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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]
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9624
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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]
|