Gottlob Frege created modern logic including "for all," "there exists," and rules of proof. Leibniz and Boole had dealt only with what we now call "propositional logic" (that is, no "for all" or "there exists"). They also did not concern themselves with rules of proof, since their aim was to reach truth by pure calculation with symbols for the propositions. Frege took the opposite track: instead of trying to reduce logic to calculation, he tried to reduce mathematics to logic, including the concept of number.

'Tis well to restrain the wicked, and in any case not to join him in his wrong-doing.

No one should forget: Eros alone can fulfill life; knowledge, never. Only Eros makes sense; knowledge is empty infinity; - for thoughts, there is always time; life has its time; there is no thought that comes too late; any desire can become a regret.

The work of charity, of the love of God, is to endeavor to to liberate God from brute matter, to endeavor to give consciousness to everything, to spiritualize or universalize everything; it is to dream that the very rocks may find a voice and work in accordance with the spirit of this dream; it is to dream that everything that exists may become conscious, that the Word may become life.

Concern for the symbol has completely disappeared from our science. And yet, if one were to give oneself the trouble, one could easily find, in certain parts at least of contemporary mathematics... symbols as clear, as beautiful, and as full of spiritual meaning as that of the circle and mediation. From modern thought to ancient wisdom the path would be short and direct, if one cared to take it.

Till women are more rationally educated, the progress in human virtue and improvement in knowledge must receive continual checks.

The key to a Christian conception of studies is the realization that prayer consists of attention. It is the orientation of all the attention of which the soul is capable toward God. The quality of the attention counts for much in the quality of the prayer. Warmth of heart cannot make up for it.

But love for an object eternal and infinite feeds the mind with joy alone, and a joy which is free from all sorrow. This is something greatly to be desired and to be sought with all our strength.

The materialists say, it is by means of a series of straight lines more or less perfect that one imagines the perfect straight line as an ideal limit. That is right, but the progression in itself necessarily contains what is infinite; it is in relation to the perfect straight line that one can say that such and such a straight line is less twisted than some other. ... Either one conceives the infinite or one does not conceive at all.

Our Traders in Men (an unnatural commodity!) must know the wickedness of that Slave-Trade, if they attend to reasoning, or the dictates of their own hearts; and such as shun and stiffle all these, wilfully sacrifice Conscience, and the character of integrity to that golden Idol.

To be in touch with senses and emotions beyond conquest is to enter the realm of the mysterious.

Go where he will, the wise man is at home, His hearth the earth, his hall the azure dome.

This is the end of the web of the statesman activity: the direct interweaving of the characters of restrained and courageous men, when the kingly science has drawn them together by friendship and community of sentiment into a common life, and having perfected the most glorious and the best of all textures, clothes with it all the inhabitants of the state, both slaves and freemen, holds them together by this fabric, and omitting nothing which ought to belong to a happy state, rules and watches over them.

Political independence, as the right to owe his existence and continuance in society not to the arbitrary will of another, but to his own rights and powers as a member of the commonwealth.

Where knowledge is a duty, ignorance is a crime. 

A nihilist is not one who believes in nothing, but one who does not believe in what exists.

Whoever imposes severe punishment becomes repulsive to the people; while he who awards mild punishment becomes contemptible. But whoever imposes punishment as deserved becomes respectable. For punishment when awarded with due consideration, makes the people devoted to righteousness and to works productive of wealth and enjoyment; while punishment, when ill-awarded under the influence of greed and anger or owing to ignorance, excites fury even among hermits and ascetics dwelling in forests, not to speak of householders.

True confessions are written with tears only. But my tears would drown the world, as my inner fire would reduce it to ashes.

I believe that the nature of man is a contradiction rooted in the conditions of human existence that requires a search for solutions, which in their turn create new contradictions and now the need for answers. I believe that every answer to these contradictions can really satisfy the condition of helping man to overcome the sense of separation and to achieve a sense of agreement, of unity, and of belonging. I believe that in every answer to these contradictions, man has the possibility of choosing only between going forward or going back; these choices, which are translated into specific actions, are means toward the regressing or toward the progressing of the humanity that is in us.

It is impossible for any man, when the most favourable circumstances concur, to acquire sufficient knowledge and strength of mind to discharge the duties of a king, entrusted with uncontrolled power; how then must they be violated when his very elevation is an insuperable bar to the attainment of either wisdom or virtue; when all the feelings of a man are stifled by flattery, and reflection shut out by pleasure! Surely it is madness to make the fate of thousands depend on the caprice of a weak fellow creature, whose very station sinks him NECESSARILY below the meanest of his subjects! But one power should not be thrown down to exalt another--for all power intoxicates weak man; and its abuse proves, that the more equality there is established among men, the more virtue and happiness will reign in society.

The most disadvantageous peace is better than the most just war.

As for me, I am mean: that means that I need the suffering of others to exist. A flame. A flame in their hearts. When I am all alone, I am extinguished.

For why do you hasten to remove things that hurt your eyes, but if anything gnaws your mind, defer the time of curing it from year to year?

Some books are to be tasted, others to be swallowed, and some few to be chewed and digested; that is, some books are to be read only in parts; others to be read, but not curiously; and some few to be read wholly, and with diligence and attention.

What a singular destiny has been that of this remarkable man! To be regarded in his own age as a classic, and in ours as a companion! To receive from his contemporaries that full homage which men of genius have in general received only from posterity! To be more intimately known to posterity than other men are known to their contemporaries!

