Educators From England

"What’s missing from public conversation and public policy conversation is precisely a sort of moral underpinning, a sense of the moral purposes that bind people together in functional societies. And part of the attraction of someone who otherwise didn’t appeal to me in the least—like, say, Pope John Paul II—was how he managed to connect with young people. Whether it was in Eastern Europe or Latin America or wherever, his was the sense of an absolutely, unambiguously, morally noncompromising view about what is right and what is wrong. It seems to me that we need to reintroduce some of that. We need to reintroduce confidently and unashamedly that kind of language into the public realm. And not expel it, so to speak, into church for Sunday. It’s not only on Sunday that some things are right and some things are wrong."

"I am, I discover in late middle age, a work in progress."

"It is the liberals, then, who count. They are, as it might be, the canaries in the sulphurous mineshaft of modern democracy. The alacrity with which many of America's most prominent liberals have censored themselves in the name of the War on Terror, the enthusiasm with which they have invented ideological and moral cover for war and war crimes and proffered that cover to their political enemies: all this is a bad sign. Liberal intellectuals used to be distinguished precisely by their efforts to think for themselves, rather than in the service of others. Intellectuals should not be smugly theorising endless war, much less confidently promoting and excusing it. They should be engaged in disturbing the peace – their own above all."

"Some people, myself included, advocated foreign intervention in Bosnia and Kosovo while opposing our adventure in Iraq. Sam Moyn might find this inconsistent, but (on this occasion at least) it is the world that is inconsistent, not us. During the Balkan wars individuals’ rights were under ascertainable threat in real time. Outside intervention could make a difference, and it did. This was not the case in Iraq. We should always be suspicious of the invocation of universal “rights” as a cover for sectional interests. But it doesn’t follow from this that talk of rights is “really” always about something else. Sometimes it is, and sometimes it isn’t. How, then, should we adjust our response? Well, there is a serviceable Keynesian answer to that: "When the facts change, I change my mind. What do you do?""

"My concern tonight is the following: Why is it that here in the United States we have such difficulty even imagining a different sort of society from the one whose dysfunctions and inequalities trouble us so? We appear to have lost the capacity to question the present, much less offer alternatives to it. Why is it so beyond us to conceive of a different set of arrangements to our common advantage?"

"What, then, is to be done? We have to begin with the state: as the incarnation of collective interests, collective purposes, and collective goods. If we cannot learn to “think the state” once again, we shall not get very far. But what precisely should the state do? Minimally, it should not duplicate unnecessarily: as Keynes wrote, “The important thing for Government is not to do things which individuals are doing already, and to do them a little better or a little worse; but to do those things which at present are not done at all.” And we know from the bitter experience of the past century that there are some things that states should most certainly not be doing."

"The war changed everything. East of the Elbe, the Soviets and their local representatives inherited a sub-continent where a radical break with the past had already taken place. What was not utterly discredited was irretrievably damaged. Exiled governments from Oslo, Brussels or the Hague could return from London and hope to take up the legitimate authority they had been forced to relinquish in 1940. But the old rulers of Bucharest and Sofia, Warsaw, Budapest and even Prague had no future: their world had been swept aside by the Nazis' transformative violence. It remained only to decide the political shape of the new order that must now replace the unrecoverable past."

"I was brought up on English food. But not fish and chips, spotted dick, toad in the hole, Yorkshire pud, or other delicacies of British home cooking. These my mother scorned as somehow unhealthy; she may have grown up surrounded by non-Jews, but for just that reason she and her family kept to themselves and knew little of the domestic world of their neighbors, which they looked upon with fear and suspicion. In any case, she had no idea how to prepare "English delicacies." Her occasional encounters, via my father's friends in the Socialist Party of Great Britain, with vegetarians and vegans had taught her the virtues of brown bread, brown rice, green beans, and other "healthy" staples of an Edwardian left-wing diet. But she could no more cook brown rice than she could have prepared "chop suey." And so she did what every other cook in England in those days did: she boiled everything to death."

"The two perspectives—doctrine and calculation—were not necessarily in conflict. Ulbricht and his colleagues certainly believed that the way to expunge Nazism from Germany was by effecting a socio-economic transformation: they were not particularly interested in individual responsibility or moral re-education. But they also understood that Nazism was not just a trick perpetrated on an innocent German proletariat."

