“Toward the end of his life Einstein confided to Morgenstern that he came to the Institute merely to have the privilege of walking home with Gödel.” 

GÖDEL’s LOOPHOLEödels-Loophole

“…Gödel’s intense logic sometimes overwhelmed his common sense. For example, when he decided to become a U.S. citizen in 1947, he took his preparation for the exam very seriously and studied the U.S. Constitution carefully and critically (as might be expected by the man who formulated “the incompleteness theory”). On December 5, 1947, Einstein and another friend accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses. Gödel had confided in them that he had discovered an inconsistency and logical flaw in the U.S. Constitution that could allow the U.S. to become a dictatorship; this has since been dubbed Gödel’s Loophole. Einstein was concerned that his friend’s unpredictable behavior might jeopardize his application if Godel argued with the Judge. The judge turned out to be Phillip Forman, who knew Einstein and had administered the oath at Einstein’s own citizenship hearing. Everything went smoothly until Forman happened to ask Gödel if he thought a dictatorship like the Nazi regime could happen in the U.S. Gödel then started to explain his discovery of a flaw in the U.S. Constitution. The judge understood what was going on, cut Gödel off, and moved the hearing on to other questions and a routine conclusion.”


“The mathematician and philosopher Kurt Gödel reportedly discovered a deep logical contradiction in the US Constitution. What was it? In this paper, the author revisits the story of Gödel’s discovery and identifies one particular “design defect” in the Constitution that qualifies as a “Gödelian” design defect. In summary, Gödel’s loophole is that the amendment procedures set forth in Article V self-apply to the constitutional statements in Article V themselves, including the entrenchment clauses in Article V. Furthermore, not only may Article V itself be amended, but it may also be amended in a downward direction (i.e., through an “anti-entrenchment” amendment making it easier to amend the Constitution). Lastly, the Gödelian problem of self-amendment or anti-entrenchment is unsolvable. In addition, the author identifies some “non-Gödelian” flaws or “design defects” in the Constitution and explains why most of these miscellaneous design defects are non-Gödelian or non-logical flaws.”

Is There a Logical Inconsistency in the Constitution?
by Dan Rockmore / Aug 06, 2018

“Gödel was Austrian by birth and had come to the United States in 1940 to escape the fascist regime of his homeland to assume a professorship at Princeton’s Institute for Advanced Study. Following World War II, he was encouraged by many to apply for U.S. citizenship. Despite the assurances of his friends (including the great physicist Albert Einstein and Oskar Morgenstern, the father of game theory) that the process was a formality, Gödel addressed the task with diligence and seriousness, taking the time to study local and national law, and finally the Constitution. One of Gödel’s most important (and best known) mathematical achievements is his proof of “The Incompleteness Theorem,” a result that reveals a fundamental incompatibility between the logical properties of “completeness” and “consistency.” “Completeness” means that all statements can either be proved true or false within a basic system of formal reasoning (like the axiom-based deductive proofs of high school geometry). “Consistency” is the idea that the system does not allow for any statement to be both true and false. Gödel’s Incompleteness Theorem says that if a system is sufficiently complicated, it cannot be both consistent and complete. (“Sufficiently complicated” means complex enough to encode basic arithmetic.) In most logical systems—and certainly in mathematics—we must have consistency. So that leaves us without completeness, which means we have statements that can neither be proved true or false. The great mystery is that we don’t know a priori which ones they are. Gödel proved his theorem by using logical rules to produce the statement “This Theorem is False.” Try the mental exercise of chasing your tail by assuming that this is either true or false. … If the theorem is false, then the statement is true. If the theorem is true, the statement is false.

Does democracy follow from the Constitution like a proof of Euclidean geometry? Can we check to make sure it really holds? But here is the real kicker: If you did identify any such “independent” statement, it or its negation could be appended to the system of axioms (fundamental assumed truths), and leave it consistent, thereby producing alternative logical systems, both consistent, but each containing statements that contradict statements in the other. For example, some of you might recall that in good old high school Euclidean geometry there are five axioms, one of which is the “parallel axiom.” It says that given a line and a point not on the line, you can only draw one line parallel through the point that is parallel to the original line. (Try it out!). Seems obvious, right? Well, for centuries mathematicians tried to prove that this statement actually followed from the other four axioms of Euclidean geometry—but as it turned out, the parallel axiom is actually independent of them. Thus, there is the possibility (and as we now know, the reality) of consistent Euclidean geometries with unique parallel lines and non-Euclidean geometries without unique parallel lines. This was an earthshaking discovery that exploded traditional intuitions and assumptions of the certitude of mathematical work.

