Quotes about respect
page 4

Barack Obama photo

“People ask me… "What do you still bring from Hawaii? How does it affect your character, how does it affect your politics?" I try to explain to them something about the Aloha Spirit. I try to explain to them this basic idea that we all have obligations to each other, that we're not alone, that if we see somebody who's in need we should help… that we look out for one another, that we deal with each other with courtesy and respect, and most importantly, that when you come from Hawaii, you start understanding that what's on the surface, what people look like — that doesn't determine who they are.
And that the power and strength of diversity, the ability of people from everywhere … whether they're black or white, whether they're Japanese-Americans or Korean-Americans or Filipino-Americans or whatever they are, they are just Americans, that all of us can work together and all of us can join together to create a better country.
And it's that spirit, that I'm absolutely convinced, is what America is looking for right now.
Because we've been divided for so long, we've been arguing for so long, a lot of times about things that aren't even worth arguing about, and ignoring the things that we should be doing to make the next generation have a better life — that I think people are hungry for a new politics, they're hungry for change, and that's why I decided to run for President of the United States.”

Barack Obama (1961) 44th President of the United States of America

Speech in Keehi Lagoon Beach Park, Hawaii, (8 August 2008) http://vids.myspace.com/index.cfm?fuseaction=vids.individual&VideoID=40384154
2008

Bertrand Russell photo
Theodore Roosevelt photo
Malcolm X photo
Friedrich Nietzsche photo
Abraham Lincoln photo
Pythagoras photo

“Holding fast to these things, you will know the worlds of gods and mortals which permeates and governs everything. And you will know, as is right, nature similar in all respects, so that you will neither entertain unreasonable hopes nor be neglectful of anything.”

Pythagoras (-585–-495 BC) ancient Greek mathematician and philosopher

As quoted in Divine Harmony: The Life and Teachings of Pythagoras by John Strohmeier and Peter Westbrook. (1999)
The Golden Verses

Livy photo
Hu Jintao photo
Don Soderquist photo

“How you treat everyone you encounter is the measure of the genuineness of your respect—and the heights you can each as a leader.”

Don Soderquist (1934–2016)

Don Soderquist “ Live Learn Lead to Make a Difference https://books.google.com/books?id=s0q7mZf9oDkC&lpg=pg=PP1&dq=Don%20Soderquist&pg=PP1#v=onepage&q&f=false, Thomas Nelson, April 2006 p. 135.
On Treating Everyone with Respect

“I never sought glory. Basic respect would suffice.”

Source: From the Notebooks of Dr. Brain (2007), Chapter 3 “Clash of the Icons” (p. 69)

Jordan Peterson photo

“You can't have the conversation about rights without the conversation about responsibility, because your rights are my responsibility. That's what they are technically. So, you just can't have only half of that discussion. And we're only having half of that discussion. Then the questions is, 'well what are you leaving out if you're only having that half of the discussion.' And the answer is, 'well, you're leaving out responsibility.' And then the questions is, 'Well, what are you leaving out if you're leaving out responsibility.' And the answer might be: 'Well maybe you're leaving out the meaning of life.' Here you are, suffering away. What makes it worthwhile? Rights? It's almost impossible to describe how bad an idea that is. Responsibility. That's what gives life meaning. Lift a load. Then you can tolerate yourself. Look at yourself. You're useless. Easily hurt. Easily killed. Why should you have any self-respect? Pick something up and carry it. Make it heavy enough so that you can think, yah, well, useless as I am, at least I can move that from there to there. For men, there's nothing but responsibility. Women have their sets of responsibilities. They're not the same. Women have to take primary responsibility for having infants at least, then also for caring for them. They're structured differently than men for biological necessity. Women know what they have to do. Men have to figure out what they have to do. And if they have nothing worth living for, then they stay Peter Pan. And why the hell not? The alternative to valued responsibility is low class pleasure. Why lift a load if there's nothing in it for you? And that's what we're doing to men and boys that's a very bad idea. Basically we give them the message, 'you're pathological and oppressive.' They often respond, 'fine then, why the hell should I play? If I get no credit for bearing responsibility, then you can be sure I won't bear any.”

