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April 10, 2026
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"Toward the end of his life, GĂśdel feared that he was being poisoned, and he starved himself to death. His theorem is one of the most extraordinary results in mathematics, or in any intellectual field in this century. If ever potential mental instability is detectable by genetic analysis, an embryo of someone with Kurt GĂśdel's gifts might be aborted."
"... according to what Veblen told me, the association between Einstein and GĂśdel arose in the following way. Veblen felt that he had to look out for GĂśdel, and spent quite a lot of time talking with him. And then, he thought that he might perhaps get Einstein to take over part of this responsibility. And that seemed to go so extremely well that Veblen removed himself, essentially, from the picture. Einstein and GĂśdel remained very close. They tended to come to the Institute together, and leave the Institute together, very often. Of course, GĂśdel's interest in the theory of relativity theory undoubtedly goes back to this association with Einstein. ... I don't think he had any interest in physics before that. I know he had some philosophical interests, but I think the specific interest in the theory of relativity, in which he did write some papers and create some results of significance, that goes back to that association."
"In the 1970s I even got to meet Kurt GĂśdel a few times. The king of the logicians. GĂśdel once told me, âThe a priori is very powerful.â By this he meant that pure logic can take you farther than you might believe possible."
"Not even mathematics can be considered as a closed and complete system of axioms and theorems. The mathematical world is inexhaustible, no finite set of postulates and deductions will ever be able to give us the answer to all questions. GĂśdel's theorem, whose statement dates back to about half a century ago, brutally put an end to all attempts to condense mathematics into a list of axioms from which the truth or falsity of each of its assertions should follow. If the same mathematical language that physics uses to describe the world remains intrinsically incomplete, it is not reasonable to expect that the universe can be describable starting from a finite set of natural laws. The incompleteness of mathematics and consequently that of physics is repugnant to many, but it must be said that for the exact sciences, GĂśdel's theorem is by no means a defeat: on the contrary, it provides us with an intellectual push towards ever broader and more fruitful developments."
"After Einstein's death, GĂśdel's sense of exile must have deepened enormously. When Einstein had been ordered by his doctor to take a rest cure, there had been nobody, as GĂśdel complained to his mother, for him to speak to. Now there would permanently be nobody."
"The progenitor of information theory, and perhaps the pivotal figure in the recent history of human thought, was Kurt GĂśdel, the eccentric Austriac genius and intimate of Einstein who drove determinism from its strongest and most indispensable redoubt; the coherence, consistency, and self-sufficiency of mathematics. GĂśdel demonstrated that every logical scheme, including mathematics, is dependent upon axioms that it cannot prove and that cannot be reduced to the scheme itself. In an elegant mathematical proof, introduced to the world by the great mathematician and computer scientist John von Neumann in September 1930, GĂśdel demonstrated that mathematics was intrinsically incomplete. GĂśdel was reportedly concerned that he might have inadvertently proved the existence of God, a faux pas in his Viennese and Princeton circle. It was one of the famously paranoid GĂśdel's more reasonable fears."
"In the end we search out the beginnings. Established, beyond comparison, as the most important logician of our times by his remarkable results of the 1930s, Kurt GĂśdel was also most unusual in the ways of his life and mind. Deeply private and reserved, he had a superb all embracing rationality, which could descend into a maddening attention to detail in matters of everyday life."
"GĂśdel published comparatively little, but almost always to maximum effect; his papers are models of precision and incisive presentation."
"Fifty years ago Kurt GĂśdel... proved that the world of pure mathematics is inexhaustible. No finite set of axioms and rules of inference can ever encompass the whole of mathematics. Given any finite set of axioms, we can find meaningful mathematical questions which the axioms leave unanswered. This discovery... came at first as an unwelcome shock to many mathematicians. It destroyed... the hope that they could solve the problem of deciding by a systematic procedure the truth or falsehood of any mathematical statement. ...GĂśdel's theorem, in denying ...the possibility of a universal algorithm to settle all questions, gave... instead, a guarantee that mathematics can never die. ...there will always be, thanks to GĂśdel, fresh questions to ask and fresh ideas to discover."
"If a 'religion' is defined to be a system of ideas that contains unprovable statements, then GĂśdel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one."
"The more I think about language, the more it amazes me that people ever understand each other at all."
