&quot;Gödel incompleteness is even unpopular among logicians. They are ambivalent. On the one hand, Gödel is the most famous logician ever. But, on the other hand, the incompleteness theorem says that logic is a failure.&quot;<p>I suspect Gödel himself didn&#x27;t like the incompleteness for similar being very much an idealist who even created (but didn&#x27;t) publish a modal-logic proof of the existence of God.<p>The thing is that if one takes a formalist position, that mathematics is a game played by pencil and paper (or computers) then the completeness and incompleteness theorems mean that foundational questions are simply done. oppositely, the position that foundations-people now have to take is that even though you create a universe compatible with any true-but-unprovable position (like the continuum hypothesis or its negation), some of these true-but-unprovable hypotheses are more plausible, aesthetically appealing or something and these hypotheses should be the one considered &quot;true&quot; in some ideal reality (I&#x27;m trying to crudely paraphrase Raymund Smullyan here).