By Alex Gordon
HAIFA, Israel — Science is international. Therefore, to do science, I worked in many countries. These were Western countries that considered themselves democratic. In almost every country, at the beginning of my stay, I listened to a story from a local scientist, from which it emerged that his country was very badly governed. As a result, to his great regret, it is ridiculous, impractical, degenerating, and voluntarily pushing itself into the abyss.
The English writer George Bernard Shaw, winner of the Nobel Prize for literature, was fond of saying, “Democracy is a device which ensures that we are governed no better than we deserve.” To criticize the governance of the country in which you live is a remarkable fate, for in a totalitarian state such criticism leads to prison. Only an undemocracy can be worse than a democracy. But judging by what Shaw said, there is a kind of vicious circle in democracy: those who are in opposition to the government in parliament and on the streets know how to remedy the terrible state of the nation, but they know it only when they are far from running the state. If some of them manage to become rulers, they will make the same or even bigger mistakes than those they criticize. Canadian educator Lawrence Peter wrote: “The chief defect of democracy is that only a party deprived of power knows how to govern.”
The average citizen in a democratic country receives a constant message that the situation in the country is getting worse and worse, more dangerous and more dangerous, more tragic and more tragic. The average citizen in a totalitarian state receives signals that his country’s situation is very good and that it can only get even better. Both signals can drive the citizen to depression. So, practicing politics, listening to the news all the time, can lead the activist and the listener to clinical depression.
I prefer the occupation of exact sciences to the management of government and political activities. In exact sciences a scientist knows what he is doing. He can correctly evaluate the results of his research and the degree of possible errors. In state management, a ruler often does not know what he is doing and what mistakes his activity may lead to. Even in mathematics, which was considered an exact science, scientists have realized that they are engaged in inaccurate, incomplete and even contradictory science. Such an epiphany is not possible in the minds of those engaged in governing the state, or those who think they know how to properly govern the state, as opposed to those who are currently elected to do so.
In 1931, the Austrian-American logician and mathematician Kurt Gödel proved two theorems about incompleteness and inconsistency in mathematics. This was a true revolution in mathematics. Before Gödel, mathematicians believed that their science was complete, consistent, and that its theorems could be derived logically unambiguously from axioms, as in Euclid’s geometry. Mathematics before Gödel was considered a logically rigorous, perfect axiomatic science. Gödel proved that if formal arithmetic is consistent, then it is impossible to derive a formula asserting the consistency of arithmetic and that the consistency of any axiomatic theory cannot be proved by means of the theory itself. Such a rigorous, slender and seemingly logical science as mathematics is incomplete and contradictory, and can democracy be a complete and consistent system?
The latter question was answered by the same Gödel at the time he obtained U.S. citizenship. In 1948, he appeared for the exam accompanied by his colleague at the Institute for Advanced Study at Princeton, Albert Einstein. From a mathematician’s point of view, a country’s constitution is a set of logical connected axioms. Knowing the incompleteness of axiomatic systems, Gödel found contradictions in the U.S. Constitution, allowing under the guise of democracy and freedom to establish a dictatorial regime. One of the members of the examination board asked Gödel:
– Until now you have been a German citizen.
Gödel corrected the examiner:
– Not Germany, but Austria.
– It doesn’t matter, said the examiner. – In any case you have lived under a monstrous dictatorship, which is impossible in our country.
But Gödel contradicted him:
– On the contrary, I am going to prove mathematically that a dictatorship is possible in the United States.
Einstein managed to convince Gödel not to anger the examiner, otherwise he would not get US citizenship. Gödel could indeed prove the conditions for the emergence of dictatorship in the USA and in any other democratic country. It followed that an intensified effort to improve democracy could lead to its significant deterioration, no matter what fine ideas the slogans of the reformers might contain. Since the time of the philosophers who created the doctrine of the foundations of democracy and the necessity of separation of powers, the English philosopher John Locke and the French philosopher Charles Louis Montesquieu, it is clear that a struggle between the executive, legislative and judicial powers is preferable to the harmony between them that exists under a dictatorship. However, the problem of the correct quantitative separation of powers has no single solution, since democracy, like mathematics, cannot be complete and consistent.
In 1951, the American mathematician and economist Kenneth Joseph Arrow, a professor at Chicago, Stanford and Harvard Universities, proved in a general way the theorem proved by Gödel in mathematics. When applied to political structures, it is called the “impossibility of democracy” theorem as a “collective choice” or “dictator’s inevitability theorem.” This theorem, also called the Gödel-Arrow theorem, states that the equilibrium of a system depends on the preferences of voters who have no idea of the system’s margin of safety and are not inclined to trust it when deviations from the norm occur in it.
Arrow identified five conditions, now generally recognized as essential axioms of democracy, in which social decisions are made by voting. Using elementary mathematical apparatus, Arrow showed that these conditions are contradictory: it is impossible to create an electoral system that would not violate at least one of them. Such a violation occurs not because of someone’s evil will, but because of an inherent defect of the system, incomplete and contradictory.
Arrow received the Nobel Prize in economics in 1972 for proving the impossibility of simultaneously meeting the requirements of reasonableness and equality and the impossibility of establishing the ranking of social priorities. According to the Gödel-Arrow theorem, any electoral system is flawed.
In a totalitarian state, this theorem also works, but anyone who wants to prove that there is a dictatorship in a dictatorial country faces imprisonment. In a democratic country this theorem works perfectly well, but nobody pays attention to it. Maybe it is because the struggle for democracy is much more important than its preservation. The struggle for democracy takes place in a fog of ignorance of the extent of its durability and its limits.
In his book Transitions to Democracy, Polish-American political scientist Adam Przeworski writes, “Democracy is the realm of uncertainty; it is not in the business of predetermining the future.” In his view, democracy leads to uncertainty of results with certainty of procedures. Democracy is a regime of government whose ways of strengthening it may lead to its weakening. Democracy fighters in democracies are unaware of the Gödel-Arrow theorem and do not realize that their efforts to improve democracy can damage it.
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Alex Gordon is professor emeritus of physics at the University of Haifa and at Oranim, the academic college of education, and the author of 10 books.