"Secondly, even disregarding the intrinsic necessity of some new axiom, and even in case it has no intrinsic necessity at all, a probable decision about its truth is possible also in another way, namely, inductively by studying its "success." Success here means fruitfulness in consequences, in particular in "veriďŹable" consequences, i.e. consequences veriďŹable without the new axiom, whose proofs with the help of the new axiom, however, are considerably simpler and easier to discover, and make it possible to contract into one proof many different proofs. The axioms for the system of real numbers, rejected by the intuitionists, have in this sense been veriďŹed to some extent, owing to the fact that analytic number theory frequently allows one to prove number-theoretical theorems which, in a more cumbersome way, can subsequently be veriďŹed by elementary methods. A much higher degree of veriďŹcation than that, however, is conceivable. There might exists axioms so abundant in their veriďŹable consequences, shedding so much light upon a whole ďŹeld, and yielding such powerful methods for solving problems, (and even solving them constructively, as far as that is possible) that, no matter whether or not they are intrinsically necessary, they would have to be accepted at least in the same sense as any well-established physical theory."
"The meaning of the world is the separation of wish and fact. Wish is a force as applied to thinking beings, to realize something. A fulfilled wish is a union of wish and fact. The meaning of the whole world is the separation and the union of fact and wish."
"Ninety percent of [contemporary philosophers] see their principal task as that of beating religion out of men's heads. ⌠We are far from being able to provide scientific basis for the theological world view."
"Religions are, for the most part, bad-but religion is not."
"To every ω-consistent recursive class κ of formulae there correspond recursive class signs r, such that neither v Gen r nor Neg (v Gen r) belongs to Flg (κ) (where v is the free variable of r)."
"There are other worlds and rational beings of a different and higher kind. The world in which we live is not the only one in which we shall live or have lived."
"I like Islam, it is a consistent idea of religion and open-minded."
"The formation in geological time of the human body by the laws of physics (or any other laws of similar nature), starting from a random distribution of elementary particles and the field is as unlikely as the separation of the atmosphere into its components. The complexity of the living things has to be present within the material [from which they are derived] or in the laws [governing their formation]."
"It turns out, of course, that Mises was right. The Soviet system has long been dogged by a method of pricing that produced grotesque misallocations of effort. The difficulties were not so visible in the early days of Soviet industrialization or in the post-Second World War reconstruction period. The dams and mills and entire new cities of the nineteen-thirties astonished the world, as did the Chinese Great Leap Forward of the nineteen-fifties, which performed similar miracles from a still lower base. But those undertakings, like the building of the Pyramids or the Great Wall, depended less on economic coordination than on the political capacity for marshalling vast labor forces. Inefficiency set in when projects had to be joined into a complex whole â a process that required knowing how much things should cost. As Mises foresaw, setting prices became a hopeless problem, because the economy never stood still long enough for anyone to decide anything correctly."
"Mises was born in 1881 in my hometown of Lvov, in what is now Ukraine. He emigrated from Eastern Europe to New York in 1940 and became perhaps the most thoroughgoing American defender of laissez-faire capitalism. Years later Milton Friedman would recount a story about the first meeting of the Mont Pelerin Society, held in 1947. The group was meant to bring together what Europeans would call liberal intellectuals and what Americans would describe as libertarians. As Friedman recalled, âWe were discussing the distribution of income, and whether you should have progressive income taxes. Some of the people there were expressing the view that there could be a justification for it.â Furiously and famously, Mises declared, âYouâre all a bunch of socialists!â and stormed out. Much like Rand with rent control, Mises felt that once income distribution is on the table, the jig is basically up. It simply becomes a matter of haggling over how much socialism there is."
"Mises (pronounced Mee-zis) was by far the most important figure of the Austrian School of economics. The Austrians eschewed economic calculation for a more philosophical approach to issues of finance and trade. They viewed modern theories as highly mathematical, heavily conceptual, and largely divorced from reality. For them, virtually every contemporary economist is akin to a geocentrist using increasingly complicated models to predict how celestial bodies circled the Earth. Difficult math doesnât make a calculation true, and neither does it make its practitioner smart. This disdain for statistics can be seen in the New Rightâs contempt for using numeric data as a mechanism of persuasion. Itâs about the story, not the numbers."
"The dictatorship of the proletariat was the logical extension of Leninâs agitprop; Fascism was more than the logical extension of liberty â it was embraced by Ludwig von Mises (1985 [1927], 42â51), the co-leader of the third generation Austrian School, [...] Misesâ political activity was consistent with his ideology: on 1 March 1934, he joined the Austro-Fascist Patriotic Front and their Werk Neues Leben social club (HĂźlsmann 2007, 677, n149). Mises may also have been a victim of propaganda: his justification for this tactical embrace was that fascists would protect property â the protection of which he saw as the very essence of liberty. [...] The Jewish-born Mises was lucky to escape with his life; he devoted much of the rest of it to describing his opponents as âFascistsâ."