Jordan Peterson (1962) Canadian clinical psychologist, cultural critic, and professor of psychology

Then your life is useless and meaningless, and you're full of self contempt and nihilism, and that's not good. And so that's what I think is going on at a deeper level with regard to men needing this direction. A man has to decide that he's going to do something. He has to decide that."
Concepts

Marquis de Sade photo
E. L. James photo
Kurt Vonnegut photo
Nathan Bedford Forrest photo
George Washington photo
Barack Obama photo
Abraham Lincoln photo

“Whereas, on the twenty-second day of September, in the year of our Lord one thousand eight hundred and sixty-two, a proclamation was issued by the President of the United States, containing, among other things, the following, to wit: That on the first day of January, in the year of our Lord one thousand eight hundred and sixty-three, all persons held as slaves within any State or designated part of a State, the people whereof shall then be in rebellion against the United States, shall be then, thenceforward, and forever free; and the Executive Government of the United States, including the military and naval authority thereof, will recognize and maintain the freedom of such persons, and will do no act or acts to repress such persons, or any of them, in any efforts they may make for their actual freedom. That the Executive will, on the first day of January aforesaid, by proclamation, designate the States and parts of States, if any, in which the people thereof, respectively, shall then be in rebellion against the United States; and the fact that any State, or the people thereof, shall on that day be, in good faith, represented in the Congress of the United States by members chosen thereto at elections wherein a majority of the qualified voters of such State shall have participated, shall, in the absence of strong countervailing testimony, be deemed conclusive evidence that such State, and the people thereof, are not then in rebellion against the United States.”

Abraham Lincoln (1809–1865) 16th President of the United States

1860s, Emancipation Proclamation (1863)

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Eric Shinseki photo
Pope Francis photo
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Bertrand Russell photo
I. K. Gujral photo
Louis C.K. photo
Justin Bieber photo

“I don't want to start singing about things like sex, drugs and swearing. I'm into love, and maybe I'll get more into making love when I'm older. But I want to be someone who is respected by everybody.”

Justin Bieber (1994) Canadian singer-songwriter, record producer, and actor

Source: Interview with V Magazine, as quoted in UsMagazine: Justin Bieber Talks Sex, Drugs and Turning 18 http://www.usmagazine.com/celebrity-news/news/justin-bieber-talks-sex-drugs-and-turning-18-2012101, January 2012

Theodore Roosevelt photo

“Among the wise and high-minded people who in self-respecting and genuine fashion strive earnestly for peace, there are the foolish fanatics always to be found in such a movement and always discrediting it — the men who form the lunatic fringe in all reform movements.”

Theodore Roosevelt (1858–1919) American politician, 26th president of the United States

Source: 1910s, Theodore Roosevelt — An Autobiography (1913), Ch. VII : The War of American and the Unready.

Jean Jacques Rousseau photo

“As a man's conduct is controlled by public fact, so is her religion ruled by authority. The daughter should follow her mother's religion, the wife her husband's. Were that religion false, the docility which leads mother and daughter to submit to nature's laws would blot out the sin of error in the sight of Goddess. Unable to judge for themselves they should accept the judgment of father and husband as that of the church. While men unaided cannot deduce the rules of their faith, neither can they assign limits to that faith by the evidence of reason; they allow themselves to be driven hither and thither by all sorts of external influences, they are ever above or below the truth. Extreme in everything, they are either altogether reckless or altogether pious; you never find them able to combine virtue and piety. Their natural exaggeration is not wholly to blame; the ill-regulated control exercised over them by men is partly responsible. Loose morals bring religion into contempt; the terrors of remorse make it a tyrant; this is why women have always too much or too little religion. As a woman's religion is controlled by authority it is more important to show her plainly what to believe than to explain the reasons for belief; for faith attached to ideas half-understood is the main source of fanaticism, and faith demanded on behalf of what is absurd leads to madness or unbelief. Whether our catechisms tend to produce impiety rather than fanaticism I cannot say, but I do know that they lead to one or other. In the first place, when you teach religion to little girls never make it gloomy or tiresome, never make it a task or a duty, and therefore never give them anything to learn by heart, not even their prayers. Be content to say your own prayers regularly in their presence, but do not compel them to join you. Let their prayers be short, as Christ himself has taught us. Let them always be said with becoming reverence and respect; remember that if we ask the Almighty to give heed to our words, we should at least give heed to what we mean to say.”

Emile, or On Education (1762), Book V

Lotfi A. Zadeh photo
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Abraham Lincoln photo
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Bertrand Russell photo

“There is no need to worry about mere size. We do not necessarily respect a fat man more than a thin man. Sir Isaac Newton was very much smaller than a hippopotamus, but we do not on that account value him less.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

"The Expanding Mental Universe", Saturday Evening Post (July 1959)
1950s

Apollonius of Tyana photo
Kurt Vonnegut photo

“Eliza and I composed a precocious critique of the Constitution of the United States of America … We argued that is was as good a scheme for misery as any, since its success in keeping the common people reasonably happy and proud depended on the strength of the people themselves — and yet it prescribed no practical machinery which would tend to make the people, as opposed to their elected representatives, strong.
We said it was possible that the framers of the Constitution were blind to the beauty of persons who were without great wealth or powerful friends or public office, but who were nonetheless genuinely strong.
We thought it was more likely, though, that their framers had not noticed that it was natural, and therefore almost inevitable, that human beings in extraordinary and enduring situations should think of themselves of composing new families. Eliza and I pointed out that this happened no less in democracies than in tyrannies, since human beings were the same the wide world over, and civilized only yesterday.
Elected representatives, hence, could be expected to become members of the famous and powerful family of elected representatives — which would, perfectly naturally, make them wary and squeamish and stingy with respect to all the other sorts of families which, again, perfectly naturally, subdivided mankind.
Eliza and I … proposed that the Constitution be amended so as to guarantee that every citizen, no matter how humble, or crazy or incompetent or deformed, somehow be given membership in some family as covertly xenophobic and crafty as the one their public servants formed.”

Source: Slapstick (1976), Ch. 6

Nâzım Hikmet photo
Leonardo Da Vinci photo
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Kenzaburō Ōe photo
Kurt Vonnegut photo
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Barack Obama photo
Barack Obama photo
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Max Scheler photo

“Jesus’ “mysterious” affection for the sinners, which is closely related to his ever-ready militancy against the scribes and pharisees, against every kind of social respectability … contains a kind of awareness that the great transformation of life, the radical change in outlook he demands of man (in Christian parlance it is called “rebirth”) is more accessible to the sinner than to the “just.” … Jesus is deeply skeptical toward all those who can feign the good man’s blissful existence through the simple lack of strong instincts and vitality. But all this does not suffice to explain this mysterious affection. In it there is something which can scarcely be expressed and must be felt. When the noblest men are in the company of the “good”—even of the truly “good,” not only of the pharisees—they are often overcome by a sudden impetuous yearning to go to the sinners, to suffer and struggle at their side and to share their grievous, gloomy lives. This is truly no temptation by the pleasures of sin, nor a demoniacal love for its “sweetness,” nor the attraction of the forbidden or the lure of novel experiences. It is an outburst of tempestuous love and tempestuous compassion for all men who are felt as one, indeed for the universe as a whole; a love which makes it seem frightful that only some should be “good,” while the others are “bad” and reprobate. In such moments, love and a deep sense of solidarity are repelled by the thought that we alone should be “good,” together with some others. This fills us with a kind of loathing for those who can accept this privilege, and we have an urge to move away from them.”

Max Scheler (1874–1928) German philosopher

Source: Das Ressentiment im Aufbau der Moralen (1912), L. Coser, trans. (1961), pp. 100-101

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Oswald Spengler photo

“If by "democracy" we mean the form which the Third Estate as such wishes to impart to public life as a whole, it must be concluded that democracy and plutocracy are the same thing under the two aspects of wish and actuality, theory and practice, knowing and doing. It is the tragic comedy of the world‑ improvers' and freedom‑ teachers' desperate fight against money that they are ipso facto assisting money to be effective. Respect for the big number—expressed in the principles of equality for all, natural rights, and universal suffrage—is just as much a class‑ ideal of the unclassed as freedom of public opinion (and more particularly freedom of the press) is so. These are ideals, but in actuality the freedom of public opinion involves the preparation of public opinion, which costs money; and the freedom of the press brings with it the question of possession of the press, which again is a matter of money; and with the franchise comes electioneering, in which he who pays the piper calls the tune. The representatives of the ideas look at one side only, while the representatives of money operate with the other. The concepts of Liberalism and Socialism are set in effective motion only by money. … There is no proletarian, not even a Communist movement, that has not operated in the interests of money, and for the time being permitted by money—and that without the idealists among its leaders having the slightest suspicion of the fact.”

