Well, the only thing that Godel showed was that if you have consistent assignment of a truth value to every well-formed statement in a given logic language (at least as complex the Peano postulates), you will get some statements which are assigned "true" or "false" but whose truth cannot be deduced in a given axiom system for the language. However, the above statement very much involves a statement about "truth" in much transcendent sense - see the discussion of Godel's Platonism and religious beliefs in the article.