I found that people citing Gödel almost invariably think that he has proven the epistemological impotence of mathematics, in their hearts even freeing them from the stifling dictates of logic and probability. (Instead, Gödel has disproven one of the ways of defining truth.)
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To qualify, metamathematics is the domain of all languages built upon first order Aristotlean logic. But it does not encompass all languages, nor all logic based systems. I was in touch with Grahm Priest about Gödel under paraconsistent logics; he was unaware of any proof.
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