more from John P. Burgess

Single Idea 10187

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

Full Idea

Abstract algebra, such as group theory, is not concerned with the features common to all models of the axioms, but rather with the relationships among different models of those axioms (especially homomorphic relation functions).


'Homomorphisms' are mapping relations

Gist of Idea

Abstract algebra concerns relations between models, not common features of all the models


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

A Reaction

It doesn't seem to follow that structuralism can't be about the relations (or patterns) found when abstracting away and overviewing all the models. One can study family relations, or one can study kinship in general.