more from Michael Dummett

Single Idea 9192

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

Full Idea

The number 4 cannot be characterized solely by its position in a system, because it has different positions in the system of natural numbers and that of the positive whole numbers, whereas these systems have the very same structure.

Gist of Idea

The number 4 has different positions in the naturals and the wholes, with the same structure


Michael Dummett (The Philosophy of Mathematics [1998], 6.1)

Book Reference

'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.162

A Reaction

Dummett seems to think this is fairly decisive against structuralism. There is also the structure of the real numbers. We will solve this by saying that the wholes are abstracted from the naturals, which are abstracted from the reals. Job done.