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Full Idea
'Jupiter has four moons' is semantically and syntactically on all fours with 'Jupiter has many moons'. But it would be brave to construe the latter proposition as a transformation of 'The number of Jupiter's moons is identical with the number many'.
Gist of Idea
'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many'
Source
comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Ian Rumfitt - Concepts and Counting p.49
Book Ref
-: 'Aristotelian Society' [], p.49
A Reaction
I take this to be an important insight. Number words are continuous with (are in the same category as) words for general numerical quantity, such as 'just a few' or 'many' or 'rather a lot'. Numbers are part of normal language.
Related Idea
Idea 8645 Convert "Jupiter has four moons" into "the number of Jupiter's moons is four" [Frege]
| 9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
| 9624 | Numbers are a very general property of objects [Mill, by Brown,JR] |
| 9951 | It appears that numbers are adjectives, but they don't apply to a single object [Frege, by George/Velleman] |
| 9952 | Numerical adjectives are of the same second-level type as the existential quantifier [Frege, by George/Velleman] |
| 11031 | 'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many' [Rumfitt on Frege] |
| 8637 | The number 'one' can't be a property, if any object can be viewed as one or not one [Frege] |
| 9999 | For science, we can translate adjectival numbers into noun form [Frege] |
| 14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
| 9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| 13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |