Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, by stripping off the irrelevant accretions which veil it from the eye of the mind.

Money expresses all qualitative differences of things in terms of "how much?" Money, with all its colorlessness and indifference, becomes the common denominator of all values; irreparably it hollows out the core of things, their individuality, their specific value, and their incomparability. All things float with equal specific gravity in the constantly moving stream of money. All things lie on the same level and differ from one another only in the size of the area which they cover.

What has been shown by Machiavelli, who is often (like Nietzsche) congratulated for tearing off hypocritical masks, brutally revealing the truth, and so on, is not that men profess one thing and do another (although no doubt he shows this too) but that when they assume that the two ideals are compatible, or perhaps are even one and the same ideal, and do not allow this assumption to be questioned, they are guilty of bad faith (as the existentialists call it, or of "false consciousness," to use a Marxist formula) which their actual behavior exhibits. Machiavelli calls the bluff not just of official morality-the hypocrisies of ordinary life-but of one of the foundations of the central Western philosophical tradition, the belief in the ultimate compatibility of all genuine values. His own withers are unwrung. He has made his choice. He seems wholly unworried by, indeed scarcely aware of, parting company with traditional Western morality.

The remembrance of forbidden fruit is the earliest thing in the memory of each of us, as it is in that of mankind.

No longer able to believe in the Church religion, whose falsehood they had detected, and incapable of accepting true Christian teaching, which denounced their whole manner of life, these rich and powerful people, stranded without any religious conception of life, involuntarily returned to that pagan view of things which places life's meaning in personal enjoyment. And then among the upper classes what is called the "Renaissance of science and art" took place, which was really not only a denial of every religion, but also an assertion that religion was unnecessary.

To study the meaning of man and of life - I am making significant progress here. I have faith in myself. Man is a mystery: if you spend your entire life trying to puzzle it out, then do not say that you have wasted your time. I occupy myself with this mystery, because I want to be a man.

Scientific truth is characterized by its exactness and the certainty of its predictions. But these admirable qualities are contrived by science at the cost of remaining on a plane of secondary problems. leaving intact the ultimate and decisive questions. ... Yet science is but a small part of the human mind and organism. Where it stops, man does not stop.

As Christ had recommended peace during the whole of his life, mark with what anxiety he enforces it at the approach of his dissolution. Love one another, says he; as I have loved you, so love one another; and again, my peace I give unto you, my peace I leave you. Do you observe the legacy he leaves to those whom he loves? Is it a pompous retinue, a large estate, or empire? Nothing of this kind. What is it then? Peace he giveth, his peace he leaveth; peace, not only with our near connections, but with enemies and strangers!

An increase in the productivity of labour means nothing more than that the same capital creates the same value with less labour, or that less labour creates the same product with more capital.

Heroic love is the property of those superior natures who are called insane not because they do not know, but because they over-know.

If the gist of the controversy were to be expressed in a single sentence, one might say that the mechanists represented the opposition of the natural sciences to philosophic interference, while the dialecticians stood for the supremacy of philosophy over the sciences and thus reflected the characteristic tendency of Soviet ideological development. The mechanists' outlook might be called negative, while the dialecticians ascribed immense importance to philosophy and regarded themselves as specialists. The mechanists, however, had a much better idea of what science was about. The dialecticians were ignoramuses in this sphere and confined themselves to general formulas about the philosophical need to "generalize" and unify the sciences; on the other hand, they knew more than the mechanists about the history of philosophy. (Eventually the party condemned both camps, and created a dialectical synthesis of both forms of ignorance.)

The charlatan takes very different shapes according to circumstances; but at bottom he is a man who cares nothing about knowledge for its own sake, and only strives to gain the semblance of it that he may use it for his own personal ends, which are always selfish and material.

My hearers, this discourse has not wandered out into the world to look for conflict, it has not tried to get the better of anybody, it has not even tried to uphold anybody, as though there was battle without. It has spoken to you; not by way of explaining anything to you, but trying to speak secretly with you about your relationship to that secret wisdom mentioned in our text. Oh that nothing may upset you in respect to this, “neither life nor death nor things present nor things to come nor any other creature” (Romans 8:38) –not this discourse, which, though it may have profited you nothing, yet has striven for what after all is the first and the last, to help you have what the Scripture calls “faith in yourself before God.

Freedom can be manifested only in the void of beliefs, in the absence of axioms, and only where the laws have no more authority than a hypothesis.

The whole world is in some ways better than it's ever been in the past. And, indeed, I think for many people the meaning of their lives really depends on that belief. If you strip out that belief in progress, if you start thinking of the world in the way in which the ancient pre-Christian Europeans did, or the Buddhists and the Hindus or the Taoists of China do, many people think that's a kind of despair. I don't know how many times I've been told "If I thought that, John, I wouldn't get up in the morning" and "If I agreed with you, John, that history had no pattern of that kind, I wouldn't get up in the morning." I said, "Well, stay in bed a bit longer, you might find a better reason for getting up."

To look at a work of art in order to see how well certain rules are observed and canons conformed to impoverished perception. But to strive to note the ways in which certain conditions are fulfilled, such as the organic means by which the media is made to express and carry definite parts, or how the problem of adequate individualization is solved, sharpens esthetic perception and enriches its content.

Assembled in a crowd, people lose their powers of reasoning and their capacity for moral choice.

As the French say, there are three sexes - men, women, and clergymen.

This is a fine saying of Plato: That he who is discoursing about men should look also at earthly things as if he viewed them from some higher place; should look at them... a mixture of all things and an orderly combination of contraries.

[E]xperience has taught me that those who give their time to the absorbing claims of what is called society, not having leisure to keep up a large acquaintance with the organs of opinion, remain much more ignorant of the general state either of the public mind, or of the active and instructed part of it, than a recluse who reads the newspapers need be.

How did they meet? By chance, like everybody ... Where did they come from? From the nearest place. Where were they going? Do we know where we are going?

Cartan developed a general scheme of infinitesimal geometry in which Klein's notions were applied to the tangent plane and not to the n-dimensional manifold M itself. On the foundations of general infinitesimal geometry.

Religion in so far as it is a source of consolation is a hindrance to true faith; and in this sense atheism is a purification. I have to be an atheist with that part of myself which is not made for God. Among those in whom the supernatural part of themselves has not been awakened, the atheists are right and the believers wrong.

Now what is science? ...it is before all a classification, a manner of bringing together facts which appearances separate, though they are bound together by some natural and hidden kinship. Science, in other words, is a system of relations. ...it is in relations alone that objectivity must be sought. ...it is relations alone which can be regarded as objective.External objects... are really objects and not fleeting and fugitive appearances, because they are not only groups of sensations, but groups cemented by a constant bond. It is this bond, and this bond alone, which is the object in itself, and this bond is a relation.

An unlearned carpenter of my acquaintance once said in my hearing: "There is very little difference between one man and another; but what little there is, is very important." This distinction seems to me to go to the root of the matter.

It is time to be old, To take in sail: - The god of bounds, Who sets to seas a shore, Came to me in his fatal rounds, And said: 'No more!

Poetry and imagination begin life. A child will fall on its knees on the gravel walk at the sight of a pink hawthorn in full flower, when it is by itself, to praise God for it.

Reason can make little headway on its own and struggles to be heard; often it has to be - so to speak - armed by the fearsome epigram. French wit pricks like a needle, so that the thread goes through the hole.

But let there be no misunderstanding: it is not that a real man, the object of knowledge, philosophical reflection or technological intervention, has been substituted for the soul, the illusion of theologians. The man described for us, whom we are invited to free, is already in himself the effect of a subjection more profound than himself. A 'soul' inhabits him and brings him to existence, which is itself a factor in the mastery that power exercises over the body. The soul is the effect and instrument of a political anatomy; the soul is the prison of the body.

The history of other cultures is non-existent until it erupts in confrontation with the United States.

Nature must not win the game, but she cannot lose. And whenever the conscious mind clings to hard and fast concepts and gets caught in its own rules and regulations-as is unavoidable and of the essence of civilized consciousness-nature pops up with her inescapable demands.

Patriotism ruins history.

There are a thousand hacking at the branches of evil to one who is striking at the root, and it may be that he who bestows the largest amount of time and money on the needy is doing the most by his mode of life to produce that misery which he strives in vain to relieve.

We should have with each person the relationship of one conception of the universe to another conception of the universe, and not to a part of the universe.

The mental operation by which one achieves new concepts and which one denotes generally by the inadequate name of induction is not a simple but rather a very complicated process. Above all, it is not a logical process although such processes can be inserted as intermediary and auxiliary links. The principle effort that leads to the discovery of new knowledge is due to abstraction and imagination.

It reminds us that a man driven to desire to possess a certain female is a highly purposive individual. We have already noted that evolution tends to mark time when individuals have no reason to evolve. The same applies to individuals; they may be talented and intelligent, and yet waste their lives because they somehow lack the motivation to make use of these faculties. The best piece of luck that can befall any individual is to have a strong sense of purpose.

It is the principle of antipathy which leads us to speak of offences as deserving punishment. It is the corresponding principle of sympathy which leads us to speak of certain actions as meriting reward. This word merit can only lead to passion and error. It is effects good or bad which we ought alone to consider.

He who has injured thee was either stronger or weaker than thee. If weaker, spare him; if stronger, spare thyself.

The chalk is no unimportant element in the masonry of the earth's crust, and it impresses a peculiar stamp, varying with the conditions to which it is exposed, on the scenery of the districts in which it occurs.

In summary, then, the set theoretic 'needs' of physics are surprisingly similar to the set theoretic needs of pure logic. Both disciplines need some set theory to function at all. Both disciplines can 'live' - but live badly - on the meager diet of only predicative sets. Both can live extremely happily on the rich diet of impredicative sets. Insofar, then, as the indispensability of quantification over sets is any argument for their existence - and we will discuss why it is in the next section - we may say that it is a strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.

Our own experience provides the basic material for our imagination, whose range is therefore limited. It will not help to try to imagine that one has webbing on one's arms, which enables one to fly around at dusk and dawn catching insects in one's mouth; that one has very poor vision, and perceives the surrounding world by a system of reflected high-frequency sound signals; and that one spends the day hanging upside down by one's feet in an attic. Insofar as I can imagine this (which is not very far), it tells me only what it would be like for me to behave as a bat behaves. But that is not the question. I want to know what it is like for a bat to be a bat. Yet if I try to imagine this, I am restricted to the resources of my own mind, and those resources are inadequate to the task.

The medieval peasant prior to the 13th century does not compare himself to the feudal lord, nor does the artisan compare himself to the knight. ... From the king down to the hangman and the prostitute, everyone is "noble" in the sense that he considers himself as irreplaceable. In the "system of free competition," on the other hand, the notions on life's tasks and their value are not fundamental, they are but secondary derivations of the desire of all to surpass all the others. No "place" is more than a transitory point in this universal chase.