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According to this document, Kurt Gödel had discovered logical inconsistiencies in the U.S. constitution that could theoretically allow it to become a dictatorship. Morgenstern told him not to bring it up during his U.S. citizenship exam, but:

And then [the examiner] turned to Gödel and said, "Now Mr. Gödel, where do you come from?"

Gödel: "Where I come from? Austria."

The Examinor: "What kind of government did you have in Austria?"

Gödel: "It was a republic, but the constitution was such that it finally changed into a dictatorship."

The Examinor: "Oh! This is very bad. This could not happen in this country."

Gödel: "Oh, yes, I can prove it."

Luckily, the examiner changed the subject and Gödel could become a U.S. citizen.

What was his proof?

Rodrigo de Azevedo
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Christopher King
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    Try this https://www.quora.com/What-was-the-flaw-Kurt-Gödel-discovered-in-the-US-constitution-that-would-allow-conversion-to-a-dictatorship – Gerald Edgar Jun 27 '16 at 21:38
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    As Gerald Edgar has commented, the quora page gives full details. Interestingly, in true Gödel fashion, the argument he constructed was one of self-reference, involving the application of the terms of the articles to the articles themselves. Both Morgenstern and Einstein pleaded with Gödel not to bring it up at the ceremony, but their pleas fell on deaf ears apparently. Shrewdly, the judge cut him off before he could get into full stride. – nwr Jun 27 '16 at 22:59
  • @NickR I read that, and it said that the author's theory as to what Godel had discovered. – Christopher King Jun 27 '16 at 23:01
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    The version I have read is in Palle Yourgrau's biography of Gödel, though he doesn't spell out the argument in detail. Yourgrau sites no source for the story, but adds that Morgenstern and Einstein's concerns were well founded since the FBI had been intercepting Gödel's correspondences with his mother for years. Yourgrau also states that years later, when asked for a legal analogy to his incompleteness theorem, Gödel restated his argument concerning the constitution - but again no source is given. – nwr Jun 27 '16 at 23:08
  • @NickR Some of that sounds unlikely. I'm guessing that the loophole Godel found was highly theoretical in nature, not something that would get him arrested (although his ontological proof was quite good, so I could be mistaken). I doubt that the FBI would be concerned. Also, self-reference with regards to Article V probably isn't a huge deal. (Something else in the above source said a possibility is that Godel had identified a weakness in the checks and balances: the fact that nine men where the absolute authority on what the constitution said.) – Christopher King Jun 27 '16 at 23:44
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    Already discussed in this post. – Mauro ALLEGRANZA Jun 28 '16 at 07:45

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I think this is an apocryphal story because it makes a good story. The exact 'loophole' is not known. However, according to Wikipedia, one academic suggests that it is article V on amending the Constitution in a downward spiral and thus allowing a fascist takeover.

I think it apocryphal as Goedel was naturalised as an American citizen in 1948 and only seven years later the US embarked upon the disastrous Vietnam war which destroyed its reputation after the goodwill it enjoyed for helping end WWII and where Bertrand Russell made direct accusations in the New York Times that how the US treated the Vietnamese distinguished them not at all from Nazi Germany. This is worse than fascism. Russell was of course a logician but coming from a family with a tradition of public service he understood quite well - in a way that fascism and the doorway to fascism - isn't merely to be found in arcane rules in a constitution but has many different sources for example, within politics and the evil in mens heart.

Mozibur Ullah
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