"Socialists have certainly good reason to be grateful to Professor Mises, the great advocatus diaboli of their cause. For it was his powerful challenge that forced the socialists to recognise the importance of an adequate system of economic accounting to guide the allocation of resources in a socialist economy. Even more, it was chiefly due to Professor Mises' challenge that many socialists became aware of the very existence of such a problem.... [T]he merit of having caused the socialists to approach this problem systematically belongs entirely to Professor Mises. Both as an expression of recognition for the great service rendered by him and as a memento of the prime importance of sound economic accounting, a statue of Professor Mises ought to occupy an honorable place in the great hall of the Ministry of Socialisation or of the Central Planning Board of the socialist state."
"I probably was ... when I began my study, called the Fabian kind of approach and convinced that there must be intelligent solution of the many dissatisfactory events of this world. And so it was as a mild socialist, that I decided I must study economics. I was very soon 'cured' of these beliefs that socialism was the solution because I came after three years, and as a direct influence of Ludwig von Mises, who had then published his great book on Socialism demonstrating that the socialist solution was impossible in a technical sense."
"...there I came to know him (Mises) mainly as a tremendously efficient executive, the kind of man who, as was said of John Stuart Mill, because he does a normal day's work in two hours, always has a clear desk and time to talk about anything. I came to know him as one of the best educated and informed men I have ever known..."
"Though I learned that he [Mises] usually was right in his conclusions, I wasn't always satisfied by his arguments, and retained to the end a certain critical attitude which sometimes forced me to build different constructions, which however, to my great pleasure, usually led to the same conclusions. I am to the present moment pursuing the questions which he made me see, and that, I believe is the greatest benefit one scientist can confer on one of the next generation."
"There is no single man to whom I owe more intellectually, even though he [Mises] was never my teacher in the institutional sense of the word."
"As readers will remember, Mises in his famous socialist calculation argument proved that a fully socialist economy would collapse into chaos. If this is right, how can ostensibly socialist economies such as Soviet Russia exist? In answer, Mises said that these economies werenât fully socialist. They allowed scope for private enterprise, albeit of a limited sort. Misesâs point applies to the German form of socialism as well as the Russian."
"The market, even more than the wheel, is one of the great commonplace servants of man. Professor Mises powerfully defends it against those who would subvert it to the service of selfish or shortsighted ends. But it is possible that the defense is stronger when in the hands of somewhat more moderate men. One is also bound to be puzzled over who is to vote in and support the economic and political order that Professor Mises demands. He is a vigorous foe of autocrats and dictators but he also has little respect for people at large. Defending advertising, to choose one example among many, he observes: "Like all things designed to suit the taste of the masses, it is repellent to people of delicate feeling." I wouldn't suppose that the people of delicate feeling are yet in the strength to take over."
"Professor von Mises has a splendid analytical mind and an admirable passion for liberty; but as a student of human nature he is worse than null and as a debater he is of Hyde Park standard."
"While it is possible to imagine Mises without Hayek, it is not possible to imagine Hayek without Mises."
"Among Misesâs greatest personal attributes was courage. He had the force of will and character to maintain a position that he thought true even if almost no one else did."
"Just when the hopes of socialism seemed to be about to come true, Mises voiced the thoughts uppermost in the minds of so many who lacked the courage to speak out. Socialism could not work or keep its promises, he argued, because under such a system economic calculations in terms of value were rendered impossible."
"In the 1920s, Mises made important contributions to monetary economics, business cycle theory and of course socialist economics, but his later writings on the foundations of economic science are so idiosyncratic and dogmatically stated that we can only wonder that they have been taken seriously by anyone."
"It is a double-edged makeshift to entrust an individual or a group of individuals with the authority to resort to violence. The enticement implied is too tempting for a human being. The men who are to protect the community against violent aggression easily turn into the most dangerous aggressors. They transgress their mandate. They misuse their power for the oppression of those whom they were expected to defend against oppression. The main political problem is how to prevent the police power from becoming tyrannical. This is the meaning of all the struggles for liberty."
"The criterion of truth is that it works even if nobody is prepared to acknowledge it."
"People do not cooperate under the division of labor because they love or should love one another. They cooperate because this best serves their own interests. Neither love nor charity nor any other sympathetic sentiments but rightly understood selfishness is what originally impelled man to adjust himself to the requirements of society, to respect the rights and freedoms of his fellow men and to substitute peaceful collaboration for enmity and conflict."
"Value is not intrinsic, it is not in things. It is within us; it is the way in which man reacts to the conditions of his environment. Neither is value in words and doctrines, it is reflected in human conduct. It is not what a man or groups of men say about value that counts, but how they act."
