Full Idea
A theory is 'non-conservative' if it allows us to prove mathematical facts that go beyond what the background mathematical theory can prove on its own.
Gist of Idea
A theory is 'non-conservative' if it facilitates new mathematical proofs
Source
Leon Horsten (The Tarskian Turn [2011], 01.4)
Book Reference
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.7
A Reaction
This is an instance of the relationship with mathematics being used as the test case for explorations of logic. It is a standard research method, because it is so precise, but should not be mistaken for the last word about a theory.