more from this thinker
|
more from this text
Single Idea 17829
[filed under theme 6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
]
Full Idea
Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on.
Gist of Idea
Number words are unusual as adjectives; we don't say 'is five', and numbers always come first
Source
Penelope Maddy (Sets and Numbers [1981], IV)
Book Ref
'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.350
A Reaction
[She is citing Benacerraf's arguments]
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]
|