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Who said: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”
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Paradox Quotes (31 quotes)

Ihm in vollem Maaße das Schicksal werde, welches in jeder Erkenntniß, … allezeit der Wahrheit zu Theil ward, der nur ein kurzes Siegesfest beschieden ist, zwischen den beiden langen Zeiträumen, wo sie als parador verdammt und als trivial geringgeschätzt wird.
[It] has always fallen to the lot of truth in every branch of knowledge, … [that] to truth only a brief celebration of victory is allowed between the two long periods during which it is condemned as paradoxical, or disparaged as trivial. The author of truth also usually meets with the former fate.
Conclusion for Preface, written at Dresden in August 1818, first German edition, Die Welt als Wille und Vorstellung, 4 Bücher nebst einem Anhange der die Kritik der Kentischen Philosophie (1819), xvi. As translated by E.F.J. Payne in The World as Will and Representation (1958, 1969), Vol. 1, xvii. In the preface, Schopenhauer is writing his hope that what he has written in the book will be accepted by those it reaches. Notice the statement of three stages of truth: condemnation; acceptance; trivializing. It may be the source of a condensed quote attributed (wrongly?) to Schopenhauer—seen in this collection as the quote that begins, “All truth passes through three stages…”
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Le paradoxe, c'est de la graine de vérité. Il suffit d'un terrain propice pour que cela germe, fleurisse et fructifie.
The paradox is the seed of truth. This germ just needs a fertile ground to flourish and bear fruit.
In Recueil d'Œuvres de Léo Errera: Botanique Générale (1908), 198. Google translation by Webmaster.
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A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more.
Science and the Common Understanding (1954), 53-4.
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A line is not made up of points. … In the same way, time is not made up of parts considered as indivisible “nows.”
Part of Aristotle’s reply to Zeno's paradox concerning continuity.
A succinct summary, not a direct quotation of Aristotle's words. From Aristotle's Physics, Book VI. Sections 1 and 9 as given by Florian Cajori in part 2 of an article 'The History of Zeno's Arguments on Motion', in The American Mathematical Monthly (Feb 1915), 22:2, 41.
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All those who think it paradoxical that so great a weight as the earth should not waver or move anywhere seem to me to go astray by making their judgment with an eye to their own affects and not to the property of the whole. For it would not still appear so extraordinary to them, I believe, if they stopped to think that the earth's magnitude compared to the whole body surrounding it is in the ratio of a point to it. For thus it seems possible for that which is relatively least to be supported and pressed against from all sides equally and at the same angle by that which is absolutely greatest and homogeneous.
'The Almagest 1', in Ptolemy: the Almagest; Nicolaus Copernicus: On the Revolutions of the Heavenly Spheres; Johannes Kepler: Epitome of Copernican Astronomy: IV - V The Harmonies of the World: V, trans. R. Catesby Taliaferro (1952), 11.
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Disinterestedness is as great a puzzle and paradox as ever. Indeed, strictly speaking, it is a species of irrationality, or insanity, as regards the individual’s self; a contradiction of the most essential nature of a sentient being, which is to move to pleasure and from pain.
In On the Study of Character: Including an Estimate of Phrenology (1861), 202.
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How quaint the way of paradox—
At common sense she gaily mocks.
In libretto of The Pirates of Penzance, collected in Original Plays (1907), 328.
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How wonderful that we have met this paradox. Now we have some hope of making progress.
Comment to observers when an experiment took an unexpected turn. In Bill Becker, 'Pioneer of the Atom', New York Times Sunday Magazine (20 Oct 1957), 52. Also in quoted in Ruth Moore Niels Bohr: the Man, His Science, & The World They Changed (1966), 140.
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I am afraid all we can do is to accept the paradox and try to accommodate ourselves to it, as we have done to so many paradoxes lately in modern physical theories. We shall have to get accustomed to the idea that the change of the quantity R, commonly called the 'radius of the universe', and the evolutionary changes of stars and stellar systems are two different processes, going on side by side without any apparent connection between them. After all the 'universe' is an hypothesis, like the atom, and must be allowed the freedom to have properties and to do things which would be contradictory and impossible for a finite material structure.
Kosmos (1932), 133.
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I find it [science] analytical, pretentious and superficial—largely because it does not address itself to dreams, chance, laughter, feelings, or paradox—in other words,—all the things I love the most.
My Last Sigh, trans. Abigail Israel (1983), 174.
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In its famous paradox, the equation of money and excrement, psychoanalysis becomes the first science to state what common sense and the poets have long known—that the essence of money is in its absolute worthlessness.