Source: Vol. II, Alfred A. Knopf, 1928, pp. 401–02 https://archive.org/details/in.ernet.dli.2015.49906/page/n893/mode/2up
Der Untergang des Abendlandes, Welthistorische Perspektiven (1922)
The Decline of the West (1918, 1923)

Barack Obama photo
Adolph Freiherr Knigge photo

“Act well and properly, less to please others, more to keep your own self-respect.”

Handle gut und anständig, weniger anderen zu gefallen, eher um deine eigene Achtung nicht zu verscherzen.
Über den Umgang mit Menschen (1788)

Bertrand Russell photo

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

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Quoted in Alan Wood Bertrand Russell: The Passionate Skeptic: A Biography, Vol. 2 (1958), p. 233
1950s

Barack Obama photo
Barack Obama photo
Martin Luther photo

“Heretics cannot themselves appear good unless they depict the Church as evil, false, and mendacious. They alone wish to be esteemed as the good, but the Church must be made to appear evil in every respect.”

Martin Luther (1483–1546) seminal figure in Protestant Reformation

Dictata super Psalterium (Dictations on the Psalter). This is Luther's first major work from the years 1513 to 1515. (See What Luther Says, Ewald Martin Plass, ed., vol. 3, p. 1590. http://www.google.com/search?hl=en&lr=&tbs=bks%3A1&q=%22This+is+Luther%27s+first+major+work.+It+was+begun+in+the+summer+of+1513%22&btnG=Search&aq=f&aqi=&aql=&oq=&gs_rfai=)
Denifle, Heinrich, Luther and Lutherdom http://www.archive.org/details/cu31924029249567, p. 15; primary source: D. Martin Luthers Werke: kritische Gesamtausgabe, Weimar, Herman Bohlau, 1883, Vol. 3, p. 445. http://books.google.com/books?id=9YkVtSs8WdUC&pg=PA1&dq=%22Dictata+Super+Psalterium%22&hl=en&ei=Ms4qTJ3VGIe5nAewp8iqAQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCQQ6AEwADgK#v=onepage&q=%22Dictata%20Super%20Psalterium%22&f=false

Barack Obama photo

“And one of the rules of good civil society I believe is that you’re respectful of the people who disagree with you. And that's part of what makes civil society work. If you can have civil disagreements, and you can listen to each other and not just shout, that's what creates an environment that leads to progress over the long term.”

Barack Obama (1961) 44th President of the United States of America

Remarks by President Obama in Conversation with Members of Civil Society at YALI Regional Leadership Center, Kenyatta University,Nairobi, Kenya https://www.whitehouse.gov/the-press-office/2015/07/26/remarks-president-obama-conversation-members-civil-society (July 26, 2015)
2015

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Rabindranath Tagore photo

“That which transcends country, which is greater than country, can only reveal itself through one’s country. God has manifested his one eternal nature in just such a variety of forms… I can assure you that through the open sky of India you will be able to see the sun therefore there is no need to cross the ocean and sit at the window of a Christian church. … “I have nothing more to say,” answered Gora, “only this much I would add. You must understand that the Hindu religion takes in its lap, like a mother, people of different ideas and opinions, in other words, the Hindu religion looks upon man as man and does not count him as belonging to a particular party. It honours not only the wise but the foolish also and it shows respect not merely to one form of wisdom but to wisdom in all its aspects. Christians do not want to acknowledge diversity; they say that on one side is Christian religion and on the other eternal destruction, and between these two there is no middle path. And because we have studied under these Christians we have become ashamed of the variety that is there in Hinduism. We fail to see that through this diversity Hinduism is coming to realise the oneness of all. Unless we can free ourselves from this whirlpool of Christian teaching we shall not become fit for the glorious truths of Hindu religion.””

