more from John P. Burgess

Single Idea 10186

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

Full Idea

It is to set theory that one turns for the very definition of 'structure', ...and this creates a problem of circularity if we try to impose a structuralist interpretation on set theory.

Gist of Idea

If set theory is used to define 'structure', we can't define set theory structurally

Source

John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], 1)


A Reaction

This seems like a nice difficulty, especially if, like Shapiro, you wade in and try to give a formal account of structures and patterns. Resnik is more circumspect and vague.