A set is a Many that allows itself to be thought of as a One. — Georg Cantor

"I realize that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers."

"The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false."

"That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices."

"Every transfinite consistent multiplicity, that is, every transfinite set, must have a definite aleph as its cardinal number."

"[T]here exist no other sets than finite and denumerably infinite sets and continua... [I]n mathematics we can create only finite sequences, further by means of... and so on the order type ω, but only consisting of equal elements... but no other sets. Cantor and his disciples... think they have knowledge of all sorts of further sets; their fundamental principle... comes to about the same as the axiomaticians. ...[T]his principle is unjustified and... we assert that the several paradoxes of the Mengenlehre... have no right to exist... [I]t would have been the duty of Cantorians, immediately to reject a notion which gives rise to contradictions, because it is... not built... mathematically."

"I have never proceeded from any Genus supremum of the actual infinite. Quite the contrary, I have rigorously proved that there is absolutely no Genus supremum of the actual infinite. What surpasses all that is finite and transfinite is no Genus; it is the single, completely individual unity in which everything is included, which includes the Absolute, incomprehensible to the human understanding. This is the Actus Purissimus, which by many is called God. I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not — I do not say divisible — but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures."

"At one point a heated discussion arose over the possible interpretation of Lolita as a grandiose metaphor of the classic Europeans hopeless love for young, seductive, barbaric America. In his afterword to the novel Nabokov himself mentions this as the naive theory of one of the publishers who turned the book down. And although there cant be the slightest doubt that Nabokov did not mean to limit Lolita to that interpretation, there is no reason to exclude it as one of the novels many dimensions. The point, I felt, became obvious when one drew the line between Lolita as a delightfully frivolous story on the verge of pornography and Lolita as a literary masterpiece, the only convincing love story of our century."

"I did not go to join Kurtz there and then. I did not. I remained to dream the nightmare out to the end, and to show my loyalty to Kurtz once more. Destiny. My destiny! Droll thing life is — that mysterious arrangement of merciless logic for a futile purpose. The most you can hope from it is some knowledge of yourself — that comes too late — a crop of unextinguishable regrets. I have wrestled with death. It is the most unexciting contest you can imagine. It takes place in an impalpable grayness, with nothing underfoot, with nothing around, without spectators, without clamor, without glory, without the great desire of victory, without the great fear of defeat, in a sickly atmosphere of tepid skepticism, without much belief in your own right, and still less in that of your adversary. If such is the form of ultimate wisdom, then life is a greater riddle than some of us think it to be. I was within a hairs-breadth of the last opportunity for pronouncement, and I found with humiliation that probably I would have nothing to say. This is the reason why I affirm that Kurtz was a remarkable man. He had something to say. He said it. Since I had peeped over the edge myself, I understand better the meaning of his stare, that could not see the flame of the candle, but was wide enough to embrace the whole universe, piercing enough to penetrate all the hearts that beat in the darkness. He had summed up — he had judged. The horror! He was a remarkable man. After all, this was the expression of some sort of belief; it had candor, it had conviction, it had a vibrating note of revolt in its whisper, it had the appalling face of a glimpsed truth — the strange commingling of desire and hate."

"The Spanish Republic did not find itself free of obligations. For the most part the leaders were Freemasons. Before their duty to their country came their obligations to the Grand Orient. In my opinion, Freemasonry, with all its international influence, is the organization principally responsible for the political ruin of Spain, as well as the murder of Calvo Sotelo, who was executed in accordance with orders from the Grand Secretary of Freemasonry in Geneva."

"There can be no Good Will. Will is always Evil; it is persecution to others or selfishness."

"He was obeyed, yet he inspired neither love nor fear, nor even respect. He inspired uneasiness. That was it! Uneasiness. Not a definite mistrust — just uneasiness — nothing more. You have no idea how effective such a... a... faculty can be. He had no genius for organizing, for initiative, or for order even. That was evident in such things as the deplorable state of the station. He had no learning, and no intelligence. His position had come to him — why? Perhaps because he was never ill . . . He had served three terms of three years out there . . . Because triumphant health in the general rout of constitutions is a kind of power in itself."

"Well buy a lot of clothes, but we dont really need em Things we buy to cover up whats inside Cause they made us hate ourself and love their wealth."