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |