Logicians from the United Kingdom

"The answer to this problem is: as implied by Hume, we certainly are not justified in reasoning from an instance to the truth of the corresponding law. But to this negative result a second result, equally negative, may be added: we are justified in reasoning from a counterinstance to the falsity of the corresponding universal law (that is, of any law of which it is a counterinstance). Or in other words, from a purely logical point of view, the acceptance of one counterinstance to 'All swans are white' implies the falsity of the law 'All swans are white' - that law, that is, whose counterinstance we accepted. Induction is logically invalid; but refutation or falsification is a logically valid way of arguing from a single counterinstance to - or, rather, against - the corresponding law.This shows that I continue to agree with Hume's negative logical result; but I extend it.This logical situation is completely independent of any question of whether we would, in practice, accept a single counterinstance - for example, a solitary black swan - in refutation of a so far highly successful law. I do not suggest that we would necessarily be so easily satisfied; we might well suspect that the black specimen before us was not a swan.""

"You can choose whatever name you like for the two types of government. I personally call the type of government which can be removed without violence "democracy", and the other "tyranny"."

"Piecemeal social engineering resembles physical engineering in regarding the ends as beyond the province of technology. (All that technology may say about ends is whether they are compatible with each other or realizable.)"

"If we are uncritical we shall always find what we want: we shall look for, and find, confirmations, and we shall look away from, and not see, whatever might be dangerous to our pet theories. In this way it is only too easy to obtain what appears to be overwhelming evidence in favor of a theory which, if approached critically, would have been refuted."

"Scientists try to eliminate their false theories, they try to let them die in their stead. The believer—whether animal or man—perishes with his false beliefs."

"Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve."

"For it was my master who taught me not only how very little I knew but also that any wisdom to which I might ever aspire could consist only in realizing more fully the infinity of my ignorance."

"Before we as individuals are even conscious of our existence we have been profoundly influenced for a considerable time (since before birth) by our relationship to other individuals who have complicated histories, and are members of a society which has an infinitely more complicated and longer history than they do (and are members of it at a particular time and place in that history); and by the time we are able to make conscious choices we are already making use of categories in a language which has reached a particular degree of development through the lives of countless generations of human beings before us. . . . We are social creatures to the inmost centre of our being. The notion that one can begin anything at all from scratch, free from the past, or unindebted to others, could not conceivably be more wrong."

"Appealing to his Einstein's] way of expressing himself in theological terms, I said: If God had wanted to put everything into the universe from the beginning, He would have created a universe without change, without organisms and evolution, and without man and man's experience of change. But he seems to have thought that a live universe with events unexpected even by Himself would be more interesting than a dead one."

"From Plato to Karl Marx and beyond, the fundamental problem has always been: who should rule the state? (One of my main points will be that this problem must be replaced by a totally different one.)"

"There is an almost universal tendency, perhaps an inborn tendency, to suspect the good faith of a man who holds opinions that differ from our own opinions. ... It obviously endangers the freedom and the objectivity of our discussion if we attack a person instead of attacking an opinion or, more precisely, a theory."

"Science may be described as the art of systematic over-simplification — the art of discerning what we may with advantage omit."

"It seems to me that I may be living too long. Indeed: my nearest relations have all died, and so have some of my best friends, and even some of my best pupils. However, I do not have a reason to complain. I am grateful and happy to be alive, and still be able to continue with my work, if only just. My work seems to me more important than ever."

"I think so badly of philosophy that I don't like to talk about it. ... I do not want to say anything bad about my dear colleagues, but the profession of teacher of philosophy is a ridiculous one. We don't need a thousand of trained, and badly trained, philosophers — it is very silly. Actually most of them have nothing to say."

"I appeal to the philosophers of all countries to unite and never again mention Heidegger or talk to another philosopher who defends Heidegger. This man was a devil. I mean, he behaved like a devil to his beloved teacher, and he has a devilish influence on Germany. ... One has to read Heidegger in the original to see what a swindler he was."

"If the many, the specialists, gain the day, it will be the end of science as we know it - of great science. It will be a spiritual catastrophe comparable in its consequences to nuclear armament."

"When I speak of reason or rationalism, all I mean is the conviction that we can learn through criticism of our mistakes and errors, especially through criticism by others, and eventually also through self-criticism. A rationalist is simply someone for whom it is more important to learn than to be proved right; someone who is willing to learn from others — not by simply taking over another's opinions, but by gladly allowing others to criticize his ideas and by gladly criticizing the ideas of others. The emphasis here is on the idea of criticism or, to be more precise, critical discussion. The genuine rationalist does not think that he or anyone else is in possession of the truth; nor does he think that mere criticism as such helps us achieve new ideas. But he does think that, in the sphere of ideas, only critical discussion can help us sort the wheat from the chaff. He is well aware that acceptance or rejection of an idea is never a purely rational matter; but he thinks that only critical discussion can give us the maturity to see an idea from more and more sides and to make a correct judgement of it."

"Those who promise us paradise on earth never produced anything but a hell."

"Philosophers should consider the fact that the greatest happiness principle can easily be made an excuse for a benevolent dictatorship. We should replace it by a more modest and more realistic principle — the principle that the fight against avoidable misery should be a recognized aim of public policy, while the increase of happiness should be left, in the main, to private initiative."

"Good tests kill flawed theories; we remain alive to guess again."

"...no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white."

"A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method: "... this principle", says Reichenbach, "determines the truth of scientific theories. To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet's mind." Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in inductive logic. Thus the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. So the question arises why such a principle should be accepted at all, and how we can justify its acceptance on rational grounds."

"The game of science is, in principle, without end. He who decides one day that scientific statements do not call for any further test, and that they can be regarded as finally verified, retires from the game."

"...non-reproducible single occurrences are of no significance to science."

"Science does not rest upon solid bedrock. The bold structure of its theories arises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or 'given' base; and if we stop driving the piles deeper, it is not because we have reached firm ground. We simply stop when we are satisfied that the piles are firm enough to carry the structure, at least for the time being."

"Science is not a system of certain, or well established, statements; nor is it a statement which steadily advances towards state of finality. Our science is not knowledge (epistēmē): it can newer claim to have attained truth, or even substitute for it, such as probability. . . . We do not know; we can only guess."

"I believe that the advance of science depends upon the free competition of thought, and thus upon freedom, and that it must come to an end if freedom is destroyed (though it may well continue for some time in some fields, especially in technology)."

"Bold ideas, unjustified anticipations, and speculative thought, are our only means for interpreting nature: our only organon, our only instrument, for grasping her. And we must hazard them to win our prize. Those among us who are unwilling to expose their ideas to the hazard of refutation do not take part in the scientific game."

"If in this book harsh words are spoken about some of the greatest among the intellectual leaders of mankind, my motive is not, I hope, the wish to belittle them. It springs rather from my conviction that, if our civilization is to survive, we must break with the habit of deference to great men. Great men may make great mistakes; and as the book tries to show, some of the greatest leaders of the past supported the perennial attack on freedom and reason. Their influence, too rarely challenged, continues to mislead those on whose defence civilization depends, and to divide them. The responsibility of this tragic and possibly fatal division becomes ours if we hesitate to be outspoken in our criticism of what admittedly is a part of our intellectual heritage. By reluctance to criticize some of it, we may help to destroy it all."

"I see now more clearly than ever before that even our greatest troubles spring from something that is as admirable and sound as it is dangerous — from our impatience to better the lot of our fellows. For these troubles are the by-products of what is perhaps the greatest of all moral and spiritual revolutions of history, a movement which began three centuries ago. It is the longing of uncounted unknown men to free themselves and their minds from the tutelage of authority and prejudice. It is their attempt to build up an open society which rejects the absolute authority to preserve, to develop, and to establish traditions, old or new, that measure up to their standards of freedom, of humaneness, and of rational criticism. It is their unwillingness to sit back and leave the entire responsibility for ruling the world to human or superhuman authority,and their readiness to share the burden of responsibility for avoidable suffering, and to work for its avoidance. This revolution has created powers of appalling destructiveness; but they may yet be conquered."

"This book raises issues that might not be apparent from the table of contents. It sketches some of the difficulties faced by our civilization — a civilization which might be perhaps described as aiming at humanness and reasonableness, at equality and freedom; a civilization which is still in its infancy, as it were, and which continues to grow in spite of the fact that it has been so often betrayed by so many of the intellectual leaders of mankind. It attempts to show that this civilization has not yet fully recovered from the shock of its birth — the transition from the tribal or "enclosed society," with its submission to magical forces, to the 'open society' which sets free the critical powers of man. It attempts to show that the shock of this transition is one of the factors that have made possible the rise of those reactionary movements which have tried, and still try, to overthrow civilization and to return to tribalism."

"We may become the makers of our fate when we have ceased to pose as its prophets."

"What a monument of human smallness is this idea of the philosopher king. What a contrast between it and the simplicity of humaneness of Socrates, who warned the statesmen against the danger of being dazzled by his own power, excellence, and wisdom, and who tried to teach him what matters most — that we are all frail human beings. What a decline from this world of irony and reason and truthfulness down to Plato's kingdom of the sage whose magical powers raise him high above ordinary men; although not quite high enough to forgo the use of lies, or to neglect the sorry trade of every shaman — the selling of spells, of breeding spells, in exchange for power over his fellow-men."

