Wed, 12 Sep 2007
The loophole in the U.S. Constitution: the answer
Apparently, the "inconsistency" noted by Gödel is simply that the Constitution provides for its own amendment. Suber says: "He noticed that the AC had procedural limitations but no substantive limitations; hence it could be used to overturn the democratic institutions described in the rest of the constitution." I am gravely disappointed. I had been hoping for something brilliant and subtle that only Gödel would have noticed.
Thanks to Greg Padgett, Julian Orbach, Simon Cozens, and Neil Kandalgaonkar for bringing this to my attention.
M. Padgett also pointed out that the scheme I proposed for amending the constitution, which I claimed would require only the cooperation of a majority of both houses of Congress, 218 + 51 = 269 people in all, would actually require a filibuster-proof majority in the Senate. He says that to be safe you would want all 100 senators to conspire; I'm not sure why 60 would not be sufficient. (Under current Senate rules, 60 senators can halt a filibuster.) This would bring the total required to 218 + 60 = 278 conspirators.
He also pointed out that the complaisance of five Supreme Court justices would give the President essentially dictatorial powers, since any legal challenge to Presidential authority could be rejected by the court. But this train of thought seems to have led both of us down the same path, ending in the idea that this situation is not really within the scope of the original question.
As a final note, I will point out what I think is a much more serious loophole in the Constitution: if the Vice President is impeached and tried by the Senate, then, as President of the Senate, he presides over his own trial. Article I, section 3 contains an exception for the trial of the President, where the Chief Justice presides instead. But the framers inexplicably forgot to extend this exception to the trial of the Vice President.
[ Addendum 20090121: Jeffrey Kegler has discovered Oskar Morgenstern's lost eyewitness account of Gödel's citizenship hearing. Read about it here. ]
[ Addendum 20110525: As far as I know, there is no particular reason to believe that Peter Suber's theory is correct. Morgenstern knew, but did not include it in his account. ]