We are also free to point out the obvious nonsense that is extrapolating the axioms of arithmetic, on which the theorem depends, to whatever we want them to.
Philosophical insights can start from all kinds of empirical facts and theoretical proofs -- this includes a mathematical theorem like Godel's.
Philosophers don't (or don't all) use Godel's theorem to _prove_ something beyond that in an axiomatic way. They don't extrapolate, they use it as a raw information / material for further thinking.
In that role, the limited conditions under which the proof is true doesn't really matter. Only the fact that under such limited conditions, this (Godel's) result can occur matters -- which is philosophical far from evident, Hilbert/Russel etc thought they could axiomatize math without such contradictions.
