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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).
Clarification
'Homomorphisms' are mapping relations
Gist of Idea
Abstract algebra concerns relations between models, not common features of all the models
Source
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.
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |