Single Idea 23443

[catalogued under 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation]

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 Reference

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.