Gödel’s reading of the Constitution seems to have led him to an analogous finding about the United States. As the day of his naturalization interview drew near, Gödel horrified Morgenstern by telling him that it would be completely possible within the laws of the Constitution for a dictator to emerge and put a Fascist regime in place. In Gödel’s Incompleteness-primed mind, both democracy and anti-democracy were consistent with the Constitution. Morgenstern and Einstein did their best to steer Gödel away from this line of thought, worrying that it would undermine his citizenship application. As luck would have it, during his exam, the subject came up. Gödel tried to explain this constitutional conundrum to his examiner. The examiner quickly changed topic and Gödel became a U.S. citizen, presumably saved by finding yet another person who didn’t like to talk about math. The exact argument that Gödel had in mind—effectively a proof of Gödel’s “Un-Democracy Theorem”—is unknown. But in recent months, I’ve found myself thinking about it more and more, especially as I think about the United States our children will inherit.

I’ve found myself wondering what was the weak point that Gödel identified? Just what kind of government and country does “follow” from the Constitution? As a mathematician, did Gödel immediately understand the implications of the weird non-Euclidean geometry of gerrymandering? Did he see the inherent arithmetic inconsistencies in the Electoral College process and understand how the system could be gamed to empower a minority? Lately, I wonder if he had zeroed in on the potential inconsistencies of the presidential pardon. A full-blown ability to pardon anyone—including himself—might so weaken the separation of powers as to enable a de facto dictatorship.

Indeed, the notion of a “President who pardons all and only those who can’t pardon themselves” is strikingly close to the kind of self-referencing logical antinomy (“This Theorem is False”) that underlies Gödel’s Incompleteness Theorem proof. On the other hand, maybe it was something as simple as the inconsistency of a document about freedom being drafted—at least in part—by slaveholders. We have yet to discover an actual text outlining Gödel’s theory that our Constitution could enable fascism, but the larger lesson is worth considering. Does our Constitution ensure the democratic ideals it espouses? Does the fact of our Constitution and the institutions that have evolved under those who have “guarded” it, guarantee the freedoms and rights we unconsciously assume? There are plenty of countries with high-minded and floridly written constitutions that would not make anyone’s top 10 list of homes for safe living and free thought. Since the time of the first modern national constitution (our own), constitutions have on average survived for 17 years before being rewritten. Gödel is also known—if perhaps less so—for work in mathematical physics, where he discovered a solution to Einstein’s equations for the structure of the universe that describe a world very different from the one we live in. Among the possibilities of this world is time travel. I’m hoping that we don’t need to rely on that discovery in order to avoid the constitutional alternate reality Gödel may have foreseen.”

When Constitutions Took Over the World
by Jill Lepore  /  March 22, 2021

“In 1947, Kurt Gödel, Albert Einstein, and Oskar Morgenstern drove from Princeton to Trenton in Morgenstern’s car. The three men, who’d fled Nazi Europe and become close friends at the Institute for Advanced Study, were on their way to a courthouse where Gödel, an Austrian exile, was scheduled to take the U.S.-citizenship exam, something his two friends had done already. Morgenstern had founded game theory, Einstein had founded the theory of relativity, and Gödel, the greatest logician since Aristotle, had revolutionized mathematics and philosophy with his incompleteness theorems. Morgenstern drove. Gödel sat in the back. Einstein, up front with Morgenstern, turned around and said, teasing, “Now, Gödel, are you really well prepared for this examination?” Gödel looked stricken. To prepare for his citizenship test, knowing that he’d be asked questions about the U.S. Constitution, Gödel had dedicated himself to the study of American history and constitutional law. Time and again, he’d phoned Morgenstern with rising panic about the exam. (Gödel, a paranoid recluse who later died of starvation, used the telephone to speak with people even when they were in the same room.) Morgenstern reassured him that “at most they might ask what sort of government we have.” But Gödel only grew more upset. Eventually, as Morgenstern later recalled, “he rather excitedly told me that in looking at the Constitution, to his distress, he had found some inner contradictions and that he could show how in a perfectly legal manner it would be possible for somebody to become a dictator and set up a Fascist regime, never intended by those who drew up the Constitution.” He’d found a logical flaw.