Rabindranath Tagore, Gora, translated into English, Calcutta, 1961. Quoted from Goel, S. R. (2016). History of Hindu-Christian encounters, AD 304 to 1996. Chapter 13 ISBN 9788185990354 https://web.archive.org/web/20120501043412/http://voiceofdharma.org/books/hhce/

Plato photo
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Barack Obama photo
Kurt Vonnegut photo
Barack Obama photo
Barack Obama photo

“Treat people with respect, whoever they are, and expect your governments to treat everybody with respect. And if you do that, then you’re going to be okay.”

Barack Obama (1961) 44th President of the United States of America

2014, Young Southeast Asian Leaders Initiative Town Hall (April 2014)

G. H. Hardy photo
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A.C. Bhaktivedanta Swami Prabhupada photo
Anne Frank photo
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Abraham Lincoln photo

“We think Slavery a great moral wrong, and while we do not claim the right to touch it where it exists, we wish to treat it as a wrong in the Territories, where our votes will reach it. We think that a respect for ourselves, a regard for future generations and for the God that made us, require that we put down this wrong where our votes will properly reach it. We think that species of labor an injury to free white men — in short, we think Slavery a great moral, social and political evil, tolerable only because, and so far as its actual existence makes it necessary to tolerate it, and that beyond that, it ought to be treated as a wrong.”

Abraham Lincoln (1809–1865) 16th President of the United States

1860s, Allow the humblest man an equal chance (1860)
Context: To us it appears natural to think that slaves are human beings; men, not property; that some of the things, at least, stated about men in the Declaration of Independence apply to them as well as to us. I say, we think, most of us, that this Charter of Freedom applies to the slave as well as to ourselves, that the class of arguments put forward to batter down that idea, are also calculated to break down the very idea of a free government, even for white men, and to undermine the very foundations of free society. We think Slavery a great moral wrong, and while we do not claim the right to touch it where it exists, we wish to treat it as a wrong in the Territories, where our votes will reach it. We think that a respect for ourselves, a regard for future generations and for the God that made us, require that we put down this wrong where our votes will properly reach it. We think that species of labor an injury to free white men — in short, we think Slavery a great moral, social and political evil, tolerable only because, and so far as its actual existence makes it necessary to tolerate it, and that beyond that, it ought to be treated as a wrong.

Pim Fortuyn photo

“I will not change my opinion, dear people, it is 5 minutes before twelve. Not just here in Holland. but in the whole of Europe. And is that what you want? I take my stand for this country, that which has been build up in the last five or six centuries. Damn it, we have a fifth column… Okay, let me tell you now straight the way it is! A fifth column of people who want to destroy this country! I will not go for that, and I say, "you can stay here, but you must adapt." I must hear "Allah is great", that I am a "dirty pig"… you are a "Christian dog". That is what they say, and you think that is okay… And I have so far been very reserved. I have never repeated that… but you accept being walked over, and I will not let that happen anymore. And that's where I get all those seats from (in the polls). Because this country is fed up! … C'est ça! That is what I stand for. And if I must express that otherwise, well, fine… but it is about your children, your grandchildren. For what else is this about? Must I explain more here? I can not do it any other way, and will not do it any other way. Then I would rather be finished off. Okay, fine… but the problem sir, will remain. That will remain. People have had more than enough of it. Damn it, in my city, Moroccan boys, Turkish boys… who do not rob the Turks, the Moroccans, but rob you and me and little old ladies. And the police? What they do? Damn it… nothing. They tell you: "If you say that, you discriminate". And that is what I express from the Dutch people. And I stand for it, I stand for it. Is that not allowed? Okay, I respect that. C'est ça”

Pim Fortuyn (1948–2002) Dutch politician

That’s all
Nederland 2 documentary "The Night of Fortuyn" https://www.youtube.com/watch?v=fgM9JozWOf0

Paul Valéry photo

“Great things are accomplished by men who are not conscious of the impotence of man. Such insensitiveness is precious.
But we must admit that criminals are not unlike our heroes in this respect.”

