Single Idea 9949

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

Full Idea

For Frege, the extension of the concept F is an object, as revealed by the fact that we use a name to refer to it. ..We must distinguish the concept, the object that falls under it, and the extension of the concept, which is the set containing the object.

Gist of Idea

There is the concept, the object falling under it, and the extension (a set, which is also an object)


report of Gottlob Frege (On Concept and Object [1892]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.21

A Reaction

This I take to be the key distinction needed if one is to grasp Frege's account of what a number is. When we say that Frege is a platonist about numbers, it is because he is committed to the notion that the extension is an object.