ABSTRACT
In the opinion of most commentators, either logicians or mathematicians, the importance and influence of Gödel's incompleteness results were nil. According to Kreisel [1988], Gödel's theorems have had absolutely no use, and properly so, since they were tailored to refute— or confirm, it does not matter—a specific thesis about the completeness of mathematical systems. Bourbaki [1960] dutifully recalled Gödel's two incompleteness theorems, but only in the historical notes of the section ‘Metamathematics’ and nowhere else in the treatise. The theorems were likewise seen as a negative answer to Hilbert's program. Bourbaki hinted at their proofs and the technique used, saying that it was based on a one-to-one correspondence between metamathematical sentences and certain propositions of formalized arithmetic.
