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Single Idea 13873

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

Full Idea

Treating numbers adjectivally is, in effect, treating the numbers as quantifiers. Frege observes that we can always parse out any apparently adjectival use of a number word in terms of substantival use.

Gist of Idea

Treating numbers adjectivally is treating them as quantifiers

Source

Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iii)

Book Ref

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.10

A Reaction

The immediate response to this is that any substantival use can equally be expressed adjectivally. If you say 'the number of moons of Jupiter is four', I can reply 'oh, you mean Jupiter has four moons'.

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]