"The open society is one in which men have learned to be to some extent critical of taboos, and to base decisions on the authority of their own intelligence."

"In speaking of sociological laws or natural laws of social life I have in mind such laws as are formulated by modern economic theories, for instance, the theory of international trade, or the theory of the trade cycle. These and other important sociological laws are connected with the functioning of social institutions. These laws play a role in our social life corresponding to the role played in mechanical engineering by, say, the principle of the lever. For institutions, like levers, are needed if we want to achieve anything which goes beyond the power of our muscles. Like machines, institutions multiply our power for good or evil. Like machines, they need intelligent supervision by someone who understands their way of functioning and, most of all, their purpose, since we cannot build them so that they work entirely automatically."

"The so-called paradox of freedom is the argument that freedom in the sense of absence of any constraining control must lead to very great restraint, since it makes the bully free to enslave the meek. The idea is, in a slightly different form, and with very different tendency, clearly expressed in Plato. Less well known is the paradox of tolerance: Unlimited tolerance must lead to the disappearance of tolerance. If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them. — In this formulation, I do not imply, for instance, that we should always suppress the utterance of intolerant philosophies; as long as we can counter them by rational argument and keep them in check by public opinion, suppression would certainly be unwise. But we should claim the right to suppress them if necessary even by force; for it may easily turn out that they are not prepared to meet us on the level of rational argument, but begin by denouncing all argument; they may forbid their followers to listen to rational argument, because it is deceptive, and teach them to answer arguments by the use of their fists or pistols. We should therefore claim, in the name of tolerance, the right not to tolerate the intolerant. We should claim that any movement preaching intolerance places itself outside the law, and we should consider incitement to intolerance and persecution as criminal, in the same way as we should consider incitement to murder, or to kidnapping, or to the revival of the slave trade, as criminal."

"Although my own position is, I believe, clearly enough implied in the text, I may perhaps briefly formulate what seems to me the most important principles of humanitarian and equalitarian ethics. (1) Tolerance towards all who are not intolerant and who do not propagate intolerance. ... This implies, especially, that the moral decisions of others should be treated with respect, as long as such decisions do not conflict with the principle of tolerance. (2) The recognition that all moral urgency has its basis in the urgency of suffering or pain. I suggest, for this reason, to replace the utilitarian formula 'Aim at the greatest amount of happiness for the greatest number', or briefly, 'Maximize happiness' by the formula 'The least amount of avoidable suffering for all', or briefly, 'Minimize suffering'. Such a simple formula can, I believe, be made one of the fundamental principles (admittedly not the only one) of public policy. (The principle 'Maximize happiness', in contrast, seems to be apt to produce a benevolent dictatorship.) We should realize that from the moral point of view suffering and happiness must not be treated as symmetrical; that is to say, the promotion of happiness is in any case much less urgent than the rendering of help to those who suffer, and the attempt to prevent suffering. (The latter task has little to do with 'matters of taste', the former much.)"

"I believe that there is, from the ethical point of view, no symmetry between suffering and happiness, or between pain and pleasure. Both the greatest happiness principle of the Utilitarians and Kant's principle 'Promote other people's happiness ..' seem to me (at least in their formulations) wrong on this point which, however, is not completely decidable by rational argument. (For the irrational aspect of ethical beliefs, see note 11 to the present chapter, and for the rational aspect, sections II and especially III of chapter 24). In my opinion (cp. note 6 (2) to chapter 5) human suffering makes a direct moral appeal, namely, the appeal for help, while there is no similar call to increase the happiness of a man who is doing well anyway. (A further criticism of the Utilitarian formula 'Maximize pleasure' is that it assumes, in principle, a continuous pleasure-pain scale which allows us to treat degrees of pain as negative degrees of pleasure. But, from the moral point of view, pain cannot be outweighed by pleasure, and especially not one man's pain by another man's pleasure. Instead of the greatest happiness for the greatest number, one should demand, more modestly, the least amount of avoidable suffering for all; and further, that unavoidable suffering—such as hunger in times of an unavoidable shortage of food—should be distributed as equally as possible.)"

"We must plan for freedom, and not only for security, if for no other reason than that only freedom can make security secure."

"No rational argument will have a rational effect on a man who does not want to adopt a rational attitude."

"I do not overlook the fact that there are irrationalists who love mankind, and that not all forms of irrationalism engender criminality. But I hold that he who teaches that not reason but love should rule opens up the way for those who rule by hate. (Socrates, I believe, saw something of this when he suggested that mistrust or hatred of argument is related to mistrust or hatred of man)."

"... the attempt to make heaven on earth invariably produces hell. It leads to intolerance. It leads to religious wars, and to the saving of souls through the inquisition. And it is, I believe, based on a complete misunderstanding of our moral duties. It is our duty to help those who need help; but it cannot be our duty to make others happy, since this does not depend on us, and since it would only too often mean intruding on the privacy of those towards whom we have such amiable intentions."

"... the fight against suffering must be considered a duty, while the right to care for the happiness of others must be considered a privilege confined to the close circle of their friends. ... Pain, suffering, injustice, and their prevention, these are the eternal problems of public morals, the 'agenda' of public policy ..."

"There is no history of mankind, there is only an indefinite number of histories of all kinds of aspects of human life. And one of these is the history of political power. This is elevated into the history of the world. But this, I hold, is an offence against every decent conception of mankind. It is hardly better than to treat the history of embezzlement or of robbery or of poisoning as the history of mankind. For the history of power politics is nothing but the history of international crime and mass murder (including it is true, some of the attempts to suppress them). This history is taught in schools, and some of the greatest criminals are extolled as heroes."

"Not only do I hate violence, but I firmly believe that the fight against it is not hopeless. I realize that the task is difficult. I realize that, only too often in the course of history, it has happened that what appeared at first to be a great success in the fight against violence was followed by a defeat. I do not overlook the fact that the new age of violence which was opened by the two World wars is by no means at an end. Nazism and Fascism are thoroughly beaten, but I must admit that their defeat does not mean that barbarism and brutality have been defeated. On the contrary, it is no use closing our eyes to the fact that these hateful ideas achieved something like a victory in defeat. I have to admit that Hitler succeeded in degrading the moral standards of our Western world, and that in the world of today there is more violence and brutal force than would have been tolerated even in the decade after the first World war. And we must face the possibility that our civilization may ultimately be destroyed by those new weapons which Hitlerism wished upon us, perhaps even within the first decade after the second World war; for no doubt the spirit of Hitlerism won its greatest victory over us when, after its defeat, we used the weapons which the threat of Nazism had induced us to develop."

"A rationalist, as I use the word, is a man who attempts to reach decisions by argument and perhaps, in certain cases, by compromise, rather than by violence. He is a man who would rather be unsuccessful in convincing another man by argument than successful in crushing him by force, by intimidation and threats, or even by persuasive propaganda."

"We all remember how many religious wars were fought for a religion of love and gentleness; how many bodies were burned alive with the genuinely kind intention of saving souls from the eternal fire of hell. Only if we give up our authoritarian attitude in the realm of opinion, only if we establish the attitude of give and take, of readiness to learn from other people, can we hope to control acts of violence inspired by piety and duty."

"There are many difficulties impeding the rapid spread of reasonableness. One of the main difficulties is that it always takes two to make a discussion reasonable. Each of the parties must be ready to learn from the other. You cannot have a rational discussion with a man who prefers shooting you to being convinced by you."

"Do not allow your dreams of a beautiful world to lure you away from the claims of men who suffer here and now. Our fellow men have a claim to our help; no generation must be sacrificed for the sake of future generations, for the sake of an ideal of happiness that may never be realised."

"The true Enlightenment thinker, the true rationalist, never wants to talk anyone into anything. No, he does not even want to convince; all the time he is aware that he may be wrong. Above all, he values the intellectual independence of others too highly to want to convince them in important matters. He would much rather invite contradiction, preferably in the form of rational and disciplined criticism. He seeks not to convince but to arouse — to challenge others to form free opinions."

"Although I consider our political world to be the best of which we have any historical knowledge, we should beware of attributing this fact to democracy or to freedom. Freedom is not a supplier who delivers goods to our door. Democracy does not ensure that anything is accomplished — certainly not an economic miracle. It is wrong and dangerous to extol freedom by telling people that they will certainly be all right once they are free. How someone fares in life is largely a matter of luck or grace, and to a comparatively small degree perhaps also of competence, diligence, and other virtues. The most we can say of democracy or freedom is that they give our personal abilities a little more influence on our well-being."

"It is wrong to think that belief in freedom always leads to victory; we must always be prepared for it to lead to defeat. If we choose freedom, then we must be prepared to perish along with it. Poland fought for freedom as no other country did. The Czech nation was prepared to fight for its freedom in 1938; it was not lack of courage that sealed its fate. The Hungarian Revolution of 1956 — the work of young people with nothing to lose but their chains — triumphed and then ended in failure. ... Democracy and freedom do not guarantee the millennium. No, we do not choose political freedom because it promises us this or that. We choose it because it makes possible the only dignified form of human coexistence, the only form in which we can be fully responsible for ourselves. Whether we realize its possibilities depends on all kinds of things — and above all on ourselves."