A people represents not so much an aggregate of ideas and theories as of obsessions.

No, you cannot expect people to understand the higher reaches of philosophy. Culture should be taken out of the hands of the dollar chasers. We need a national subsidy for literature. It is disgraceful that artists are treated like peddlers and that art works have to be sold like soap.

All that is Life in me urges me to give up God.

A fundamental economic reconstruction, bringing with it very far-reaching changes in ways of thinking and feeling, in philosophy and art and private relations, seems absolutely necessary if industrialism is to become the servant of man instead of his master. In all this, I am at one with the Bolsheviks; politically, I criticize them only when their methods seem to involve a departure from their own ideals.

Perhaps the promise of phallus is always dissatisfying in some way.

Underlying the concept of positivity is the conviction that the positive is intrinsically positive in itself, without anyone pausing to ask what is to be regarded as positive. ... It is significant and really quite interesting that the term 'positive' actually contains this ambivalence. On the one hand, 'positive' means what is given, is postulated, is there-as when we speak of positivism as the philosophy that sticks to the facts. But, equally, 'positive' also refers to the good, the approvable, in a certain sense, the ideal. And I imagine that this semantic constellation expresses with precision what countless people actually feel to be the case.

Anyone can escape into sleep, we are all geniuses when we dream, the butcher's the poet's equal there.

Do not fight against these harmful spells. For you do not know what God wants with them. You do not know the greater divine plan behind it all.

Against the diseases of the mind, philosophy provides sufficient antidotes. The instruments which it employs for this purpose are the virtues; the root of which, whence all the rest proceed, is prudence. This virtue comprehends the whole art of living discreetly, justly, and honorably, and is, in fact, the same thing with wisdom. It instructs men to free their understandings from the clouds of prejudice; to exercise temperance and fortitude in the government of themselves: and to practice justice towards others. Although pleasure, or happiness, which is the end of living, be superior to virtue, which is only the means, it is every one's interest to practice all the virtues; for in a happy life, pleasure can never be separated from virtue.

Do not resist the evil-doer and take no part in doing so, either in the violent deeds of the administration, in the law courts, the collection of taxes, or above all in soldiering, and no one in the world will be able to enslave you.

An extra-terrestrial philosopher, who had watched a single youth up to the age of twenty-one and had never come across any other human being, might conclude that it is the nature of human beings to grow continually taller and wiser in an indefinite progress towards perfection; and this generalisation would be just as well founded as the generalisation which evolutionists base upon the previous history of this planet.

Seek after the good, and with much toil shall ye find it; the evil turns up of itself without your seeking it.

The case of mere titles is so absurd that it would deserve to be treated only with ridicule were t not for the serious mischief they impose on mankind. The feudal system was a ferocious monster, devouring, where it came, all that the friend of humanity regards with attachment and love. The system of titles appears under a different form. The monster is at length destroyed, and they who followed in his train, and fattened upon the carcasses of those he slew, have stuffed his skin, and, b exhibiting it, hope still to terrify mankind into patient and pusillanimity.

Everything that is possible demands to exist.

When one is a stranger to oneself then one is estranged from others too. If one is out of touch with oneself, then one cannot touch others.

The people are led to find in the productive apparatus the effective agent of thought and action to which their personal thought and action can and must be surrendered. And in this transfer, the apparatus also assumes the role of a moral agent.

There are in our minds in solution a vast number of emotional attitudes, feelings ready to be re-excited when the proper stimulus arrives, and more than anything else it is these forms, this residue of experience, which, fuller and richer than in the mind if the ordinary man, constitute the artist's capital. What is called the magic of the artist resides in his ability to transfer these values from one field of experience to another, to attach them to objects of our common life, and by his imaginative insight make these objects poignant and momentous. Not colors, not sense qualities as such, are either matter or form, but these qualities as thoroughly imbued, impregnated, with transferred value. And then they are either matter or form according to the direction of our interest.

I felt less alone when I didn't know you yet: I was waiting for the other. I thought only of his strength and never of my weakness. And now here you are, Orestes, it was you. I look at you and I see that we are two orphans.

Men seem to pursue honour in order that they may believe themselves to be good. Accordingly, they seek to be honoured by the wise, and by those who know them well, and on the score of virtue; it is clear, therefore, that in their opinion at any rate, virtue is superior to honour. Perhaps, then, one ought to say that virtue rather than honour is the end of the political life; yet even virtue is plainly too imperfect: for it seems that a man might have all the virtues and yet be asleep, or fail to achieve anything all his life; moreover, such a person may suffer the greatest evils and misfortunes. And no one, in this case, would call a man, who passed his life in this manner, happy, except for argument's sake.

There is more to a science fiction story than the science it contains.

The more cunning a man is, the less he suspects that he will be caught in a simple thing. The more cunning a man is, the simpler the trap he must be caught in.

I have always taken as the standard of the mode of teaching and writing, not the abstract, particular, professional philosopher, but universal man, that I have regarded man as the criterion of truth, and not this or that founder of a system, and have from the first placed the highest excellence of the philosopher in this, that he abstains, both as a man and as an author, from the ostentation of philosophy, i.e., that he is a philosopher only in reality, not formally, that he is a quiet philosopher, not a loud and still less a brawling one.