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Full Idea
Considered in isolation, the axioms of group theory are not assertions but comprise an implicit definition of some abstract structure,
Gist of Idea
The axioms of group theory are not assertions, but a definition of a structure
Source
Øystein Linnebo (Philosophy of Mathematics [2017], 3.5)
Book Ref
Linnebo,Øystein: 'Philosophy of Mathematics' [Princeton 2017], p.52
A Reaction
The traditional Euclidean approach is that axioms are plausible assertions with which to start. The present idea sums up the modern approach. In the modern version you can work backwards from a structure to a set of axioms.