"The more we learn about the world, and the deeper our learning, the more conscious, specific, and articulate will be our knowledge of what we do not know, our knowledge of our ignorance. For this, indeed, is the main source of our ignorance — the fact that our knowledge can be only finite, while our ignorance must necessarily be infinite."

"What we should do, I suggest, is to give up the idea of ultimate sources of knowledge, and admit that all knowledge is human; that it is mixed with our errors, our prejudices, our dreams, and our hopes; that all we can do is to grope for truth even though it be beyond our reach. We may admit that our groping is often inspired, but we must be on our guard against the belief, however deeply felt, that our inspiration carries any authority, divine or otherwise. If we thus admit that there is no authority beyond the reach of criticism to be found within the whole province of our knowledge, however far it may have penetrated into the unknown, then we can retain, without danger, the idea that truth is beyond human authority. And we must retain it. For without this idea there can be no objective standards of inquiry; no criticism of our conjectures; no groping for the unknown; no quest for knowledge."

"Science must begin with myths, and with the criticism of myths."

"The history of science, like the history of all human ideas, is a history of irresponsible dreams, of obstinacy, and of error. But science is one of the very few human activities — perhaps the only one — in which errors are systematically criticized and fairly often, in time, corrected. This is why we can say that, in science, we often learn from our mistakes, and why we can speak clearly and sensibly about making progress there."

"Put in a nut-shell, my thesis amounts to this. The repeated attempts made by Rudolf Carnap to show that the demarcation between science and metaphysics coincides with that between sense and nonsense have failed. The reason is that the positivistic concept of 'meaning' or 'sense' (or of verifiability, or of inductive confirmability, etc.) is inappropriate for achieving this demarcation — simply because metaphysics need not be meaningless even though it is not science. In all its variations demarcation by meaninglessness has tended to be at the same time too narrow and too wide: as against all intentions and all claims, it has tended to exclude scientific theories as meaningless, while failing to exclude even that part of metaphysics which is known as 'rational theology'."

"It is often asserted that discussion is only possible between people who have a common language and accept common basic assumptions. I think that this is a mistake. All that is needed is a readiness to learn from one's partner in the discussion, which includes a genuine wish to understand what he intends to say. If this readiness is there, the discussion will be the more fruitful the more the partner's backgrounds differ."

"It seems to me certain that more people are killed out of righteous stupidity than out of wickedness."

"If I were to give a simple formula or recipe for distinguishing between what I consider to be admissible plans for social reform and inadmissible Utopian blueprints, I might say: Work for the elimination of concrete evils rather than for the realization of abstract goods. Do not aim at establishing happiness by political means. Rather aim at the elimination of concrete miseries."

"Do not allow your dreams of a beautiful world to lure you away from the claims of men who suffer here and now."

"In brief, it is my thesis that human misery is the most urgent problem of a rational public policy and that happiness is not such a problem."

"Besides, we should never attempt to balance anybody's misery against somebody else's happiness."

"As for Adler, I was much impressed by a personal experience. Once, in 1919, I reported to him a case which to me did not seem particularly Adlerian, but which he found no difficulty in analyzing in terms of his theory of inferiority feelings, although he had not even seen the child. Slightly shocked, I asked him how he could be so sure. "Because of my thousandfold experience," he replied; whereupon I could not help saying: "And with this new case, I suppose, your experience has become thousand-and-one-fold.""

"I may illustrate this by two very different examples of human behaviour: that of a man who pushes a child into the water with the intention of drowning it; and that of a man who sacrifices his life in an attempt to save the child. Each of these two cases can be explained with equal ease in Freudian and in Adlerian terms. According to Freud the first man suffered from repression (say, of some component of his Oedipus complex), while the second man had achieved sublimation. According to Adler the first man suffered from feelings of inferiority (producing perhaps the need to prove to himself that he dared to commit some crime), and so did the second man (whose need was to prove to himself that he dared to rescue the child). I could not think of any human behaviour which could not be interpreted in terms of either theory. It was precisely this fact — that they always fitted, that they were always confirmed — which in the eyes of their admirers constituted the strongest argument in favour of these theories. It began to dawn on me that this apparent strength was in fact their weakness."

"There are all kinds of sources of our knowledge; but none has authority ... The fundamental mistake made by the philosophical theory of the ultimate sources of our knowledge is that it does not distinguish clearly enough between questions of origin and questions of validity."

"Always remember that it is impossible to speak in such a way that you cannot be misunderstood: there will always be some who misunderstand you."

"One of the ideas I had discussed in The Poverty of Historicism was the influence of a prediction upon the event predicted. I had called this the "Oedipus effect", because the oracle played a most important role in the sequence of events which led to the fulfilment of its prophecy. ... For a time I thought that the existence of the Oedipus effect distinguished the social from the natural sciences. But in biology, too—even in molecular biology—expectations often play a role in bringing about what has been expected."

"Darwinism is not a testable scientific theory, but a metaphysical research program."

"As a rule, begin my lectures on Scientific Method by telling my students that scientific method does not exist. ...having been ...the one and only professor of this non-existent subject within the British Commonwealth."

"[S]ubject matters in general do not exist. There are no subject matters; no branches of learning—or, rather, of inquiry: there are only problems, and the urge to solve them."

"[E]ven serious students are misled by the myth of the subject."

"Scientific Method... [is] even less existent than some other non-existent subjects."

"Plato, Aristotle, Bacon and Descartes, as well... successors... [e.g.,] John Stuart Mill, believed that there existed a method of finding scientific truth. ...[L]ater ...slightly more sceptical ...methodologists ...believed that there existed a method, if not of finding a true theory, then ...of ascertaining whether ...some ...hypothesis was true; or (even more sceptical) whether some ... hypothesis was ...'probable' ..."

"I assert (1) There is no method of discovering a scientific theory. (2) There is no method of ascertaining the truth [i.e., verification] of a scientific hypothesis... (3) There is no method of ascertaining whether a hypothesis is 'probable', in the sense of the probability calculus."

"I am a rationalist. ...I mean ...[I] wish... to understand the world, and to learn by arguing with others. (...I do not say a rationalist holds the mistaken theory that men are... rational.)"

"By 'arguing...' I mean... criticizing... inviting... criticism; and trying to learn from it."

"[[Argument|[A]rgument]] is a... form of the art of fighting—with words... inspired by... getting nearer to... truth..."

"Diversity makes critical argument fruitful. ...[P]artners in an argument must share ...the wish to know, and the readiness to learn from the other ...by severely criticizing his views... and hearing... [the] reply. ...the so-called method of science consists in this kind of criticism."

"Scientific theories are distinguished from myths... in being criticizable, and... open to modifications... They can be neither verified nor probabilified."

"[T]he history of mankind could... be described as a history of outbreaks of fashionable philosophical and religious maladies. These... have... one serious function... evoking criticism."

"I... believe in the rationalist tradition of a commonwealth of learning, and in the urgent need to preserve this tradition."

"The doctrine that there is as much science in a subject as... mathematics in it, or as much... measurement or 'precision' in it, rests upon... misunderstanding."

"Never aim at more precision than... required by the problem..."

"I have no faith in precision: ...simplicity and clarity are values in themselves, but not... [of] precision or exactness..."

"I do not believe in what is often called... 'exact '... [or] in definitions... [they] do not... add to exactness... I especially dislike pretentious terminology and... pseudo-exactness concerned with it."

"What can be said can and should always be said more and more simply and clearly."

"I disbelieve in specialization and... experts. ...[P]aying too much respect to the specialist ...[is] destroying the commonwealth of learning, the rationalist tradition, and science ..."

"[T]here is only one way to science—or to philosophy... to meet a problem, to see its beauty and fall in love with it; to get married to it, and to live with it happily, till death do ye part—unless you should meet another... more fascinating problem, or... obtain a solution. But even if you do... you may... discover, to your delight, the... a whole family of enchanting... perhaps difficult problem children for whose welfare you may work, with a purpose, to the end of your days."

"'[S]cientific knowledge' always remained sheer guesswork... controlled by criticism and experiment. ...[T]his assumption is sufficient for solving the problem of induction—called by Kant 'the problem of Hume'— without sacrificing empiricism...[i.e.,] without adopting a principle of induction and ascribing to it a priori validity. For guesses are not 'induced from observations' (although they may ...be suggested ...by observations). This ... allows us to accept ...(...without Russell's limits of empiricism) Hume's logical criticism of induction and to give up ...an inductive logic, for certainty, and even for probability, while continuing ...scientific search for truth."

"All things living are in search of a better world."

"The belief in a political Utopia is especially dangerous. This is possibly connected with the fact that the search for a better world, like the investigation of our environment, is (if I am correct) one of the oldest and most important of all the instincts."

"Our aim as scientists is objective truth; more truth, more interesting truth, more intelligible truth. We cannot reasonably aim at certainty. Once we realize that human knowledge is fallible, we realize also that we can never be completely certain that we have not made a mistake."

