In summary, Gödel’s loophole is that the amendment procedures set forth in Article V apply to the constitutional statements in Article V themselves. In addition, not only may Article V itself be amended, but also it may be amended in an upward or downward direction. Lastly, the Gödelian problem of self-amendment or antientrenchment is unsolvable.
This is taken from a review (8-guerra-pujol-1) of the alleged logical flaw found by logician Kurt Godel in his study of the US constitution. So , the argument runs, one first amends Article V to allow, say, simple majority or even a uncontested change by the President. Then one can amend away. Godel, it is argued, discovered this and was only with some difficulty dissuaded by Oscar Morganstern and Albert Einstein, his sponsors, at expounding at length on it at his citizenship hearing. There is a good discussion here, and here also.
For those not familiar with the US constitution Article V states
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress; Provided that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article; and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
So to amend the US constitution right now requires a triple lock : a 2/3 vote by each house of congress and a 3/4 vote by states.
Hmm… 3/4 of 50 is 37. Republicans control 32 and 5 are divided. Thats 37. The house of representatives and the senate are, in essence 51-49 Republican. But dont forget, its those that turn up to vote that make the 2/3 not those eligible to vote.
Do I think Trump will do this? No. There are, I am sure, enough deeply constitutional republicans in both state legislatures and the congress to be aghast at the prospect. Trump seems more interested in the trappings of power and its potential to enrich family and discomfit enemies than in becoming King Donald I. But, one has to wonder. We live in strange times.