Single Idea 10029

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

Full Idea

The fact that numbers are objects guarantees the availability of a supply of n+1 objects, which can be used to define the concept F for the successor of n, by defining the objects which fall under F.

Gist of Idea

Numbers need to be objects, to define the extension of the concept of each successor to n

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.33


A Reaction

[compressed] This is the key step which takes from from numbers being adjectival to numbers being objectual. One wonders whether physical objects might do the necessary job at the next level down. Numbers need countables.