"There are uncertain truths — even true statements that we may take to be false — but there are no uncertain certainties. Since we can never know anything for sure, it is simply not worth searching for certainty; but it is well worth searching for truth; and we do this chiefly by searching for mistakes, so that we have to correct them."

"Why do I think that we, the intellectuals, are able to help? Simply because we, the intellectuals, have done the most terrible harm for thousands of years. Mass murder in the name of an idea, a doctrine, a theory, a religion — that is all our doing, our invention: the invention of the intellectuals. If only we would stop setting man against man — often with the best intentions — much would be gained. Nobody can say that it is impossible for us to stop doing this."

"Ignorance is not a simple lack of knowledge but an active aversion to knowledge, the refusal to know, issuing from cowardice, pride or laziness of mind."

"To be ignorant of the past is to remain a child."

"The deepest, the only theme of human history, compared to which all others are of subordinate importance, is the conflict of skepticism with faith."

"Leadership is solving problems. The day soldiers stop bringing you their problems is the day you have stopped leading them. They have either lost confidence that you can help or concluded you do not care. Either case is a failure of leadership."

"When we enter a new situation in life and are confronted by a new person, we bring with us the prejudices of the past and our previous experiences of people. These prejudices we project upon the new person. Indeed, getting to know a person is largely a matter of withdrawing projections; of dispelling the smoke screen of what we imagine he is like and replacing it with the reality of what he is actually like."

"A theory that explains everything, explains nothing."

"I referred above to the Popperian school as a school, and yet it was not until I came to Sydney from London that I fully realised the extent to which I had been in a school. I found, to my surprise, that there were philosophers influenced by Wittgenstein or Quine or Marx who thought that Popper was quite wrong on many issues, and some who even thought that his views were positively dangerous. I think I have learnt much from that experience. One of the things that I have learnt is that on a number of major issues Popper is indeed wrong, as is argued in the latter portions of this book. However, this does not alter the fact that the Popperian approach is infinitely better than the approach adopted in most philosophy departments that I have encountered."

"The first article republished in Studies in Philosophy, Politics and Economics, "Degrees of Explanation," originally published in 1955, was largely consistent with Popper's methodology. Hayek embraced Popper's "hypothetico-deductive" approach to science: "The conception of science as a hypothetico-deductive system has been expounded by Karl Popper in a manner which brings out clearly some very important points." Here, as elsewhere in his work, Hayek distinguished between the facts of the natural and social sciences primarily on the basis of their complexity."

"I learned from Popper what for me is the essence of scientific investigation—how to be speculative and imaginative in the creation of hypotheses, and then to challenge them with the utmost rigor, both by utilizing all existing knowledge and by mounting the most searching experimental attacks. In fact, I learned from him even to rejoice in the refutation of a cherished hypothesis, because that, too, is a scientific achievement and because much has been learned by the refutation."

"Through my association with Popper I experienced a great liberation in escaping from the rigid conventions that are generally held with respect to scientific research. ... When one is liberated from these restrictive dogmas, scientific investigation becomes an exciting adventure opening up new visions; and this attitude has, I think, been reflected in my own scientific life since that time."

"[T]he paradox lurking at the heart of Karl Popper's career... Everyone says this opponent of dogmatism is almost pathologically dogmatic. ...Popper scoffs at scientists’ hope that they can achieve a final theory of nature. "...I think we have gone very far, but we are much further away." He... returns with his book Conjectures and Refutations... [and] reads his own words with reverence: "In our infinite ignorance we are all equal." ...Can a skeptic avoid self-contradiction... the Popper paradox? And if he doesn’t, if he preaches but fails to practice intellectual doubt and humility, does that negate his work? Not at all. Such paradoxes corroborate the skeptic’s point... the quest for truth is endless, twisty and riddled with pitfalls, into which even sharp-eyed seekers tumble. In our infinite ignorance we are all equal."

"The leading critic of the positivists in their heyday was of course Popper. There has been a tendency for philosophers of science to regard Popper as something of an embarrassment. However, naturalistic philosophers should take it as an interesting fact about science that Popper has long been the favourite philosopher of science among scientists; and it would be condescending to attribute this entirely to the fact that Popper's philosophy is relatively non-complex, self-contained, and flattering to scientists."

"Popper was kind of an egocentric jerk."

"Socrates (and so Plato) makes it quite clear that the rule of wisdom is tyrannical, and that it cannot tolerate words or deeds, laws or traditional institutions, and certainly political theories that impinge upon its rule. In this sense, modern enemies of Plato's political thought, of whom the most prominent in our time is no doubt Karl Popper, are correct in their objections, although they are ingenuous or let us say insufficiently rigorous in their consideration of the political consequences of theoretical truth. In Popper's case, this is probably due to his conviction that we can establish the falsehood of a proposition but not its truth. This conviction may well be more compatible with democracy in the modern sense of the term than the conviction that genuine philosophers know the truth. The argument of the Republic on the other hand is that, if we did know the truth, we would be led to support a city very much like the one constructed in the Republic under the leadership of Socrates."

"I do have a great respect for Popper. I mean, I think... he's nearer to... I mean, Popper's ambition, in relation to science, at least, was to discriminate between, sort of, science and what he called pseudo-science."

"Popper believed that any idea of Utopia is necessarily closed owing to the fact that it chokes its own refutations. The simple notion of a good society that cannot be left open for falsification is totalitarian. I learned from Popper, in addition to the difference between an open and a closed society, that between an open and a closed mind."

"I read Karl Popper's The Open Society and its Enemies. Popper, whose analysis in many ways complemented that of Hayek, approached Marxism from the point of view of the philosopher of the natural sciences. This meant that he was ideally equipped to expose the fraudulent claim of Marxists to have discovered immutable laws of history, social development or "progress" – laws which were comparable to the laws of natural science. It was not just that the "inevitable" course of events which Marx had prophesied had not occurred and showed no signs of occurring. Marx and Marxists had not even understood the scientific method, let alone practised it in their analysis. Unlike the Marxists – whether historians, economists or social scientists – who tried to "prove" their theories by accumulating more and more facts to sustain them, "the method of science is rather to look out for facts which may refute the theory... and the fact that all tests of the theory are attempted falsifications of predictions derived with its help furnishes the clue to scientific method". The political consequences of this basic error – perhaps more properly described as basic fraud – were summed up by Popper in the dedication of his later book The Poverty of Historicism: "In memory of the countless men, women and children of all creeds or nations or races who fell victims to the fascist and communist belief in Inexorable Laws of Historical Destiny.""

"I got to know Bertrand Russell in the last years of his life. I knew Karl Popper quite well, and they were a whole class above me in intelligence. It wasn’t that I was jealous, it was that I was trying to grapple with these problems with inadequate weaponry… Popper had this originality, Russell had it, and Einstein had it in spades."

"All existing things upon this earth, which have knowledge of their own existence, possess, some in one degree and some in another, the power of thought, accompanied by perception, which is the awakening of thought by the effects of external objects upon the senses."

"There never has been, and till we see it we never shall believe that there can be, a system of geometry worthy of the name, which has any material departures (we do not speak of corrections or extensions or developments) from the plan laid down by Euclid."

"The moving power of mathematical invention is not reasoning, but imagination."

"We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of exact science are mathematics and logic: the mathematical sect puts out the logical eye, the logical sect puts out the mathematical eye; each believing that it can see better with one eye than with two."

"I did not hear what you said, but I absolutely disagree with you."

"The two races which have founded the mathematics, those of the Sanscrit and Greek languages, have been the two which have independently formed systems of logic."

"They [the English] forget that at this moment there still exists [in India] a body of literature and science which might well be the nucleus of a new civilisation, though every trace of Christian and Mohammedan civilization were blotted out of existence."

"The number of mathematical students, increased as it has been of late years, would be much augmented if those who hold the highest rank in science would condescend to give more effective assistance in clearing the elements of the difficulties which they present. If any one claiming that title should think my attempt obscure or enormus, he must share the blame with me, since it is through his neglect that I have been enabled to avail myself of an opportunity to perform a task which I would gladly have seen confided to more skilful hands."

"The Object of this Treatise is—(1) To point out to the student of Mathematics, who has not the advantage of a tutor, the course of study which it is most advisable that he should follow, the extent to which he should pursue one part of the science before he commences another, and to direct him as to the sort of applications which he should make. (2) To treat fully of the various points which involve difficulties and which are apt to be misunderstood by beginners, and to describe at length the nature without going into the routine of the operations."

"In order to see the difference which exists between... studies,—for instance, history and geometry, it will be useful to ask how we come by knowledge in each. Suppose, for example, we feel certain of a fact related in history... if we apply the notions of evidence which every-day experience justifies us in entertaining, we feel that the improbability of the contrary compels us to take refuge in the belief of the fact; and, if we allow that there is still a possibility of its falsehood, it is because this supposition does not involve absolute absurdity, but only extreme improbability. In mathematics the case is wholly different... and the difference consists in this—that, instead of showing the contrary of the proposition asserted to be only improbable, it proves it at once to be absurd and impossible. This is done by showing that the contrary of the proposition which is asserted is in direct contradiction to some extremely evident fact, of the truth of which our eyes and hands convince us. In geometry, of the principles alluded to, those which are most commonly used are— I. If a magnitude is divided into parts, the whole is greater than either of those parts. II. Two straight lines cannot inclose a space. III. Through one point only one straight line can be drawn, which never meets another straight line, or which is parallel to it. It is on such principles as these that the whole of geometry is founded, and the demonstration of every proposition consists in proving the contrary of it to be inconsistent with one of these."

