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6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival

[numbers as properties, rather than objects]

14 ideas
Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham]
Numbers are a very general property of objects [Mill, by Brown,JR]
It appears that numbers are adjectives, but they don't apply to a single object [Frege, by George/Velleman]
Numerical adjectives are of the same second-level type as the existential quantifier [Frege, by George/Velleman]
'Jupiter has many moons' won't read as 'The number of Jupiter's moons equals the number many' [Rumfitt on Frege]
The number 'one' can't be a property, if any object can be viewed as one or not one [Frege]
For science, we can translate adjectival numbers into noun form [Frege]
Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell]
Number words are not predicates, as they function very differently from adjectives [Benacerraf]
Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock]
Treating numbers adjectivally is treating them as quantifiers [Wright,C]
Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy]
Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber]