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Single Idea 14465

[filed under theme 6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival ]

Full Idea

'Ten men' is grammatically the same form as 'white men', so that 10 might be thought to be an adjective qualifying 'men'.

Gist of Idea

Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men'

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVIII)

Book Ref

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.205

A Reaction

The immediate problem, as Frege spotted, is that such expressions can be rephrased to remove the adjective (by saying 'the number of men is ten').

The 14 ideas with the same theme [numbers as properties, rather than objects]:

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]