"There is a mistake into which several have fallen, and have deceived others, and perhaps themselves, by clothing some false reasoning in what they called a mathematical dress, imagining that by the application of mathematical symbols to their subject, they secured mathematical argument. This could not have happened if they had possessed a knowledge of the bounds within which the empire of mathematics is contained. That empire is sufficiently wide, and might have been better known, had the time which has been wasted in aggressions upon the domains of others, been spent in exploring the immense tracts which are yet untrodden."

"The lowest steps of the ladder are as useful as the highest."

"Although there is no study which presents so simple a beginning as that of geometry, there is none in which difficulties grow more rapidly as we proceed, and what may appear at first rather paradoxical, the more acute the student the more serious will the impediments in the way of his progress appear. This necessarily follows in a science which consists of reasoning from the very commencement, for it is evident that every student will feel a claim to have his objections answered, not by authority, but by argument, and that the intelligent student will perceive more readily than another the force of an objection and the obscurity arising from an unexplained difficulty, as the greater is the ordinary light the more will occasional darkness be felt. To remove some of these difficulties is the principal object of this Treatise."

"A finished or even a competent reasoner is not the work of nature alone... education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided that it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history may be chosen for this purpose. Now, of all these, it is desirable to choose the one... in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. ..Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:— 1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing. 2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general. 3. The demonstration is strictly logical, taking nothing for granted except the self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion. 4. When the conclusion is attained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if... reason is not to be the instructor, but the pupil. 5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. ...These are the principal grounds on which... the utility of mathematical studies may be shewn to rest, as a discipline for the reasoning powers. But the habits of mind which these studies have a tendency to form are valuable in the highest degree. The most important of all is the power of concentrating the ideas which a successful study of them increases where it did exist, and creates where it did not. A difficult position or a new method of passing from one proposition to another, arrests all the attention, and forces the united faculties to use their utmost exertions. The habit of mind thus formed soon extends itself to other pursuits, and is beneficially felt in all the business of life."

"The work now before the reader is the most extensive which our language contains on the subject."

"My specific... object has been to contain, within the prescribed limits, the whole of the student's course, from the confines of elementary algebra and trigonometry, to the entrance of the highest works on mathematical physics. A learner who has a good knowledge of the subjects just named, and who can master the present treatise, taking up elementary works on conic sections, application of algebra to geometry, and the theory of equations, as he wants them, will, I am perfectly sure, find himself able to conquer the difficulties of anything he may meet with; and need not close any book of Laplace, Lagrange, Legendre, Poisson, Fourier, Cauchy, Gauss, Abel, Hindenburgh and his followers. or of any one of our English mathematicians, under the idea that it is too hard for him."

"If much difficulty should be experienced in the elementary chapters, I know of no work which I can so confidently recommend to be used with the present one, as that of M. Duhamel."

"...nor have I found occasion to depart from the plan... the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange... had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits."

"I... subjoin references to those parts of the work for which I have not been indebted to my knowledge of what has been written before me: much of what is cited is probably not new, indeed it is dangerous for any one at the present day to claim anything as belonging to himself; several things which I once thought to have entered in this list have been since found (either by myself, or by a friend to whom I referred it) in preceding writers."

"It is not true, out of geometry, that the mathematical sciences are, in all their parts those models of finished accuracy which many suppose. The extreme boundaries of analysis have always been as imperfectly understood as the tract beyond the boundaries was absolutely unknown. But the way to enlarge the settled country has not been by keeping within it, but by making voyages of discovery, and I am perfectly convinced that the student should be exercised in this manner; that is, that he should be taught how to examine the boundary, as well as how to cultivate the interior. ...allowing all students whose capacity will let them read on the higher branches of applied mathematics, to have each his chance of being led to the cultivation of those parts of analysis on which rather depends its future progress than its present use in the sciences of matter."

"A large quantity of examples is indispensable."

"The following Treatise... has been endeavoured to make the theory of limits, or ultimate ratios... the sole foundation of the science, without any aid whatsoever from the theory of series, or algebraical expansions. I am not aware that any work exists in which this has been avowedly attempted, and I have been the more encouraged to make the trial from observing that the objections to the theory of limits have usually been founded either upon the difficulty of the notion itself, or its unalgebraical character, and seldom or never upon anything not to be defined or not to be received in the conception of a limit..."

"I cannot see why it is necessary that every deduction from algebra should be bound to certain conventions incident to an earlier stage of mathematical learning, even supposing them to have been consistently used up to the point in question. I should not care if any one thought this treatise unalgebraical, but should only ask whether the premises were admissible and the conclusions logical."

"I have throughout introduced the Integral Calculus in connexion with the Differential Calculus. ...Is it always proper to learn every branch of a direct subject before anything connected with the inverse relation is considered? If so why are not multiplication and involution in arithmetic made to follow addition and precede subtraction? The portion of the Integral Calculus, which properly belongs to any given portion of the Differential Calculus increases its power a hundred-fold..."

"Experience has convinced me that the proper way of teaching is to bring together that which is simple from all quarters, and, if I may use such a phrase, to draw upon the surface of the subject a proper mean between the line of closest connexion and the line of easiest deduction. This was the method followed by Euclid, who, fortunately for us, never dreamed of a geometry of triangles, as distinguished from a geometry of circles, or a separate application of the arithmetics of addition and subtraction; but made one help out the other as he best could."

"I am far from saying that this Treatise will be easy; the subject is a difficult one, as all know who have tried it."

"The absolute requisites for the study of this work... are a knowledge of algebra to the binomial at least, plane and solid geometry, plane trigonometry, and the most simple part of the usual applications of algebra to geometry. ...A. De Morgan. London July 1, 1836"

"The student of the Differential Calculus may... be brought to think it possible that the terms and ideas which that science requires may exist in his own mind in the same rude form as that of a straight line in the conceptions of a beginner in geometry. ...he must be prepared to stop his course until he can form exact notions, acquire precise ideas, both of resemblance between those things which have appeared most distinct, and of distinction between those which have appeared most alike. To do this... formal definitions would be useless; for he cannot be supposed to have one single notion in that precise form which would make it worth while to attach it to a word. One reason of the great difficulty which is found in treatises on this subject... the tacit assumption that nothing is necessary previously to actually embodying the terms and rules of the science, as if mere statement of definitions could give instantaneous power of using terms rightly. We shall here attempt... a wider degree of verbal explanation than is usual with the view of enabling the student to come to the definitions in some state of previous preparation."

"Find a fraction which, multiplied by itself, shall give 6, or... find the square root of 6. This can be shown to be an impossible problem; for it can be shown that no fraction whatsoever multiplied by itself, can give a whole number, unless it be itself a whole number disguised in a fractional form, such as 4⁄2 or 21⁄3. To this problem, then, there is but one answer, that it is self-contradictory. But if we propose the following problem,—to find a fraction which, multiplied by itself, shall give a product lying between 6 and 6 + a; we find that this problem admits of solution in every case. It therefore admits of solution however small a may be... as small as you please. ...there is such a thing as the square root of 6, and it is denoted by √6. But we do not say we actually find this, but that we approximate to it."

"Take a unit, halve it, halve the result, and so on continually. This gives—1 1⁄2 1⁄4 1⁄8 1⁄16 1⁄32 1⁄64 1⁄128 &c.Add these together, beginning from the first, namely, add the first two, the first three, the first four, &c... We see then a continual approach to 2, which is not reached, nor ever will be, for the deficit from 2 is always equal to the last term added. ...We say that—1, 1 + 1⁄2, 1 + 1⁄2 + 1⁄4, 1 + 1⁄2 + 1⁄4 + 1⁄8, &c. &c.is a series of quantities which continually approximate to the limit 2. Now the truth is, these several quantities are fixed, and do not approximate to 2. ...it is we ourselves who approximate to 2, by passing from one to another. Similarly when we say, "let x be a quantity which continually approximates to the limit 2," we mean, let us assign different values to x, each nearer to 2 than the preceding, and following such a law that we shall, by continuing our steps sufficiently far, actually find a value for x which shall be as near to 2 as we please."

"The following is exactly what we mean by a LIMIT. ...let the several values of x... bea1 a2 a3 a4. . . . &c.then if by passing from a1 to a2, from a2 to a3, &c., we continually approach to a certain quantity l [lower case L, for "limit"], so that each of the set differs from l by less than its predecessors; and if, in addition to this, the approach to l is of such a kind, that name any quantity we may, however small, namely z, we shall at last come to a series beginning, say with an, and continuing ad infinitum,an an+1 an+2. . . . &c.all the terms of which severally differ from l by less than z: then l is called the limit of x with respect to the supposition in question."

