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Single Idea 9903

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

Full Idea

The unpredicative nature of number words can be seen by noting how different they are from, say, ordinary adjectives, which do function as predicates.

Gist of Idea

Number words are not predicates, as they function very differently from adjectives

Source

Paul Benacerraf (What Numbers Could Not Be [1965], II)

Book Ref

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.283

A Reaction

He points out that 'x is seventeen' is a rare construction in English, unlike 'x is happy/green/interesting', and that numbers outrank all other adjectives (having to appear first in any string of them).

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]