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Full Idea
It is surprising that just by adding to Peano Arithmetic principles concerning the notion of truth, we increase the mathematical strength of PA. So, contrary to expectations, the 'philosophical' notion of truth has real mathematical content.
Gist of Idea
By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content!
Source
Leon Horsten (The Tarskian Turn [2011], 06.4)
Book Ref
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.77
A Reaction
Horsten invites us to be really boggled by this. All of this is in the Compositional Theory TC. It enables a proof of the consistency of arithmetic (but still won't escape Gödel's Second).