Logicians From The United States

"A just system must generate its own support."

"Properly understood, then, the desire to act justly derives in part from the desire to express most fully what we are or can be, namely free and equal rational beings with the liberty to choose."

"The fundamental criterion for judging any procedure is the justice of its likely results."

"Essentially the fault lies in the fact that the democratic political process is at best regulated rivalry; it does not even in theory have the desirable properties that price theory ascribes to truly competitive markets."

"Justice does not require that men must stand idly by while others destroy the basis of their existence."

"An intolerant sect has no right to complain when it is denied an equal liberty. … A person’s right to complain is limited to principles he acknowledges himself."

"Let us now consider whether justice requires the toleration of the intolerant, and if so under what conditions. There are a variety of situations in which this question arises. Some political parties in democratic states hold doctrines that commit them to suppress the constitutional liberties whenever they have the power. Again, there are those who reject intellectual freedom but who nevertheless hold positions in the university. It may appear that toleration in these cases is inconsistent with the principles of justice, or at any rate not required by them."

"The suppression of liberty is always likely to be irrational."

"We may reject the contention that the ordering of institutions is always defective because the distribution of natural talents and the contingencies of social circumstance are unjust, and this injustice must inevitably carry over to human arrangements. Occasionally this reflection is offered as an excuse for ignoring injustice, as if the refusal to acquiesce in injustice is on a par with being unable to accept death. The natural distribution is neither just nor unjust; nor is it unjust that persons are born into society at some particular position. These are simply natural facts. What is just and unjust is the way that institutions deal with these facts. Aristocratic and caste societies are unjust because they make these contingencies the ascriptive basis for belonging to more or less enclosed and privileged social classes. The basic structure of these societies incorporates the arbitrariness found in nature. But there is no necessity for men to resign themselves to these contingencies. The social system is not an unchangeable order beyond human control but a pattern of human action. In justice as fairness men agree to avail themselves of the accidents of nature and social circumstance only when doing so is for the common benefit. The two principles are a fair way of meeting the arbitrariness of fortune; and while no doubt imperfect in other ways, the institutions which satisfy these principles are just."

"In justice as fairness society is interpreted as a cooperative venture for mutual advantage."

"The even larger difference between rich and poor makes the latter even worse off, and this violates the principle of mutual advantage."

"A scheme is unjust when the higher expectations, one or more of them, are excessive. If these expectations were decreased, the situation of the less favored would be improved."

"In all sectors of society there should be roughly equal prospects of culture and achievement for everyone similarly motivated and endowed. The expectations of those with the same abilities and aspirations should not be affected by their social class."

"The first statement of the two principles reads as follows. First: each person is to have an equal right to the most extensive basic liberty compatible with a similar liberty for others. Second: social and economic inequalities are to be arranged so that they are both(a)reasonably expected to be to everyone's advantage, and (b) attached to positions and offices open to all."

"Our concern is solely with the basic structure of society and its major institutions and therefore with the standard cases of social justice."

"Intuitionism is not constructive, perfectionism is unacceptable."

"We may suppose that everyone has in himself the whole form of a moral conception."

"An intuitionist conception of justice is, one might say, but half a conception."

"The claims of existing social arrangements and of self interest have been duly allowed for. We cannot at the end count them a second time because we do not like the result."

"First of all, principles should be general. That is, it must be possible to formulate them without use of what would be intuitively recognized as proper names, or rigged definite descriptions."

"The circumstances of justice may be described as the normal conditions under which human cooperation is both possible and necessary."

"There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry."

"First of all, no one knows his place in society, his class position or social status; nor does he know his fortune in the distribution of natural assets and abilities, his intelligence and strength, and the like. Nor, again, does anyone know his conception of the good, the particulars of his rational plan of life, or even the special features of psychology such as his aversion to risk or liability to optimism or pessimism. More than this, I assume that the parties do not know the particular circumstances of their own society. That is, they do not know its particular economic or political situation, or the level of civilization and culture it has been able to achieve. The persons in the original position have no information as to which generation they belong."

"If A were not allowed his better position, B would be even worse off than he is."

"No one deserves his greater natural capacity nor merits a more favorable starting place in society."

"The difference principle, for example, requires that the higher expectations of the more advantaged contribute to the prospects of the least advantaged."

"Greater intelligence, wealth and opportunity, for example, allow a person to achieve ends he could not rationally contemplate otherwise."

"This is a long book, not only in pages."

"I am particularly grateful to Nozick for his unfailing help and encouragement during the last stages."

"An individual who finds that he enjoys seeing others in positions of lesser liberty understands that he has no claim whatever to this enjoyment."

"Indeed, it is tempting to suppose that it is self evident that things should be so arranged so as to lead to the most good."

"A conception of justice cannot be deduced from self evident premises or conditions on principles; instead, its justification is a matter of the mutual support of many considerations, of everything fitted together into one coherent view."

"It may be expedient but it is not just that some should have less in order that others may prosper."

"Social and economic inequalities, for example inequalities of wealth and authority, are just only if they result in compensating benefits for everyone, and in particular for the least advantaged members of society."

"The principles of justice are chosen behind a veil of ignorance."

"The concept of justice I take to be defined, then, by the role of its principles in assigning rights and duties and in defining the appropriate division of social advantages. A conception of justice is an interpretation of this role."

"Justice is the first virtue of social institutions, as truth is of systems of thought. A theory however elegant and economical must be rejected or revised if it is untrue; likewise laws and institutions no matter how efficient and well-arranged must be reformed or abolished if they are unjust. Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override. For this reason justice denies that the loss of freedom for some is made right by a greater good shared by others. It does not allow that the sacrifices imposed on a few are outweighed by the larger sum of advantages enjoyed by many. Therefore in a just society the liberties of equal citizenship are taken as settled; the rights secured by justice are not subject to political bargaining or to the calculus of social interests."

"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."

"The one man who was, during the last years, certainly by far Einstein's best friend, and in some ways strangely resembled him most, was Kurt Gödel, The great logician. They were very different in almost every personal way — Einstein gregarious, happy, full of laughter and common sense, and Gödel extremely solemn, very serious, quite solitary, and distrustful of common sense as a means of arriving at the truth. But they shared a fundamental quality: both went directly and wholeheartedly to the questions at the very center of things."

"Toward the end of his life, Gödel 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 Gödel's gifts might be aborted."

"... according to what Veblen told me, the association between Einstein and Gödel arose in the following way. Veblen felt that he had to look out for Gödel, 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 Gödel remained very close. They tended to come to the Institute together, and leave the Institute together, very often. Of course, Gödel'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 Gödel a few times. The king of the logicians. Gödel once told me, “The a priori is very powerful.” 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. Gödel'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, Gödel'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, Gödel'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 Gödel 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 Gödel, 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. Gödel 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, Gödel demonstrated that mathematics was intrinsically incomplete. Gödel 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 Gödel'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 Gödel 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."

"Gödel published comparatively little, but almost always to maximum effect; his papers are models of precision and incisive presentation."

"Fifty years ago Kurt Gödel... 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. ...Gödel'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 Gödel, 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 Gödel 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."