Single Idea 9954

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

We can view "the number of x's such that ...x..." as a functional expression that is completed by a first-level predicate and yields a name (which is of the right kind to denote an object).

Gist of Idea

"Number of x's such that ..x.." is a functional expression, yielding a name when completed

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.27


A Reaction

This is how Frege gets, in his account, from numbers being predicates to numbers being objects. He was a clever lad.