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Full Idea
Number is nothing but the actual numbered things themselves. Hence just as unity is not an accident added to the thing which is one, so number is not an accident of the things which are numbered.
Clarification
An 'accident' is the Aristotelian word for a property
Gist of Idea
Just as unity is not a property of a single thing, so numbers are not properties of many things
Source
William of Ockham (Summa totius logicae [1323], I.c.xliv)
Book Ref
Ockham,William of: 'Ockham's Philosophical Writings', ed/tr. Boehner,P [Hackett 1990], p.138
A Reaction
[William does not necessarily agree with this view] It strikes me as a key point here that any account of the numbers had better work for 'one', though 'zero' might be treated differently. Some people seem to think unity is a property of things.
| 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] |