Single Idea 9828

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique]

Full Idea

The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures.

Gist of Idea

Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1

Source

Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5)

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.53


A Reaction

This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory.