Gödel's first incompleteness theorem states that any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory (Kleene 1967, p. 250) per http://en.wikipedia.org/wiki/Gödels_incompleteness_theorems

Just because you title something an "Unanswerable question" doesn't mean it actually is, and certainly doesn't mean the first incompleteness theorem is relevant.

Godel's Incompleteness Theorems are probably some of--if not the most---misunderstood concepts in all of mathematics (rivaling Cantor's Uncountability Theorem).

While the usual analogy for the first theorem is drawn to the liar's paradox ("This is a false statement."), it's important to remember that it is only an analogy. The first theorem states, in layman's terms, that we can construct a valid mathematical statement which is complete and utter nonsense. (Much like "This is a false statement." is neither true nor false, but nonsensical.)

The second incompleteness theorem simply states (again, in layman's terms) that the consistency (where we say something is consistent if it contains no contradictions) of certain systems cannot be shown from the rules of the system itself. (Or alternatively and more correctly, if you're able to show the consistency of these systems using their own rules, then they're inconsistent.)

That said, please remember that these are mathematical theorems and as such their "applications" to other areas such as metaphysics, even by their creator, are not rigorous or necessarily meaningful. They live where they belong: in the depths of mathematical logic, in the heart of mathematics.