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.

It cannot be that axioms established by argumentation should avail for the discovery of new works, since the subtlety of nature is greater many times over than the subtlety of argument. But axioms duly and orderly formed from particulars easily discover the way to new particulars, and thus render sciences active.

In the visible world, the Milky Way is a tiny fragment; within this fragment, the solar system is an infinitesimal speck, and of this speck our planet is a microscopic dot. On this dot, tiny lumps of impure carbon and water, of complicated structure, with somewhat unusual physical and chemical properties, crawl about for a few years, until they are dissolved again into the elements of which they are compounded. They divide their time between labour designed to postpone the moment of dissolution for themselves and frantic struggles to hasten it for others of their kind.

In the same manner as we are cautioned by religion to show our faith by our works we may very properly apply the principle to philosophy, and judge of it by its works; accounting that to be futile which is unproductive, and still more so, if instead of grapes and olives it yield but the thistle and thorns of dispute and contention.

So this is something... we see happening... in the war in Ukraine. A lot of people raise the question, "Why are Ukrainians resisting the Russian invasion as ferociously as they are?" and there's been a little bit of a debate over whether this is due to the fact that Ukrain is democratic, a liberal democracy, and Russia is not, or whether it's simply a fight over sovereignty... I think that that's a false dichotomy because you really don't fight for liberalism as an abstract principle. You fight for it as it is embedded in... your nation... From my... frequent visits to Ukraine... I believe... that's what's really going on, that Ukrainians want their sovereignty, but the reason they want it so desperately is that they want to have a free Ukraine and not Putin's Ukraine, not a... centralized dictatorship, and that's why they're willing to fight so tenaciously.

I should like you to consider that these functions (including passion, memory, and imagination) follow from the mere arrangement of the machine's organs every bit as naturally as the movements of a clock or other automaton follow from the arrangement of its counter-weights and wheels.

I have never in my life met a man like him for noble simplicity, and boundless truthfulness. I understood from the way he talked that anyone who chose could deceive him, and that he would forgive anyone afterwards who had deceived him, and that was why I grew to love him.

If there may be doubts for men and for a childless woman as to the way to, fulfil the will of God, for a mother that path is firmly and clearly defined, and if she fulfils it humbly with a simple heart she stands on the highest point of perfection a human being can attain, and becomes for all a model of that complete performance of God's will which all desire. Only a mother can before her death tranquilly say to Him who sent her into this world, and Whom she has served by bearing and bringing up children whom she has loved more than herself - only she having served Him in the way appointed to her can say with tranquillity, Now lettest Thou Thy servant depart in peace. And that is the highest perfection to which, as to the highest good, men aspire.

I have always thought respectable people scoundrels, and I look anxiously at my face every morning for signs of my becoming a scoundrel.

Secrecy is an instrument of conspiracy; it ought not, therefore, to be the system of a regular government.

There are ideal series of events which run parallel with the real ones. They rarely coincide. Men and circumstances generally modify the ideal train of events, so that it seems imperfect, and its consequences are equally imperfect. Thus with the Reformation; instead of Protestantism came Lutheranism.

It is the courage to make a clean breast of it in the face of every question that distinguishes the philosopher. He must be like Sophocles' Oedipus, who, seeking enlightenment concerning his terrible fate, pursues his indefatigable inquiry even though he divines that appalling horror awaits him in the answer. But most of us carry with us the Jocasta in our hearts, who begs Oedipus, for God's sake, not to inquire further.

The late philosopher Morris R. Cohen of CCNY was asked by a student in the metaphysics course, "Professor Cohen, how do I know that I exist?" The keen old prof replied, "And who is asking?"

Those hypotheses do not a little hinder the progress of Humane knowledge, that introduce Morals and Politicks into the Explications of Corporeal Nature, where all things are indeed transacted according to Laws Mechanical.

As money grows, care follows it and the hunger for more.

There is something beautiful about virtue, Captain. But I am just a poor guy.

The most heated defenders of a science, who cannot endure the slightest sneer at it, are commonly those who have not made very much progress in it and are secretly aware of this defect.

Good nature is, of all moral qualities, the one that the world needs most, and good nature is the result of ease and security, not of a life of arduous struggle. Modern methods of production have given us the possibility of ease and security for all; we have chosen, instead, to have overwork for some and starvation for the others. Hitherto we have continued to be as energetic as we were before there were machines; in this we have been foolish, but there is no reason to go on being foolish for ever.

In modern eyes, precious though wars may be they must not be waged solely for the sake of the ideal harvest. Only when forced upon one, is a war now thought permissible. It was not thus in ancient times. The earlier men were hunting men, and to hunt a neighboring tribe, kill the males, loot the village and possess the females, was the most profitable, as well as the most exciting, way of living. Thus were the more martial tribes selected, and in chiefs and peoples a pure pugnacity and love of glory came to mingle with the more fundamental appetite for plunder. Modern war is so expensive that we feel trade to be a better avenue to plunder; but modern man inherits all the innate pugnacity and all the love of glory of his ancestors. Showing war's irrationality and horror is of no effect on him. The horrors make the fascination. War is the strong life; it is life in extremis; war taxes are the only ones men never hesitate to pay, as the budgets of all nations show us.

All forms of violence are quests for identity. When you live on the frontier, you have no identity. You're a nobody.