Paul Valéry (1871–1945) French poet, essayist, and philosopher

Source: Regards sur le monde actuel [Reflections on the World Today] (1931), p. 58

Theodore Roosevelt photo

“Let the man of learning, the man of lettered leisure, beware of that queer and cheap temptation to pose to himself and to others as a cynic, as the man who has outgrown emotions and beliefs, the man to whom good and evil are as one. The poorest way to face life is to face it with a sneer. There are many men who feel a kind of twisted pride in cynicism; there are many who confine themselves to criticism of the way others do what they themselves dare not even attempt. There is no more unhealthy being, no man less worthy of respect, than he who either really holds, or feigns to hold, an attitude of sneering disbelief toward all that is great and lofty, whether in achievement or in that noble effort which, even if it fails, comes to second achievement. A cynical habit of thought and speech, a readiness to criticize work which the critic himself never tries to perform, an intellectual aloofness which will not accept contact with life's realities — all these are marks, not as the possessor would fain to think, of superiority but of weakness. They mark the men unfit to bear their part painfully in the stern strife of living, who seek, in the affection of contempt for the achievements of others, to hide from others and from themselves in their own weakness. The role is easy; there is none easier, save only the role of the man who sneers alike at both criticism and performance.”

Theodore Roosevelt (1858–1919) American politician, 26th president of the United States

1910s, Citizenship in a Republic (1910)

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Warren Farrell photo

“Teaching the child to treat boundaries seriously teaches the child to respect the rights and needs of others. Thinking of another’s needs creates empathy.”

Warren Farrell (1943) author, spokesperson, expert witness, political candidate

Source: Father and Child Reunion (2001), p. 31.

John Nash photo

“Though I had success in my research both when I was mad and when I was not, eventually I felt that my work would be better respected if I thought and acted like a 'normal' person.”

John Nash (1928–2015) American mathematician and Nobel Prize laureate

As quoted in A Beautiful Mind, (2001); also cited in Quantum Phaith (2011), by Jeffrey Strickland, p. 197
2000s

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Thaksin Shinawatra photo

“I don't care whether I go back home or not. I just care how you can move our country forward, how the rule of law will be respected, and how the dignity of the Thai people must be respected.”

Thaksin Shinawatra (1949) Thai politician

Interview with World Policy http://www.worldpolicy.org/blog/2016/04/21/interview-thaksin-shinawatra-thailand

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Albert Schweitzer photo

“A word in conclusion about the relations between the whites and blacks. What must be the general character of the intercourse between them? Am I to treat the black man as my equal or my inferior? I must show him that I can respect the dignity of human personality in every one, and this attitude in me he must be able to see for himself; but the essential thing is that there shall be a real feeling of brotherliness. How far this is to find complete expression in the sayings and doings of daily life must be settled by circumstances. The negro is a child, and with children nothing can be done without the use of authority. We must, therefore, so arrange the circumstances of daily life that my natural authority can find expression. With regard to the negroes, then, I have coined the formula: "I am your brother, it is true, but your elder brother."”

Albert Schweitzer (1875–1965) French-German physician, theologian, musician and philosopher

Ch. VII, Social Problems in the Forest, p. 130 https://archive.org/stream/ontheedgeofthepr007259mbp#page/n163/mode/2up (1924 translation by Ch. Th. Campion); Schweitzer later repudiated such statements, saying "The time for speaking of older and younger brothers has passed.", as quoted in [Forrow, Lachlan, Foreword, Russell, C.E.B., African Notebook, Syracuse University Press, Albert Schweitzer library, 2002, 978-0-8156-0743-4, http://books.google.com/books?id=qa-TVXEkY3sC&pg=PR13, 23 June 2017, xiii]
Variant:
The African is my brother — but he is my younger brother by several centuries.
As quoted in The Observer (23 October 1955)
On the Edge of the Primeval Forest (1922)

Kurt Vonnegut photo
Barack Obama photo
Douglass C. North photo
Barack Obama photo
Epictetus photo
Georg Cantor photo

“Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

From Kant to Hilbert (1996)
Context: Mathematics is in its development entirely free and is only bound in the self-evident respect that its concepts must both be consistent with each other, and also stand in exact relationships, ordered by definitions, to those concepts which have previously been introduced and are already at hand and established. In particular, in the introduction of new numbers, it is only obligated to give definitions of them which will bestow such a determinacy and, in certain circumstances, such a relationship to the other numbers that they can in any given instance be precisely distinguished. As soon as a number satisfies all these conditions, it can and must be regarded in mathematics as existent and real.