more from Fraser MacBride

Single Idea 8926

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

Full Idea

The identification of mathematical objects with positions in structures rests upon the prior credibility of the thesis that positions are objects in their own right.

Gist of Idea

For mathematical objects to be positions, positions themselves must exist first


Fraser MacBride (Structuralism Reconsidered [2007], 3)

Book Reference

'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.585

A Reaction

Sounds devastating, but something has to get the whole thing off the ground. This is why Resnik's word 'patterns' is so appealing. Patterns stare you in the face, and they don't change if all the objects making it up are replaced by others.