[FOM] Formalization Thesis

[Kaveh Ghasemloo]

Dear Tim,
I'm having problems understanding what you meant by "ordinary
mathematics" and "faithfully expressed".
If I've understoond your examples correctly, specially the Con(PA)
one, I feel that Godel's Incompleteness answers your question
negatively, since for any reasonable theory (not just ZFC) there are
theorems of ordinary mathematics which can not be proved inside that
theory. I guess most will agree that existence/nonexistence of
solutions for Diophantine equations are ordinary mathematics.

Yours
Kaveh Ghasemloo