"When... we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit. It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1⁄0 for its limit."

"In every age of the world there has been an established system, which has been opposed from time to time by isolated and dissentient reformers. The established system has sometimes fallen, slowly and gradually: it has either been upset by the rising influence of some one man, or it has been sapped by gradual change of opinion in the many."

"During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical."

"A great many individuals ever since the rise of the mathematical method, have, each for himself, attacked its direct and indirect consequences. ...I shall call each of these persons a paradoxer, and his system a paradox. I use the word in the old sense: ...something which is apart from general opinion, either in subject-matter, method, or conclusion. ...Thus in the sixteenth century many spoke of the earth's motion as the paradox of Copernicus, who held the ingenuity of that theory in very high esteem, and some, I think, who even inclined towards it. In the seventeenth century, the depravation of meaning took place... Phillips says paradox is "a thing which seemeth strange"—here is the old meaning...—"and absurd, and is contrary to common opinion," which is an addition due to his own time."

"Spinoza's Philosophia Scripturæ Interpres, Exercitatio Paradoxa, printed anonymously ...is properly paradox, though also heterodox. It supposes, contrary to all opinion, orthodox and heterodox, that philosophy can... explain the Athanasian doctrine so as to be at least compatible with orthodoxy. The author would stand almost alone, if not quite; and this is what he meant."

"The manner in which a paradoxer will show himself, as to sense or nonsense, will not depend upon what he maintains, but upon whether he has or has not made a sufficient knowledge of what has been done by others, especially as to the mode of doing it, a preliminary to inventing knowledge for himself."

"Aspiring to lead others, they have never given themselves the fair chance of being first led by other others into something better than they can start for themselves; and that they should first do this is what both those classes of others have a fair right to expect. New knowledge... must come by contemplation of old knowledge... mechanical contrivance sometimes, not very often, escapes this rule."

"All the men who are now called discoverers, in every matter ruled by thought, have been men versed in the minds of their predecessors, and learned in what had been before them. There is not one exception. I do not say that every man has made direct acquantance with the whole of his mental ancestry... But... it is remarkable how many of the greatest names in all departments of knowledge have been real antiquaries in their several subjects. I may cite among those... in science, Aristotle, Plato, Ptolemy, Euclid, Archimedes, Roger Bacon, Copernicus, Francis Bacon, Ramus, Tycho Brahe, Galileo, Napier, Descartes, Leibnitz, Newton, Locke."

"I will not, from henceforward, talk to any squarer of the circle, trisector of the angle, duplicator of the cube, constructor of perpetual motion, subverter of gravitation, stagnator of the earth, builder of the universe, etc."

"Modern discoveries have not been made by large collections of facts, with subsequent discussion, separation, and resulting deduction of a truth thus rendered perceptible. A few facts have suggested an hypothesis, which means a supposition, proper to explain them. The necessary results of this supposition are worked out, and then, and not till then, other facts are examined to see if their ulterior results are found in nature."

"‘European science could never have reached its present height had it not been fertilised by successive wafts from the […] knowledge stored up in the East.’ ‘Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan and George Boole on the mathematical atmosphere of 1830–1865.’ ‘I do as George Boole and De Morgan did: I bow my head inreverent thankfulness to that mysterious East, whence come to us wafts of some transcendent power the nature of which we ourselves can hardly state in words.’"

"A very interesting detailed account of the peculiarities of the circle squarer, and of the futility of the attempts on the part of the Mathematicians to convince him of his errors, will be found in Augustus De Morgan's Budget of Paradoxes."

"The fact is known that having very thoroughly worked at the generalisations of Mathematics in theory and practice, Mr. De Morgan was enabled to establish with perfect precision the most highly generalised conception of Logic, perhaps, which it is possible to entertain. It is no new doctrine that Logic deals with the necessary laws of action of thought, and that Mathematics apply these laws to necessary matter of thought; but by showing that these laws can and must be applied with equal precision and equal necessity to all kinds of relations, and not only to those which the Aristotelian theory takes account of, he so enlarged the scope and intensified the power of Logic as an instrument, that we may hope for coming generations, as he must have hoped... another instalment of the kind... Mathematics are, meanwhile, and perhaps will always remain, the completest and most accurate example of the generalised Logic. At any rate, in the mind of the author, Logic and Mathematics as 'the two great branches of exact science, the study of the necessary laws of thought, the study of the necessary matter of thought, were always viewed in connection and antithesis."

"Dr. George Boole, author of The Laws of Thought had introduced himself in the year 1842 to Mr. De Morgan by a letter on the Differential and Integral Calculus then recently published. His character and pursuits were in many points like those of the author who found great pleasure in his correspondence and friendship. ...In 1847, his attention having been drawn to the subject by the publication of Mr. De Morgan's Formal Logic, he published the Mathematical Analysis of Logic and in the following year communicated... a paper on the Calculus of Logic. His great work, An Investigation into the Laws of Thought... was a development of the principle laid down in the Calculus..."

"When order is achieved among human beings by allowing them to interact with each other on their own initiative — subject only to the laws which uniformly apply to all of them — we have a system of spontaneous order in society."

"Comprehension is neither an arbitrary act nor a passive experience, but a responsible act claiming universal validity. Such knowing is indeed objective in the sense of establishing contact with a hidden reality; a contact that is defined as the condition for anticipating an indeterminate range of yet unknown (and perhaps yet inconceivable) true implications. It seems reasonable to describe this fusion of the personal and the objective as Personal Knowledge. Personal knowledge is an intellectual commitment, and as such inherently hazardous. Only affirmations that could be false can be said to convey objective knowledge of this kind."

"Ever since [Copernicus], writers eager to drive the lesson home have urged us [...] to abandon all sentimental egoism, and to see ourselves objectively in the true perspective of time and space. What precisely does this mean? In a full 'main feature' film, recapitulating faithfully the complete history of the universe, the rise of human beings from the first beginnings of man to the achievements of the twentieth century would flash by in a single second. Alternatively, if we decided to examine the universe objectively in the sense of paying equal attention to portions of equal mass, this would result in a lifelong preoccupation with interstellar dust, relieved only at brief intervals by a survey of incandescent masses of hydrogen — not in a thousand million lifetimes would the turn come to give man even a second's notice. It goes without saying that no one — scientists included — looks at the universe in this way, whatever lip-service is given to 'objectivity.'"

"The confidence placed in physical theory owes much to its possessing the same kind of excellence from which pure geometry and pure mathematics in general derive their interest, and for the sake of which they are cultivated. ... We cannot truly account for our acceptance of such theories without endorsing our acknowledgement of a beauty that exhilarates and a profundity that entrances us."

"The term 'simplicity' functions then merely as a disguise for another meaning than its own. It is used for smuggling an essential quality into our appreciation of a scientific theory, which a mistaken conception of objectivity forbids us to openly acknowledge."

"The descriptive sciences rely on skill and connoisseurship. At all these points the act of knowing includes an appraisal; and this personal coefficient, which shapes all factual knowledge, bridges in doing so the disjunction between subjectivity and objectivity. It implies the claim that man can transcend his own subjectivity by striving passionately to fulfil his personal obligations to universal standards."

"No sincere assertion of fact is essentially unaccompanied by feelings of intellectual satisfaction or of a persuasive desire and a sense of personal responsibility."

"In a strict usage the same symbol should never represent the act of sincerely asserting something and the content of what is asserted. For the symbolic distinction between the two, Frege has introduced the 'signpost' symbol. ... \vdash p is to signify the actual assertion of p, while the bare symbol p must henceforth be used only as part of a sentence. ... It should be clear from the modality of a sentence whether it is a question, a command, an invective, a complaint or an allegation of fact."

"Whitehead and Russell ... translate \vdash p imples q into the words 'it is asserted that p implies q'. But the phrase 'it is asserted' suggests an impersonal happening of assertions: 'it is asserted' as 'it is raining' or 'it happens'. The value of the assertion sign is lost if we allow ourselves to revert in our verbal translation of it to the muddle of a declaratory sentence which asserts itself or is impersonally asserted by nobody in particular."

"The correct reading of \vdash p written down by me in good faith is therefore 'I believe p', or some other words expressing the same fiduciary act."

"A declaratory sentence can be asserted, because it is an incomplete symbol, of indeterminate modality; while a question, a command, an invective, or any other sentence of fixed intention can no more be asserted than could my act of hewing wood or of drinking tea."

"While the articulate contents of science are successfully taught all over the world in hundreds of universities, the unspecifiable art of scientific research has not yet penetrated to many of these."

"To learn by example is to submit to authority. ...By watching the master and emulating his efforts in the presence of his example, the apprentice unconsciously picks up the rules of the art, including those which are not explicitly known to the master himself. These hidden rules can be assimilated only by a person who surrenders himself to that extent uncritically to the imitation of another. A society which wants to preserve a fund of personal knowledge must submit to tradition. ...Common Law ...is the most important system of strictly traditional activities."

"The recognition of certain basic impossibilities has laid the foundations of some major principles of physics and chemistry; similarly, recognition of the impossibility of understanding living things in terms of physics and chemistry, far from setting limits to our understanding of life, will guide it in the right direction. And even if the demonstration of this impossibility should prove of no great advantage in the pursuit of discovery, such a demonstration would help to draw a truer image of life and man than that given us by the present basic concepts of biology."

