more from Michael Dummett

### Single Idea 9829

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

Full Idea

The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them.

Gist of Idea

The identity of a number may be fixed by something outside structure - by counting

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 strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that.