Morgenstern told Einstein about Gödel’s theory; both of them told Gödel not to bring it up during the exam. When they got to the courtroom, the three men sat before a judge, who asked Gödel about the Austrian government. “It was a republic, but the constitution was such that it finally was changed into a dictatorship,” Gödel said. “That is very bad,” the judge replied. “This could not happen in this country.” Morgenstern and Einstein must have exchanged anxious glances. Gödel could not be stopped. “Oh, yes,” he said. “I can prove it.” “Oh, God, let’s not go into this,” the judge said, and ended the examination. Neither Gödel nor his friends ever explained what the theory, which has since come to be called Gödel’s Loophole, was. For some people, conjecturing about Gödel’s Loophole is as alluring as conjecturing about Fermat’s Last Theorem. In 1949, the year after Kurt Gödel became a U.S. citizen, Linda Colley was born in the United Kingdom, a country without a written constitution. Colley, one of the world’s most acclaimed historians, is a British citizen and a C.B.E., a Commander of the Order of the British Empire. (If there were a Nobel Prize in History, Colley would be my nominee.) She lives in the United States. For the past twenty years or so, she’s been teaching at Princeton, walking the same grounds and haunting the same library stacks that Gödel once did, by turns puzzled and fascinated, as he was, by the nature of constitutions. “I came to this subject very much as an outsider,” she writes in an incandescent, paradigm-shifting new book, “The Gun, the Ship, and the Pen: Warfare, Constitutions, and the Making of the Modern World” (Liveright). “Moving in the late twentieth century to live and work in the United States, a country which makes a cult out of its own written constitution, was therefore for me an arresting experience.” Colley has upended much of what historians believe about the origins of written constitutions.

Gödel’s Loophole is all over the Internet; you can find it on everything from Reddit to GitHub. The graver the American constitutional crisis, the greater the interest in the idea that there’s a bug in the constitutional code. But, for genuine illumination about the promise and the limits of constitutionalism, consider, instead, Colley’s Rule: Follow the violence. “For the preservation of peace and good order, and for the security of the lives and properties of the inhabitants of this colony, we conceive ourselves reduced to the necessity of establishing a form of government,” New Hampshire’s congress pronounced in January, 1776, months before the colonies declared their independence from Britain, in one of the first written constitutions in the history of the modern world. After New Hampshire, every other former colony devised its own constitution, and each new constitution, along with the Articles of Confederation, offered another lesson in what worked and what didn’t.

Eleven years later, James Madison, having dedicated himself to the study of history ever since his years as an undergraduate at Princeton, prepared for a national constitutional convention by writing an essay titled “Vices of the Political System of the United States,” and then drafting a constitution. Madison’s constitution, much tinkered with during the convention, was signed in September, 1787, and ratified in June, 1788. Many of the founders later had grave doubts about the government they’d erected, as Dennis Rasmussen argues in “Fears of a Setting Sun: The Disillusionment of America’s Founders” (Princeton). Washington regretted partisanship, Hamilton thought the federal government too weak, Adams damned the vices of the people, and Jefferson expected the divide over slavery to doom the Union, writing, a few years before his death, “I regret that I am now to die in the belief that the useless sacrifice of themselves, by the generation of ’76, to acquire self government and happiness by their country, is to be thrown away by the unwise and unworthy passions of their sons, and that my only consolation is to be that I live not to weep over it.” Still, as the usual story has it, American constitutionalism served as a model for what can be called the age of constitution-making, an era also characterized by the spread of democracy; by 1914, governments on every continent had adopted written constitutions, driven by the force of the idea that the nature of rule, the structure of government, and the guarantee of rights are the sorts of things that have got to be written down, printed, and made public.

