more from Gottlob Frege

### Single Idea 9952

#### [catalogued under 6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival]

Full Idea

A numerical adjective forms part of a predicate of second-level, needing supplementation from the first level (F). So the second-level predicate is of the same type as the existential quantifier, and can be called a 'numerical quantifier'.

Gist of Idea

Numerical adjectives are of the same second-level type as the existential quantifier

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.24

A Reaction

This seems like a highly plausible account of how numbers work in language, but it leaves you wondering what the ontological status of a quantifier is. I presume platonic heaven is not full of elite entities called quantifiers, marshalling the others.