Pure Mathematics is the class of all propositions of the form "p implies q," where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.

Death is a friend of ours; and he that is not ready to entertain him is not at home.

Of course I base my characters partly on the people I know-one can't escape it-but fictional characters are oversimplified; they're much less complex than the people one knows.

What good would it be to possess the whole universe if one were its only survivor?

The man of science who commits himself to even one statement which turns out to be devoid of good foundation loses somewhat of his reputation among his fellows, and if he be guilty of the same error often he loses not only his intellectual, but his moral standing among them. For it is justly felt that errors of this kind have their root rather in the moral than in the intellectual nature.

Is the position tenable, that certain phenomena, possible in Euclidean space, would be impossible in non-Euclidean space, so that experience, in establishing these phenomena, would directly contradict the non-Euclidean hypothesis? For my part I think no such question can be put. To my mind it is precisely equivalent to the following, whose absurdity is patent to all eyes: are there lengths expressible in meters and centimeters, but which can not be measured in fathoms, feet, and inches, so that experience, in ascertaining the existence of these lengths, would directly contradict the hypothesis that there are fathoms divided into six feet?

Many receive advice, few profit by it.

It must be borne in mind that it is through the channel of the child that the development of the mature man must go, and that the present ideas of the educating or training of the latter in the school and the family - even the family of the liberal or radical - are such as to stifle the natural growth of the child. Every institution of our day, the family, the State, our moral codes, sees in every strong, beautiful, uncompromising personality a deadly enemy; therefore every effort is being made to cramp human emotion and originality of thought in the individual into a straight-jacket from its earliest infancy; or to shape every human being according to one pattern; not into a well-rounded individuality, but into a patient work slave, professional automaton, tax-paying citizen, or righteous moralist.

It is now almost my sole rule of life to clear myself of cants and formulas, as of poisonous Nessus shirts.

books are only what we want them to be; rather, what we read into them.

He has now a second far greater success to gain: to seek out his real superiors, whom not the Tailor but the Almighty God has made superior to him, and see a little what he will do with these! Rebel against these also? Pass by with minatory eagle-glance, with calm-sniffing mockery, or even without any mockery or sniff, when these present themselves? The lion-hearted will never dream of such a thing. Forever far be it from him! His minatory eagle-glance will veil itself in softness of the dove: his lion- heart will become a lamb's; all is just indignation changed into just reverence, dissolved in blessed floods of noble humble love, how much heavenlier than any pride, nay, if you will, how much prouder!

I know. I know that I shall never again meet anything or anybody who will inspire me with passion. You know, it's quite a job starting to love somebody. You have to have energy, generosity, blindness. There is even a moment, in the very beginning, when you have to jump across a precipice: if you think about it you don't do it. I know I'll never jump again.

No power and no treasure can outweigh the extension of our knowledge.

Today I escaped from anxiety. Or no, I discarded it, because it was within me, in my own perceptions-not outside.

There is merely bad luck in not being loved; there is misfortune in not loving. All of us, today, are dying of this misfortune. For violence and hatred dry up the heart itself; the long fight for justice exhausts the love that nevertheless gave birth to it.

Scientific writing is abhorrently stylized and places a premium on poor quality.

The Public is an old woman. Let her maunder and mumble.

Art like life should be free, since both are experimental.

It is not enough for a wise man to study nature and truth; he should dare state truth for the benefit of the few who are willing and able to think.

Our colleges ought to have lit up in us a lasting relish for the better kind of man, a loss of appetite for mediocrities, and a disgust for cheapjacks. We ought to smell, as it were, the difference of quality in men and their proposals when we enter the world of affairs about us.

It is not your strength and your natural power that subjects all these people to you. Do not pretend then to rule them by force or to treat them with harshness. Satisfy their reasonable desires; alleviate their necessities; let your pleasure consist in being beneficent; advance them as much as you can, and you will act like the true king of desire.

I: My consciousness of the object is only a yet unrecognised consciousness of my production of the representation of an object. Of this production I know no more than that it is I who produce, and thus is all consciousness no more than a consciousness of myself, and so far perfectly comprehensible. Am I in the right? Spirit. Perfectly so ; but whence then is derived the necessity and universality thou hast ascribed to these propositions, to that of causality for instance?

It was mathematics, the non-empirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of nature and the universe that are concealed by appearances.

The civilized pagan recognizes life not in himself alone, but in societies of men-in the tribe, the clan, the family, the kingdom -and sacrifices his personal good for these societies. The motive power of his life is glory. His religion consists in the exaltation of the glory of those who are allied to him-the founders of his family, his ancestors, his rulers-and in worshiping gods who are exclusively protectors of his clan, his family, his nation, his government.

What one has to say to begin with is that, as humans, we are limited in intelligence and we really have no reliable foresight. So none of us will come up with answers to the whole great problem. What we can do is judge our behavior, our history, and our present situation by a better standard than "efficiency" or "profit," or those measures that we're still using to determine economic decisions.

The double meaning has been given to suit people's diverse intelligence. The apparent contradictions are meant to stimulate the learned to deeper study.

First, you know, a new theory is attacked as absurd; then it is admitted to be true, but obvious and insignificant; finally it is seen to be so important that its adversaries claim that they themselves discovered it.

If one doesn't know his mistakes, he won't want to correct them.

If there is no immortality, there is no virtue. ... Without God and immortal life? All things are lawful then, they can do what they like?

Do not be afraid. I am the First and the Last, and the living one, and I became dead, but look! I am living forever and ever, and I have the keys of death and of the Grave.

Talk of secularism is meaningful when it refers to the weakness of traditional religious belief or the lack of power of churches and other religious bodies. That is what is meant when we say Britain is a more secular country than the United States, and in this sense secularism is an achievable condition. But if it means a type of society in which religion is absent, secularism is a kind of contradiction, for it is defined by what it excludes. Post-Christian secular societies are formed by the beliefs they reject, whereas a society that had truly left Christianity behind would lack the concepts that shaped secular thought.

Even the most humble insect and the most insignificant idea are the military encampments of God. Within them, all of God is arranged in fighting position for a critical battle. Even in the most meaningless particle of earth and sky I hear God crying out: "Help me!" Everything is an egg in which God's sperm labors without rest, ceaselessly. Innumerable forces within and without it range themselves to defend it. With the light of the brain, with the flame of the heart, I besiege every cell where God is jailed, seeking, trying, hammering to open a gate in the fortress of matter, to create a gap through which God may issue in heroic attack.

Commerce with all nations, alliance with none, should be our motto.

What all these people are doing is not aggressive; they are inventing new possibilities of pleasure with strange parts of their body - through the eroticization of the body. I think it's ... a creative enterprise, which has as one of its main features what I call the desexualization of pleasure.

I understand Being in all and over all, as there is nothing without participation in Being, and there is no being without Essence. Thus nothing can be free of the Divine Presence.

When I am attacked by gloomy thoughts, nothing helps me so much as running to my books. They quickly absorb me and banish the clouds from my mind.

The world must be romanticized. In this way the originary meaning may be found again.

Waste no more time arguing what a good man should be. Be one.

The middle sort of historians (of which the most part are) spoil all; they will chew our meat for us.

In England women are still occasionally used instead of horses for hauling canal boats, because the labour required to produce horses and machines is an accurately known quantity, while that required to maintain the women of the surplus population is below all calculation.

Since Sputnik and the satellites, the planet is enclosed in a manmade environment that ends "Nature" and turns the globe into a repertory theater to be programmed.

How can it be that mathematics, being, after all, a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?

We should be offended when children are denied a proper education. We should be offended when children are told they will spend eternity in hell. We should be offended when medical science, for example stem-cell research, is compromised by the bigoted opinions of powerful and above all well-financed ignoramuses. We should be offended when voodoo, of all kinds, is given equal weight to science. We should be offended by hymen reconstruction surgery. We should be offended by 'female circumcision', euphemism for genital mutilation. We should be offended by stoning.

All teems with symbol; the wise man is the man who in any one thing can read another.

I thank thee, O Father, Lord of heaven and earth, because thou hast hid these things from the wise and prudent, and hast revealed them unto babes. Even so, Father: for so it seemed good in thy sight. All things are delivered unto me of my Father: and no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son, and he to whomsoever the Son will reveal him. Come unto me, all ye that labour and are heavy laden, and I will give you rest. Take my yoke upon you, and learn of me; for I am meek and lowly in heart: and ye shall find rest unto your souls. For my yoke is easy, and my burden is light.

If you feel irritated by the absurd remarks of two people whose conversation you happen to overhear, you should imagine that you are listening to a dialogue of two fools in a comedy.

Man has to awaken to wonder - and so perhaps do peoples. Science is a way of sending him to sleep again.