What I mean is that since Goodstein's theorem is provably true for the naturals, but is not a consequence of the Peano axioms, then the definition of the naturals used to demonstrate Goodstein's must be strictly stronger than the Peano axioms themselves. I was wondering what this definition might be.
I'm familiar with the distinction between formalism and Platonism, although I still haven't made my mind up yet :)
I'm familiar with the distinction between formalism and Platonism, although I still haven't made my mind up yet :)