Single Idea 18116

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

Full Idea

There is no ground for saying that a number IS a position, if the truth is that there is nothing to determine which number is which position.

Gist of Idea

Numbers can't be positions, if nothing decides what position a given number has

Source

David Bostock (Philosophy of Mathematics [2009], 6.4)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.190


A Reaction

If numbers lose touch with the empirical ability to count physical objects, they drift off into a mad world where they crumble away.