### Single Idea 9998

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers]

Full Idea

There are three different uses of the number words: the singular-term use (as in 'the number of moons of Jupiter is four'), the adjectival (or determiner) use (as in 'Jupiter has four moons'), and the symbolic use (as in '4'). How are they related?

Gist of Idea

What is the relation of number words as singular-terms, adjectives/determiners, and symbols?

Source

Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1)

Book Reference

-: 'Philosophical Review 114' [Phil Review 2005], p.180

A Reaction

A classic philosophy of language approach to the problem - try to give the truth-conditions for all three types. The main problem is that the first one implies that numbers are objects, whereas the others do not. Why did Frege give priority to the first?