Colley doesn’t see it this way. First, she finds the origins of constitution-writing elsewhere—all over the place, really, and often very far from Philadelphia. Second, she thinks it’s important to separate the spread of constitutionalism from the rise of democracy, not least because many nations that adopted written constitutions rejected democracy, and still do. Third, she isn’t convinced that the writing of constitutions was simply driven by the force of an idea; instead, she thinks that the writing of constitutions was driven, in large part, by the exigencies of war. States make war and wars make states, the sociologist Charles Tilly once argued. Colley offers this corollary: Wars make states make constitutions. Laws govern people; constitutions govern governments. Written (or carved) constitutions, like Hammurabi’s Code, date to antiquity, but hardly anyone read them (hardly anyone could read), and, generally, they were locked away and eventually lost. Even the Magna Carta all but disappeared after King John affixed his seal to it, in 1215. For a written constitution to restrain a government, people living under that government must be able to get a copy of the constitution, easily and cheaply, and they must be able to read it. That wasn’t possible before the invention of the printing press and rising rates of literacy. The U.S. Constitution was printed in Philadelphia two days after it was signed, in the Pennsylvania Packet and Daily Advertiser, a newspaper that cost four pence. Kurt Gödel pored over the four thousand-odd words of the U.S. Constitution and spotted a logical flaw; Linda Colley has made a meticulous study of constitutions written the world over and discovered patterns in the circumstances in which each was written, distributed, and read. Crucial to the emergence of constitutionalism, she maintains, was the growing lethality, frequency, and scale of war. This began in the mid-eighteenth century, when rulers from China to Persia to Spain found themselves committed to long-distance wars that involved vast armies and navies and cost staggering sums…

…The U.S. Constitution has been rewritten three times: in 1791, with the ratification of the Bill of Rights, the first ten amendments; after the Civil War, with the ratification of the Reconstruction Amendments; and during the Progressive Era, with the ratification of the Sixteenth, Seventeenth, Eighteenth, and Nineteenth Amendments. It is time for another reinvention. Other countries regularly amend their constitutions. Americans don’t venerate all constitutions; in fact, they’re quite keen to amend state constitutions. Albert reports, “Historically, American state constitutions have been amended over 7,500 times, amounting on average to 150 amendments per state. This paints an unmistakable contrast with the U.S. Constitution, whose average annual amendment rate is an exceedingly low 0.07, while the average across all American state constitutions is 0.35, higher than the average of 0.21 for national constitutions around the world.” Rather than being amended, the Constitution has been betrayed, circumvented, violated, and abandoned, by force of practice. Can a U.S. President compel a foreign leader to interfere in an American election? Apparently. Can a U.S. President refuse to accept the results of a free and fair election and incite a mob to attack Congress in order to prevent the certification of the vote? Apparently. The U.S. Constitution, no less than the U.K.’s unwritten constitution, is more than the sum of its words; it’s the accretion of practices and precedents. The U.S. Constitution, no less than the U.K.’s unwritten constitution, is more than the sum of its words; it’s the accretion of practices and precedents. Kurt Gödel might have been happy to hear that. Gödel’s Loophole really isn’t anything like Fermat’s Last Theorem, because constitutional scholars are pretty sure of what Gödel had in mind. It’s a constitutional version of the idea that, if a genie wafts out of an oil lamp and offers you three wishes, you should begin by wishing for more wishes. In what amounts to a genuine oversight, Article V, the amendment provision, does not prohibit amending Article V. It’s very hard to ratify a constitutional amendment, but if a President could amass enough power and accrue enough blindly loyal followers he could get an amendment ratified that revised the mechanism of amendment itself. If a revised Article V made it possible for a President to amend the Constitution by fiat (e.g., “The President, whenever he shall deem it necessary, shall make amendments to this Constitution, which shall be valid to all intents and purposes, as part of this Constitution”), he could turn a democracy into a dictatorship without ever having done anything unconstitutional. What Gödel did not realize is that it’s actually a lot easier than that.”



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