"Our view of life must account for how we know life; biological theories must allow for their own discovery and employment. Theories of evolution must provide for the creative acts which brought such theories into existence. Beginning with our own embodiment our theory of knowledge must endorse the ways we manifestly transcend our embodiment by acts of indwelling and extension into more subtle and intangible realms of being, where we meet our ultimate ends."

"Of all the questions we can ask ourselves the most important is: how is one best to live?"

"A civilized society is one which never ceases having a discussion with itself about what human life should best be."

"Folly tends to predominate over wisdom because it is usually easier to understand and more convenient (or exciting) to believe; but a little reflection usually sifts one from the other."

"The media no longer hesitate to whip up lurid anxieties in order to increase sales, in the process undermining social confidence and multiplying fears."

"Moral panics occur because the increased availability of information about what happens in our society is not matched by a public capacity to reflect upon and make sense of it. Western societies might be advanced in many ways, but if the standard of debates set by the popular media is anything to go by, their populations are woefully bad at engaging sensibly with new and evolving moral demands. This last remark is not meant to imply that there are, say, too few religious education lessons in schools. Far from it: religion is part of the problem, not the solution. And moral education is not best done by haranguing people, especially the young. On both counts standard views about moral education need rethinking. Religion is worse than an irrelevant as regards the inculcation of morality, for the following reasons: in an individualistic society, where personal wealth is the chief if not the sole measure of achievement, a morality that enjoins you to give your all to the poor that says it is easier for a camel to go through a needle’s eye than for the rich to enter heaven, and preaches selflessness towards one’s neighbor and complete obedience to a deity—such a morality, wholly opposed to the norms and practices not just accepted but extolled in our society, has little to offer. Most people ignore the contrast between such views and the universal instruction to go forth and multiply one’s income and possessions; and obey the latter. And when religious fundamentalists add a preparedness to incarcerate women, mutilate genitals, amputate hands, murder, bomb, and terrorise—all in the name of faith—then religious morality becomes not just irrelevant but dangerous. With such examples and contrasts, it has less than nothing to offer proper moral debate."

"New and challenging moral dilemmas are always likely to arise, so we need to try to make ourselves the kind of people who can respond thoughtfully."

"Emancipation is always at risk from the usual sources—demagogues, civil and international war, the tenure that superstitions have over the human imagination—so there are no guarantees that progress will continue."

"The claim is that educating moral sensibility through imagination has a general tendency, not a universal effect."

"Symbols have the unfortunate power to acquire the importance of what they symbolise."

"Worst of all, symbols sometimes live on in their own right when what they symbolise has long been forgotten."

"People not only live by symbols, but die by them, as wars of religion and nationalism attest."

"Four kinds of answer are standardly given to the question why religion exists. One is that it provides explanations—of the origin of the universe, of the way it works, of the apparently inexplicable things that happen in it, and of why it includes evil and suffering. Another is that religion provides comfort, giving hope of life after death, providing reassurance in a hostile world, and a means (by supplication, propitiation, and the practice of one or another form of prescribed behaviour) to get a better deal in it. A third is that it makes for social order, in promoting morality and social cohesion. And a fourth is that it rests on the natural ignorance, stupidity, superstitiousness and gullibility of mankind."

"Credulity, insecurity and desire form a potent combination in the human psyche. Together they make us eager to believe any nonsense if it purports to yield a glimpse of the future, or offers even the slenderest hope of success in love or fortune. On this rests the livelihood of many tricksters and charlatans—the crystal-ball gazers, palmists, astrologers, and readers of tarot cards."

"Tarot is not properly speaking, a divinatory practice, but a complex card game, invented in the fifteenth century, which somewhat like bridge, turns on capturing tricks."

"They beautifully illustrate the recipe for nonsense, which is: take something strange-looking, whose meaning is now forgotten, and liberally stir in imagination and superstition. In this respect the divinatory tarot is a paradigm of all superstitions and wonderfully illustrates humanity’s clever, ingenious, and intricate capacity for folly."

"“Evil” is first and foremost a religious notion. It means whatever a religion dislikes."

"And then, to sink the roots of this fear deep, the church introduces the idea of evil and the devil to children, for it knows that if it can cut early psychological scars it has a better chance of holding on to the minds thus wounded. All religions are anxious to proselytise the young. Society seems not to see either the absurdity or the danger in the fact that pupils in one school are taught, as truths of history, that the Normans conquered England in 1066 and that Jesus is the son of God, in another that the Normans conquered England in 1066 and Jesus is not the son of God but that Mohammed received the definitive divine revelation, in a third that the Normans conquered England in 1066 and that neither Jesus nor Mohammed is of any significance besides Guru Dev—and in a fourth that the Normans conquered England in 1066 and all three of Jesus, Mohammed and Guru Dev are false distractions, attention to whom is likely to provoke God’s jealous wrath. Yet in schools all over the country these antipathetic “truths” are being force-fed to different groups of pupils, none of whom is in a position to assess their credibility or worth. This is a serious form of child abuse. It sows the seeds of apartheids capable of resulting, in their logical conclusion, in murder and war, as history sickeningly and ceaselessly proves."

"There is no greater social evil than religion. It is the cancer in the body of humanity."

"Prudery expresses itself most forcibly as censorship."

"The growth of civilisation is measured by refinements of living and increasing distance from the immediacies of survival."

"There are even more general points to be made about “cultural politics”. Despite appearances in the absurd and often comic debate about “political correctness”, the concept of high culture is not the possession of the political Right, nor does rejection of “post-modernism” and its essence, relativism (rejection of which is required for defence not just of the notion but of the value of high culture), amount to rejection of a progressive political perspective. Political resistance against hegemonies of wealth, class, race and sex in the late-twentieth-century Western world has mistakenly included rejection of the idea that there are cultural and intellectual values which transcend accidental boundaries in human experience, and thereby constitute a possession for the species as a whole. It has been a cheap source of reputation for “theorists” to claim that “reality is the product of discourse”, which means that different discourses constitute different realities, and therefore the truth and value are relative. Those who mistake the politics of resentment for the politics of justice find such views useful, because they equate “high culture” with “culture of the politically and economically dominant class, race or sex”, and therefore take it that attacks on the former are attacks on the latter. One disastrous consequence is that it allows the political Right to present itself as the defender of art, literature and free intellectual speculation, whereas historically yet has it has been the right—from Plato onwards—which has sought to repress the best human endeavours in these respects, on the grounds that art, literature and the unrestricted play of reason threaten to set people free and make them equal. Rather than attacking the idea of a culture, therefore, reflective progressives (that is or should be a pleonasm) should assert their right to the high cultural terrain, and disentangle themselves from those aspects of movements, particularly in ethnic and sexual politics, whose tendency is not to promote the realisation of a just society but satisfaction of the petty appetite for revenge on groups perceived as historical oppressors. A better aim for progressives would be to free high culture from the citadel of inaccessibility—mainly financial—into which dominant groups have kidnapped it. They should not commit all their attention to promoting counter-culture or “mass” culture, for the excellent reason that—especially in respect of this latter—much of which passes for “mass” culture is a means of manipulating majorities into quiescence and uncritical acceptance of political and economic conditions favorable to dominant groups. This is notably the case with escapist entertainment and sports."

"Aristotle’s thought is that to live well and flourishingly, a person needs to be educated—which means: informed, and able to think. He is of course right."

"Part of the problem facing teaching in the contemporary world is that its status as a profession has been undermined by the contemptible view that only what makes money is admirable."

"When the Bible was the only book people knew, they naturally thought it embodied all that is true; but when their reading expanded, and with it the world, and a sense of other times, other voices, other possibilities and points of view, that authority could not last."

"It often enough goes too far, conjuring mountains from molehills (or from nothing), but excess is better than deficit in this instance, because unless the press were absolutely vigilant, the politicians would use their time-honoured methods—cover-up, sleight of hand, rationalisation—to get away with things. They would think themselves foolish not to. In consequence, consumers of the media have to exercise their own watchfulness. They have to exercise judgement concerning whether the media are offering a good story or a good point."

"One can judge between candidates by remembering Georges Pompidou’s remark that a statesman is a politician who puts himself at his country’s service, whereas a politician is a statesman who puts the country at his own service—or that of a group or class, usually his own."

"These amazingly recent achievements were built on dead bodies. For centuries ordinary people struggled against absolute monarchs, rich aristocrats, princely bishops, colonisers, landowners and industrial magnates for a say in the running of their own lives. They did it on barricades, in demonstrations charged by saber-wielding mounted cavalry, in sit-ins crushed by tanks. These people are dishonored by stay-at-homes on polling day."

"Sceptics and idlers think that their one vote will make no difference either way. They are wrong—wrong both in practice: some elections turn on mere handfuls of votes, as witness Al Gore’s fate in Florida—and in principle: for every refusal to vote is an act of self-disenfranchisement in which a citizen, betraying the endeavours of history, demotes himself into a serf."

