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Kurt Gdels Loophole and Donald Trumps Defiance

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In Journey to the Edge of Reason, Stephen Budiansky, a wonderfully captivating new biography of Austrian-born logician Kurt Gdel, highlights a famous story. Gdel is legendary for having published, in 1931, at the age of twenty-four, the most important logical proof of the last century, the theorems of incompleteness. Gdel has shown well that any non-mathematician who claims to understand this in a more than rudimentary way is not honest that you cannot axiomatize arithmetic or geometry, and that any system containing arithmetic will have arguments which cannot be neither proven nor refuted. The foundations of even seemingly secure systems, like mathematics, are subject to recursive paradoxes, and may always end up referring to themselves, such as an illustration by Escher or the words of Monster Mash.

Kurt Gdel never defined the constitutional loophole he found, but he was far too exacting a logician not to have spotted something. Photograph by Alfred Eisenstaedt / The LIFE Picture Collection / Shutterstock

Gdel was a remarkable character, who sadly fell into mental illness as he grew older, although his illness was always taken in the context of his fiercely logical mind. One piece of evidence, for example, of what was called his paranoia was that he had insisted with his psychiatrists that the Institute for Advanced Study, in Princeton, where he had taken a position in 1940, after the Nazi Anschluss, should fire him. , since nothing had been done of equal value to the work he had done when he was twenty-five. This illusion was, in fact, perfectly true and intensely seen that he hadn’t achieved anything equivalent, but then no one could. An institute benefits from the presence of the most famous logician of its time, even a brilliant presence. (The same was true of Albert Einstein, who was at IAS as much to be Einstein as to do physics.)

The story goes that Gdel, as he was preparing for an American citizenship test in the 1940s, imagined, in Viennese best form, that it would be a real test, not the pro forma exam it was. . He fiercely studied local laws, trying to find out why a township in New Jersey is different from a borough, and sank into the Constitution, which he studied as if it were Principia Mathematica. And he emerged confident that he had found a logical contradiction in the Constitution that could overthrow democratic government itself. He shared this discovery with Einstein, as well as with Oskar Morgenstern, co-founder of game theory and mutual friend; the two men begged him not to make it a problem during the test. But, during the ceremony, the judge asked Gdel where he was from, and he explained that he was from Austria, which was once a democracy but was now a dictatorship. Isn’t it good that such a thing can’t happen here, replied the judge. But it is possible! Gdel declared. I can prove it!

The Gdels fault, as some have called it, remains a mystery. He never defined it, and no trace of his discovery seems to linger in his papers. But he was far too precise a reader, and far too exacting a logician, not to have spotted something. Indeed, the Gdels flaw issue has inspired a remarkably large speculative literature, in serious scholarly journals as well as among academics of this magazine, and recently among academics writing online. what was that? Probably not a loophole whereby a vice president can simply refuse to recognize a voters list, during the Electoral College vote count, and substitute the one of his choice, thus keeping his boss in power. This, presumably, was a bridge too far, even for a logician. Dartmouths Dan Rockmore suggests that this could possibly involve the contradictions of gerrymandering, which is constitutional but goes against democracy, or the electoral college that empowers minorities. Another Gdel biographer, Jim Holt, turns to emeritus Harvard Law Schools professor emeritus Laurence Tribe, suggesting that what Gdel had in mind was Article V of the Constitution, as it sets no limits on how the Constitution can be changed. Holt continues,

The United States could be turned into a constitutional dictatorship through a series of amendments. But it’s more interesting than that. Article 5 makes the document self-referential: it refers to this Constitution. He says, in fact, that I can be amended by such and such a procedure. And he seems to leave open the possibility that Article 5 itself is subject to change. This would allow a very direct path to dictatorship: to amend it so that any diktat of the President is automatically an amendment.

And that would, of course, be a perfectly Gdelian recursive arrangement, with a sinister twist.

But, come to think of it, there is a glut of possible loopholes in the Constitution. The president is the commander in chief of the armed forces, without constraint of name; its power to act in this area is largely undefined and has changed considerably over the years, sometimes restricted by acts of Congress but mostly by assumptions which are not listed in the text, perhaps because no one ‘imagined they should be. The president also has, under Article II, virtually unlimited power of pardon for federal crimes, so he could, logically, arrest or even kill henchmen of elected federal officials who oppose the government. him, then pardon these same accomplices. Or, to take an example in the opposite direction: the power of impeachment resides in Congress, with the assumption that it is reserved for cases clearly involving a serious violation of the law felony or misdemeanor so extreme that it alarms all. the parts. This has long been the case, and the three modern presidential dismissals have been treated as trials, with arguments, evidence, etc. But, since serious felonies and misdemeanors are not defined in the Constitution and are effectively what a sufficient number of lawmakers decide they are, nothing prevents impeachment from being simply a ejection seat: at all times. , when a party has a majority in the House and a two-thirds majority in the Senate, it can summarily expel the president by pure decision.

The point is that it is not necessary to find a logical loophole in the Constitution, because, like any legal document, even fundamental, it inevitably contains loopholes, pitfalls, ambiguities and inconsistencies. Indeed, this is why we have a Supreme Court: to arbitrate between competing constitutional logics. But these, too, can turn out to be undecidable, since a group of performers may assert an implicit right to privacy, which is invisible to another, or even an explicit right to private ownership of weapons, which has been invisible to all previous performer groups. .

The logic of the law, which impresses most of us enough to require drivers to stop at red lights and pedestrians to wait their turns, outside of New York City, at least actually exists by mutual consent more than by careful application. As the great contemporary and opponent of Gdel, Ludwig Wittgenstein might have said: we don’t follow the rules as much as we live them. Without a social consensus of commitment to the law, no law matters. (This is why so many autocracies have admirable constitutions.)

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