"This distrust of short-term memory, the search for serviceable myths of anti-Fascism—for a Germany of anti-Nazis, a France of Resisters or a Poland of victims—was the most important invisible legacy of World War Two in Europe. In its positive form it facilitated national recovery by allowing men like Marshall Tito, Charles De Gaulle or Konrad Adenauer to offer their fellow countrymen a plausible and even prideful account of themselves. Even East Germany claimed a noble point of origin, an invented tradition: the fabled and largely fabricated Communist 'uprising' in Buchenwald in April 1945. Such accounts allowed countries that had suffered war passively, like the Netherlands, to set aside the record of their compromises, and those whose activism had proven misguided, like Croatia, to bury it in a blurred story of competing heroisms. Without such collective amnesia, Europe's astonishing post-war recovery would not have been possible. To be sure, much was put out of mind that would subsequently return in discomforting ways. But only much later would it become clear just how much post-war Europe rested on foundation myths that would fracture and shift with the passage of years. In the circumstances of 1945, in a continent covered with rubble, there was much to be gained by behaving as though the past was indeed dead and buried and a new age about to begin. The price paid was a certain amount of selective, collective forgetting, notably in Germany. But then, in Germany above all, there was much to forget."

"To withdraw our selves as much as may be from Corporeal things, that pure Reason may be heard the better; to make that use of our Senses for which they are design’d and fitted, the preservation of the Body, but not to depend on their Testimony in our Enquiries after Truth."

"Thus, whether it be wit or beauty that a man’s in love with, there are no great hopes of a lasting happiness; beauty, with all the helps of arts, is of no long date; the more it is , the sooner it decays; and he, who only or chiefly chose for beauty, will in a little time find the same reason for another choice."

"She must be a fool with a witness, who can believe a man, proud and vain as he is, will lay his boasted authority, the dignity and prerogative of his sex, on moment at her feet, but in prospect of taking it up again to more advantage; he may call himself her slave a few days, but it is only in order to make her his all the rest of his life."

"The better our lot is in this world, and the more we have of it, the greater is our leisure to prepare for the next; we have the more opportunity to exercise that God-like quality, to taste that divine pleasure, doing good to the bodies and souls of those beneath us."

"Again, if Absolute Sovereignty be not necessary in a State, how comes it to be so in a family? Or if in a Family why not in a State; since no Reason can Be alle'd for the one that will not hold more strongly for the other?"

"An ill husband may deprive a wife of the comfort and quiet of her life, give occasion of exercising her virtue, try her patience and fortitude to the utmost, which is all he can do; it is herself only that can accomplish her ruin."

"Is it the being tied to One that offends us? Why this ought rather to recommend it to us, and would really do so, were we guided by reason, and not by humor and brutish passion. He who does not make friendship the chief inducement of his choice, and prefer it before any other consideration does not deserve a good wife, and therefore should not complain if he goes without one... The Christian institution of marriage provides the best that may be for domestic quiet and content, and for the education of children."

"The numberless treatises of antiquities, philosophy, mathematics, natural and other history ... written originally in, or translated to our tongue are sufficient to lead us a great way into any science our curiosity shall prompt us to. The greatest difficulty we struggled with, was the want of a good art of reasoning, which we had not, that I know of, till that defect was supplied by Locke, whose Essay on Human Understanding makes large amends for the want of all others in that kind."

"If all Men are born free, how is it that all Women are born slaves? as they must be if the being subjected to the inconstant, uncertain, unknown, arbitrary Will of Men be the perfect Condition of Slavery?"

"Putin must be stopped. And sometimes only guns can stop guns."

"In Poland it [the fall of Communism] took ten years, in Hungary ten months, in East Germany ten weeks: perhaps in Czechoslovakia it will take ten days!"

"Mathematics has also been developed as a philosophy, in the sense in which this term is defined by A.N. Whitehead as 'the endeavor to frame a coherent, logical and necessary system of general ideas in terms of which every element of our experience can be interpreted'. Substitute 'mathematics' for 'experience' and we have an admirable description of its speculative and philosophic development. ...Philosophy of mathematics... has its paradoxes and antimonies, and also diverse schools of thought..."

"For the great majority of mathematicians, mathematics is... a whole world of invention and discovery—an art. The construction of a new theorem, the intuition of some new principle, or the creation of a new branch of mathematics is the triumph of the creative imagination of the mathematician, which can be compared to that of a poet, the painter and the sculptor."

"Most mathematicians are by nature Platonists who cheerfully, unreflectingly and habitually employ such loaded phrases as 'We assume there exists...' or 'Therefore there exists...' an entity with such and such characteristics. Challenged by the realist they would probably reply that since the truths of mathematics are absolute, universal and eternal it is hard indeed to deny them an existence independent of human intelligence."

"As a science mathematics has been adapted to the description of natural phenomena, and the great practitioners in this field... have never concerned themselves with the logical foundations of mathematics, but have boldly taken a pragmatic view of mathematics as an intellectual machine which works successfully. Description has been verified by further observation, still more strikingly be prediction, and sometimes, more ominously, by control of natural forces. Happily, unresolved problems... still remain as challenges."

