Full Idea
Gödel showed PA cannot be proved consistent from with PA. But 'reflection principles' can be added, which are axioms partially expressing the soundness of PA, by asserting what is provable. A Global Reflection Principle asserts full soundness.
Gist of Idea
If soundness can't be proved internally, 'reflection principles' can be added to assert soundness
Source
report of Kurt Gödel (On Formally Undecidable Propositions [1931]) by Halbach,V/Leigh,G.E. - Axiomatic Theories of Truth (2013 ver) 1.2
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.3
A Reaction
The authors point out that this needs a truth predicate within the language, so disquotational truth won't do, and there is a motivation for an axiomatic theory of truth.
Related Idea
Idea 19124 A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]