more from Bertrand Russell

Single Idea 14120

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure]

Full Idea

The process of counting gives us no indication as to what the numbers are, as to why they form a series, or as to how it is to be proved that there are n numbers from 1 to n. Hence counting is irrelevant to the foundations of arithmetic.

Gist of Idea

Counting explains none of the real problems about the foundations of arithmetic

Source

Bertrand Russell (The Principles of Mathematics [1903], §129)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.133


A Reaction

I take it to be the first truth in the philosophy of mathematics that if there is a system of numbers which won't do the job of counting, then that system is irrelevant. Counting always comes first.