I hold the brimming wineglass and relive the toils of my grandfathers and great-grandfathers. The sweat of my labor runs down like a fountain from my tall, intoxicated brow. I am a sack filled with meat and bones, blood, sweat, and tears, desires and visions.

In one point I fully agree with the gentlemen to whose general views I am opposed. I feel with them, that it is impossible for us, with our limited means, to attempt to educate the body of the people. We must at present do our best to form a class who may be interpreters between us and the millions whom we govern; a class of persons, Indian in blood and colour, but English in taste, in opinions, in morals, and in intellect. To that class we may leave it to refine the vernacular dialects of the country, to enrich those dialects with terms of science borrowed from the Western nomenclature, and to render them by degrees fit vehicles for conveying knowledge to the great mass of the population.

Jesus is too colossal for the pen of phrasemongers, however artful. No man can dispose of Christianity with a bon mot.

Enough had been thought, and said, and felt, and imagined. It was about time that something should be done.

He who steadily observes the moral precepts in which all religions concur, will never be questioned at the gates of heaven as to the dogmas in which they all differ.

Apparently the rise of consciousness is linked to certain kinds of privation. It is the bitterness of self-consciousness that we knowers know best. Critical of the illusions that sustained mankind in earlier times, this self-consciousness of ours does little to sustain us now. The question is: which is disenchanted, the world itself or the consciousness we have of it?

Each human reality is at the same time a direct project to metamorphose its own For-itself into an In-itself-For-itself, a project of the appropriation of the world as a totality of being-in-itself, in the form of a fundamental quality. Every human reality is a passion in that it projects losing itself so as to found being and by the same stroke to constitute the In-itself which escapes contingency by being its own foundation, the Ens causa sui, which religions call God. Thus the passion of man is the reverse of that of Christ, for man loses himself as man in order that God may be born. But the idea of God is contradictory and we lose ourselves in vain.

Much protest is naive; it expects quick, visible improvement and despairs and gives up when such improvement does not come. Protesters who hold out for longer have perhaps understood that success is not the proper goal. If protest depended on success, there would be little protest of any durability or significance. History simply affords too little evidence that anyone's individual protest is of any use. Protest that endures, I think, is moved by a hope far more modest than that of public success: namely, the hope of preserving qualities in one's own heart and spirit that would be destroyed by acquiescence.

It is not human nature we should accuse but the despicable conventions that pervert it.

The doctrines of Jesus are simple, and tend all to the happiness of man.

Creationists make it sound as though a "theory" is something you dreamt up after being drunk all night.

The art of being wise is the art of knowing what to overlook.

Women will be no longer made the slaves of, or dependent upon men ... They will be equal in education, rights, privileges and personal liberty.

As of old, the most enlightened, even, hope for a miracle from the twentieth-century deity, - suffrage. Life, happiness, joy, freedom, independence, - all that, and more, is to spring from suffrage. In her blind devotion woman does not see what people of intellect perceived fifty years ago: that suffrage is an evil, that it has only helped to enslave people, that it has but closed their eyes that they may not see how craftily they were made to submit.

If the brutes have consciousness and no souls, then it is clear that, in them, consciousness is a direct function of material changes; while, if they possess immaterial subjects of consciousness, or souls, then, as consciousness is brought into existence only as the consequence of molecular motion of the brain, it follows that it is an indirect product of material changes. The soul stands related to the body as the bell of a clock to the works, and consciousness answers to the sound which the bell gives out when it is struck.

In a constantly revolving circle every point is simultaneously a point of departure and a point of return. If we interrupt the rotation, not every point of departure is a point of return.

Hope is a good breakfast, but it is a bad supper.

Pornography and obscenity...work by specialism and fragmentation. They deal with a figure without a ground -- situations in which the human factor is suppressed in favor of sensations and kicks.

I am firmly convinced, therefore, that to set up a republic which is to last a long time, the way to set about it is to constitute it as Sparta and Venice were constituted; to place it in a strong position, and so to fortify it that no one will dream of taking it by a sudden assault; and, on the other hand, not to make it so large as to appear formidable to its neighbors. It should in this way be able to enjoy its form of government for a long time. For war is made on a commonwealth for two reasons: to subjugate it, and for fear of being subjugated by it.

For the first half of geological time our ancestors were bacteria. Most creatures still are bacteria, and each one of our trillions of cells is a colony of bacteria.

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.

The society which projects and undertakes the technological transformation of nature alters the base of domination by gradually replacing personal dependence (of the slave on the master, the serf on the lord of the manor, the lord on the donor of the fief, etc.) with dependence on the "objective order of things" (on economic laws, the market etc.).

Never buy what you do not want, because it is cheap; it will be dear to you.

The political is the most intense and extreme antagonism, and every concrete antagonism becomes that much more political the closer it approaches the most extreme point, that of the friend-enemy grouping.

It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners.

The harm that is done by a religion is of two sorts, the one depending on the kind of belief which it is thought ought to be given to it, and the other upon the particular tenets believed. As regards the kind of belief: it is thought virtuous to have faith-that is to say, to have a conviction which cannot be shaken by contrary evidence. Or, if contrary evidence might induce doubt, it is held that contrary evidence must be suppressed.

You do not know where death awaits you; so be ready for it everywhere.

Human knowledge and human power meet in one; for where the cause is not known the effect cannot be produced. Nature to be commanded must be obeyed; and that which in contemplation is as the cause is in operation as the rule.