Single Idea 10223

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism]

Full Idea

There is no 'structure of all structures', just as there is no set of all sets.

Gist of Idea

There is no 'structure of all structures', just as there is no set of all sets

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 3.4)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.95


A Reaction

If one cannot abstract from all the structures to a higher level, why should Shapiro have abstracted from the systems/models to get the over-arching structures?