"“The first principle of a civilised state,” said Walter Lippmann, “is that power is legitimate only when it is under contract.”"

"Power’s tendency to corrupt is a function of the work it does in liberating man’s worse characteristics."

"On the best view, justice is fairness."

"Thus justice is not equality but equity; as Aristotle says, “Injustice arises when equals are treated unequally, and unequals are treated equally.”"

"Politicians react to terrorism by limiting liberties….Zealots, most especially religious zealots, hate the liberality of liberal society; their terrorism aims to destroy it. To start putting handcuffs on ourselves is to achieve their goals for them."

"Tolerance is not only a key feature of liberalism, but—familiarly—its paradox too. Liberalism’s tolerance leaves the democracy of ideas to decide which among opposing viewpoints will prevail. The risk is the death of liberty itself, because those who live by hard and uncompromising views in political, moral and religious respects always, if given half a chance, silence liberals because liberalism, by its nature, threatens the hegemony they seek to impose."

"It is the technique of the baboon to try to get its way by violence."

"Anger is the chief emotion driving the deadly reciprocity of reprisal and revenge which has engulfed the recent history of the Middle East. The other dominating emotions of that tragedy—grief and terror—would bring the violence to an end without it. But anger, bitter and implacable when the only response it gets is anger returned, feeds on its reflection until it becomes insanity."

"But in vitriolic conflicts there is neither appropriateness nor proportion, so the arguments of history and justice become lost in vengeance."

"The recent discovery that humans have only twice as many genes as fruitflies has tipped the balance in the nature-nurture debate back to nurture. On this evidence it is our culture, history and belief-systems which make us what we are. We look at the rest of nature and see carnivores killing to eat, but we do not see zebras forming armies to wage war on gnus. It is only humans, with their congenital vice of inventing differences of politics and faith, who murder one another because they disagree. And what makes the tragedy more poignant is that the less secure their grounds for belief, the more anxious and violent their adherence to it—and the greater their readiness to kill and die in its defence."

"The ease with which birds and beasts, men, women and children, can now be shot into sudden oblivion is breathtaking. If the murderer had nothing but his hands, he could kill only a few on a single outing, if lucky. But a victim might fight back, and win. What a limitation, a frustration, for the poor murderer. But with a Kalashnikov – joy! – all such frustration vanishes. In a few seconds dozens of human beings can be left twitching and bleeding on the ground, their possibilities, hopes, loves and endeavours abruptly and arbitrarily obliterated, their families drowned in shock and grief. How satisfying for the murderous of mind; how fulfilling; and all thanks to those who make and sell guns."

"None of the major faiths is bloodless; history reeks with the gore of their wars and persecutions, all the more disgusting a spectacle for being, in essence, as simple as this: A kills B because B does not agree with A that there are fairies at the bottom of the garden. People should be left to believe what they like, so long as they harm no one else. Apart from normal expectations of politeness, it is not however clear why people should require their personal beliefs to be treated with special sensitivity by others, to the point that if others fail to tip-toe respectfully around them they will start throwing bombs. From a secular point of view, religious beliefs are at best absurd and at worse dangerous, and the amount of free play they are given in the public domain is a menace. Believed-in fairies should be kept at home as an entirely private matter, and their votaries encouraged to cease taking themselves so seriously that, when irritated by those who differ, they resort to Kalashnikovs. Apart from anything else, such reactions speak little confidence in their own violently-held certainties."

"“Faith-based” schools entrench and perpetuate the differences which too often lead to conflict; by educating children from all backgrounds together there is a far greater chance of mutual understanding and personal friendships. Enthusiasts of all faiths oppose secular education because exposure to other traditions has the effect of loosening the grip of their own. That, from a secular standpoint, is of course the consummation devoutly to be wished."

"At the time of writing there are, by one measure, more slaves in the world than at any time in history: 27 million people all told, in forced labour camps, debt bondage, the sex industry, professional beggary, domestic servitude, and work—work without pay and under threat of violence, which is the definition of slavery—in agriculture, mining and factories. A very large proportion of them are children, many of whom are commercially trafficked…. Those who are enslaved by history—who dwell on past wrongs, who keep ancient conflicts and quarrels alive, who even seek reparations for the wrongs suffered by their ancestors—would do the world a greater service by turning their attention to present-day slavery instead. A concerted effort might open the gates of China’s forced labour camps, free the Haitian sugar-plantation slaves, rescue the child prostitutes of Southeast Asia, and end the chattel slavery in Mauritania and the Sudan where slave markets still exist and where you can buy six children for one Kalashnikov."

"We can therefore all demand apologies from one another for mankind’s turpitude. But it is better worth remembering that we poison the present by our self-imposed slavery to unforgivingness over offences of the past—and that this explains almost all conflicts, from Northern Ireland via the Balkans to Kashmir. That is a form of slavery which we desperately need to abolish too."

"Outside the formal disciplines of logic and mathematics there are no absolute certainties—except of course in religion, which abounds in them, to the extent that people commit murder for their sake."

"It is an oddity that those who invoke the sanctity of life are not as invariably opposed to war, arms manufacture and capital punishment as they are to euthanasia and abortion. Yet these latter are intended to help the living, while the former are designed to harm them. A proper sense of what makes death good or bad has to include this premise: that the quality of life is the sacred thing, not its mere quantity."

"Remembrance Day should therefore also be about war’s causes: ugly faiths, intolerance, lust for power and revenge, mutual hatreds prompted by historical accidents or differences of colour, custom or culture."

"In one collective form of insanity, whole populations of people rise from sleep at about the same time each day, move in great herds to locations at some distance from their home territory, perform repetitive manoeuvers there, return home when evening falls, slump in front of a flickering coloured light, and after a while fall asleep again. They repeat the process day after day for decades. The disease is called “normal life”, and variations from it are regarded as eccentric; if the variations are marked enough they are even called “madness” and “delusion”. This thought is intended to show that what counts as abnormal is a relative matter."

"The nonsense people talk about cloning stems from the prison-cell of religious belief. Pious exclamations about the sanctity of life, and about not interfering with God’s purposes, conceal a farrago of confusion. Life’s sanctity resides in its quality, not its mere quantity, for there is nothing sacred in suffering. And if we were to “avoid interfering with God’s purposes” we would not use penicillin, nor raise money for the Third World’s starving, nor build a roof over our children’s heads (which, as it happens, Jesus instructed us not to—“consider the lilies of the field”—but not even Christians are foolish enough to obey)."

"If there is a deity of the kind imagined by votaries of the big mail-order religions such as Christianity and Islam, and if this deity is the creator of all things, then it is responsible for cancer, meningitis, millions of spontaneous abortions every day, mass killings of people in floods and earthquakes—and too great a mountain of other natural evils to list besides."

"This brings into focus a startling fact: that the practice of contemporary reviewing, whether fiction or non-fiction, owes nothing to self-styled “critical theorists”, those succubi of English Literature departments whose jargonings are read (if they are read at all) only by one another, and who have contributed nothing to the wider world since they hijacked the academic study of literature from its original Quiller-Couchian purpose: which was to educate, liberate, and civilise. The reason is that the professionalisation of the academy has diverted its form of criticism away from engagement with life."

"[Academic criticism] is not concerned with taste, but with technique; not with the common readers’ response to books and their connection with life as lived, but with specialist academic interest in methods and classifications, schools and “-isms”, unconscious influences, supposed hidden meanings, patriarchal oppressions, deconstruction of texts, and multiple readings."

"There are many ways that reviewing can be dishonest. Here is one illustration, drawn from no less a personnage than the self-appointed doyen of the literature dons, Terry Eagleton. A standard rhetorical device in discursive literature has the form “some say X, but I say Y.” The author might not disagree with X, but thinks Y is the more important point. A scurrilous reviewer can systematically misrepresent the author by saying, “the author says X” and omitting the author’s rider “Y”. This is one of Eagleton’s techniques of choice (chapter and verse can be abundantly supplied). Of course, this might not be intentional on Eagleton’s part; he might merely be stupid or lazy. But since it is better to doubt this, we have to conclude instead that he is guilty of wilful misrepresentation. It is alarming to think that such are the ethics of criticism he teaches his students at Manchester University."

"And sometimes Bloom is thunderously wrong—which is itself valuable, because he thereby ignites explosions of disagreement that prompt thought; and anyone who makes us think does us a service."

"Among the striking ideas that everywhere blossom in Bloom is his view that Shakespeare’s imaginative resources “transcend those of Yahweh, Jesus and Allah”, and provide a grander alternative vision of human nature. He is right. He says that genuinely intelligent people do not think ideologically; right again."

"The one thing that is more dangerous than true ignorance is the illusion of understanding."

"Ideas are the cogs of history—and too often the barricades that stand in its way."

"Confusion is the beginning of wisdom."

"Most moralists, and certainly all those of a religious persuasion, think that pupils should be “taught values” at school, not mainly so that they can apply them in thinking about the implications of science, history and other subjects, but to make them behave in ways that they (the moralists) find acceptable. But the point of equipping people to think about ethics is not to impose some partisan set of principles upon them, but to develop their powers of reflection, and to inform them of possibilities and options so that they can think for themselves."