"Pure mathematics is much more than an armoury of tools and techniques for the applied mathematician. On the other hand, the pure mathematician has ever been grateful to applied mathematics for stimulus and inspiration. From the vibrations of the violin string they have drawn enchanting harmonies of Fourier Series, and to study the triode valve they have invented a whole theory of non-linear oscillations."

"The 'language theory' is inadequate as a description of the nature of mathematics."

"What would geometry be without Gauss, mathematical logic without Boole, algebra without Hamilton, analysis without Cauchy?"

"Mathematical activity has taken the forms of a science, a philosophy and an art."

"At each stage of in the advance of mathematical thought the outstanding characteristics are novelty and originality. That is why mathematics is such a delight to study, such a challenge to practise and such a puzzle to define."

"There is the definition [of mathematics], boldly proposed by Pierce that 'Mathematics is the science which draws necessary conclusions', and more explicitly formulated by Russel that 'Pure Mathematics is the class of all propositions of the form "p implies q"... it was... the purpose of Russell's treatise to provide a complete, exact and convincing justification of this definition... instead, he and Whitehead collaborated to give a magisterial account of the Principia Mathematica."

"The function of logic in mathematics is critical rather than constructive."

"The concept of 'number' in its most elementary sense as the signless integer appears to be an immediate abstraction from quantitative reality subjected to processes of counting and measurement. Vulgar fractions arise from division of a quantity into equal parts. But in what sense is zero a number? Are there negative numbers? Are there numbers corresponding to incommensurable ratios? Each question requires for its solution a fresh exercise of that kind of creative imagination which we call mathematical abstraction."

"The history of mathematics throws little light on the psychology of mathematical invention."

"From Pythagoras to Boethius, when pure mathematics consisted of arithmetic and geometry while applied mathematics consisted of music and astronomy, mathematics could be characterized as the deductive study of 'such abstractions as quantities and their consequences, namely figures and so forth' (Acquinas ca. 1260). But since the emergence of abstract algebra it has become increasingly difficult to formulate a definition to cover the whole of the rich, complex and expanding domain of mathematics."

"The subject matter of mathematics has increased so rapidly and extensively that there is some element of truth in maintaining that mathematics is not so much a subject as a way of studying any subject, not so much a science as a way of life. We turn, then, from the attempt to characterize the material object of mathematics to an attempt to determine its formal object, i.e., its methodology."

"Logical analysis is indispensable for an examination of the strength of a mathematical structure, but it is useless for its conception and design. The great advances in mathematics have not been made by logic but by creative imagination."

"Ninety per cent of all the mathematics we know has been discovered (or invented), in the last hundred years... the advances made in each of some dozen directions are converging into one single discipline uniting algebra, topology and analysis."

"During this century mathematics has been transformed..."

"The professional mathematician can scarcely avoid specialization and needs to transcend his private interests and take a wide synoptic view of the whole landscape of contemporary mathematics. His scientific colleagues are continually seeking enlightenment on the relevance of mathematical abstractions. The undergraduate needs a guidebook to the topography of the immense and expanding world of mathematics. There seems to be only one way to satisfy these varied interests... a concise historical account of the main currents... Only by a study of the development of mathematics can its contemporary significance be understood."

"The brilliant summaries by Bourbaki (1969) and Weyl (1951)... set a high standard of exposition, but... there is room for a history of mathematical ideas which will demand less mathematical expertise and offer a more detailed account of the motivation of research."

"This book... is primarily and essentially an account of the discovery or invention of mathematical concepts, and the historical material is... divided and classified, neither chronologically nor biographically, but philosophically."

"And in the end it is because of mysticism that it is possible to say that “no man is an island” and that on the contrary every man is “a part of the main.”"

"Mystics more often than not avoid direct reference to themselves."

"It is certainly the case that there can exist an atheistic mysticism, a mystical experience naked and not clothed in any religious garb."

"Thus we see that mysticism naturally, though not necessarily, becomes intimately associated with whatever is the religion of the culture in which it appears."

"There is no such thing as natural theology. God is either known by revelation - that is to say, by intuition - or not at all."

"The word "mysticism" is popularly used in a variety of loose and inaccurate ways. Sometimes anything is called "mystical" which is misty, foggy, vague, or sloppy. It is absurd that "mysticism" should be associated with what is "misty" because of the similar sound of the words. And there is nothing misty, foggy, vague, or sloppy about mysticism."

"The incommensurability of the mystical with the sensory-intellectual consciousness is also the ultimate reason why we have to exclude visions and voices, telepathy, precognition, and clairvoyance from the category of the mystical."

"It must now be added that these attempts at proof not only fail of their purpose, and so do no good to religion, but that they positively degrade it."