Full Idea
One cannot just accept that all the theorems of Peano arithmetic are true when one accepts Peano arithmetic as the notion of truth is not available in the language of arithmetic.
Gist of Idea
You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 22.1)
Book Reference
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.322
A Reaction
This is given as the reason why Kreisel and Levy (1968) introduced 'reflection principles', which allow you to assert whatever has been proved (with no mention of truth). (I think. The waters are closing over my head).
Related Idea
Idea 16343 The global reflection principle seems to express the soundness of Peano Arithmetic [Halbach]