"If historical experience could teach us anything, it would be that private property is inextricably linked with civilization."
"If one takes pleasure in calling the gold standard a "barbarous relic," one cannot object to the application of the same term to every historically determined institution. Then the fact that the British speak English â and not Danish, German, or French â is a barbarous relic too, and every Briton who opposes the substitution of Esperanto for English is no less dogmatic and orthodox than those who do not wax rapturous about the plans for a managed currency."
"There is no means of avoiding the final collapse of a boom brought about by credit expansion. The alternative is only whether the crisis should come sooner as the result of voluntary abandonment of further credit expansion, or later as a final and total catastrophe of the currency system involved."
"...racial hatred is not a natural phenomenon innate in man. It is the product of ideologies. But even if such a thing as a natural and inborn hatred between various races existed, it would not render social cooperation futile and would not invalidate Ricardo's theory of association. Social cooperation has nothing to do with personal love or with a general commandment to love one another. People do not cooperate under the division of labor because they love or should love one another. They cooperate because this best serves their own interests. Neither love nor charity nor any other sympathetic sentiments but rightly understood selfishness is what originally impelled man to adjust himself to the requirements of society, to respect the rights and freedoms of his fellow men and to substitute peaceful collaboration for enmity and conflict."
"A man who chooses between drinking a glass of milk and a glass of a solution of potassium cyanide does not choose between two beverages; he chooses between life and death. A society that chooses between capitalism and socialism does not choose between two social systems; it chooses between social cooperation and the disintegration of society. Socialism is not an alternative to capitalism; it is an alternative to any system under which men can live as human beings."
"The state is God, deifies arms and prisons. The worship of the state is the worship of force. There is no more dangerous menace to civilization than a government of incompetent, corrupt, or vile men. The worst evils which mankind ever had to endure were inďŹicted by bad governments. The state can be and has often been in the course of history the main source of mischief and disaster."
"The capitalist system of production is an economic democracy in which every penny gives a right to vote. The consumers are the sovereign people. The capitalists, the entrepreneurs, and the farmers are the peopleâs mandatories. If they do not obey, if they fail to produce, at the lowest possible cost, what the consumers are asking for, they lose their office. Their task is service to the consumer. Profit and loss are the instruments by means of which the consumers keep a tight rein on all business activities."
"The unhampered market economy is not a system which would seem commendable from the standpoint of the selfish group interests of the entrepreneurs and capitalists. It is not the particular interests of a group or of individual persons that require the market economy, but regard for the common welfare. It is not true that the advocates of the free-market economy are defenders of the selfish interests of the rich. The particular interests of the entrepreneurs and capitalists also demand interventionism to protect them against the competition of more efficient and active men. The free development of the market economy is to be recommended, not in the interest of the rich, but in the interest of the masses of the people."
"As the liberal sees it, the task of the state consists solely and exclusively in guaranteeing the protection of life, health, liberty, and private property against violent attacks. Everything that goes beyond this is an evil. A government that, instead of fulfilling its task, sought to go so far as actually to infringe on personal security of life and health, freedom, and property would, of course, be altogether bad."
"A free man must be able to endure it when his fellow men act and live otherwise than he considers proper. He must free himself from the habit, just as soon as something does not please him, of calling for the police."
"Repression by brute force is always a confession of the inability to make use of the better weapons of the intellect â better because they alone give promise of final success. This is the fundamental error from which Fascism suffers and which will ultimately cause its downfall. The victory of Fascism in a number of countries is only an episode in the long series of struggles over the problem of property. The next episode will be the victory of Communism. The ultimate outcome of the struggle, however, will not be decided by arms, but by ideas. It is ideas that group men into fighting factions, that press the weapons into their hands, and that determine against whom and for whom the weapons shall be used. It is they alone, and not arms, that, in the last analysis, turn the scales. So much for the domestic policy of Fascism. That its foreign policy, based as it is on the avowed principle of force in international relations, cannot fail to give rise to an endless series of wars that must destroy all of modern civilization requires no further discussion. To maintain and further raise our present level of economic development, peace among nations must be assured. But they cannot live together in peace if the basic tenet of the ideology by which they are governed is the belief that one's own nation can secure its place in the community of nations by force alone. It cannot be denied that Fascism and similar movements aiming at the establishment of dictatorships are full of the best intentions and that their intervention has, for the moment, saved European civilization. The merit that Fascism has thereby won for itself will live on eternally in history. But though its policy has brought salvation for the moment, it is not of the kind which could promise continued success. Fascism was an emergency makeshift. To view it as something more would be a fatal error."