Life Against Death: the Psychoanalytical Meaning of History (1985), 254.
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It [analysis] lacks at this point such plan and unity that it is really amazing that it can be studied by so many people. The worst is that it has not at all been treated with rigor. There are only a few propositions in higher analysis that have been demonstrated with complete rigor. Everywhere one finds the unfortunate manner of reasoning from the particular to the general, and it is very unusual that with such a method one finds, in spite of everything, only a few of what many be called paradoxes. It is really very interesting to seek the reason.
In my opinion that arises from the fact that the functions with which analysis has until now been occupied can, for the most part, be expressed by means of powers. As soon as others appear, something that, it is true, does not often happen, this no longer works and from false conclusions there flow a mass of incorrect propositions.
From a letter to his professor Hansteen in Christiania, Oslo in Correspondence (1902), 23 . In Umberto Bottazzini and Warren Van Egmond, The Higher Calculus (1986), 87-88.
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On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols,'... Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient.
'The Work of Nicholas Bourbaki'American Mathematical Monthly (1970), 77, 134. In Carl C. Gaither, Alma E. Cavazos-Gaither, Mathematically Speaking: a Dictionary of Quotations (), 194.
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Paradox has been defined as “Truth standing on her head to get attention.”
In 'When Doctors Agree', The Paradoxes of Mr Pond (1937), 71.
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Paradoxical as it may at first appear, the fact is that, as W. H. George has said, scientific research is an art, not a science.
The Art of Scientific Investigation (1950, 1957), 138.
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Perhaps the greatest paradox of all is that there are paradoxes in mathematics. [Co-author with James R. Newman]
In Edward Kasner and James Newman, Mathematics and the Imagination (1940, 1949), 193.
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Science now finds itself in paradoxical strife with society: admired but mistrusted; offering hope for the future but creating ambiguous choice; richly supported yet unable to fulfill all its promise; boasting remarkable advances but criticized for not serving more directly the goals of society.
How to Win the Nobel Prize: An Unexpected Life in Science (2004), xi.
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Science starts with preconception, with the common culture, and with common sense. It moves on to observation, is marked by the discovery of paradox, and is then concerned with the correction of preconception. It moves then to use these corrections for the designing of further observation and for more refined experiment. And as it moves along this course the nature of the evidence and experience that nourish it becomes more and more unfamiliar; it is not just the language that is strange [to common culture].
From 'The Growth of Science and the Structure of Culture', Daedalus (Winter 1958), 87, No. 1, 67.
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Some may claim that is it unscientific to speak of the operations of nature as “miracles.” But the point of the title lies in the paradox of finding so many wonderful things ... subservient to the rule of law.
In Nature’s Miracles: Familiar Talks on Science (1899), Vol. 1, Introduction, v.
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The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes.
From letter (Jan 1828) to his former teacher Berndt Holmböe. In Morris Kline, Mathematics: The Loss of Certainty (1982), 170.
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The familiar idea of a god who is omniscient: someone who knows everything … does not immediately ring alarm bells in our brains; it is plausible that such a being could exist. Yet, when it is probed more closely one can show that omniscience of this sort creates a logical paradox and must, by the standards of human reason, therefore be judged impossible or be qualified in some way. To see this consider this test statement:
This statement is not known to be true by anyone.
Now consider the plight of our hypothetical Omniscient Being (“Big O”). Suppose first that this statement is true and Big O does not know it. Then Big O would not be omniscient. So, instead, suppose our statement is false. This means that someone must know the statement to be true; hence it must be true. So regardless of whether we assume at the outset that this statement is true or false, we are forced to conclude that it must be true! And therefore, since the statement is true, nobody (including Big O) can know that it is true. This shows that there must always be true statements that no being can know to be true. Hence there cannot be an Omniscient Being who knows all truths. Nor, by the same argument, could we or our future successors, ever attain such a state of omniscience. All that can be known is all that can be known, not all that is true.
In Impossibility: The Limits of Science and the Science of Limits (1999), 11.
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The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a spring of capital truths, and oneself for an oracle, is inborn in us.
In John Bartlett, Familiar Quotations: A Collection of Passages, Phrases, and Proverbs Traced (1968), 857.
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The Fundamental Regulator Paradox … The task of a regulator is to eliminate variation, but this variation is the ultimate source of information about the quality of its work. Therefore, the better the job a regulator does the less information it gets about how to improve.
In Gerald M. Weinberg and Daniela Weinberg, The Design of Stable Systems (1979), 250. As quoted in John R. Wilson, Evaluation of Human Work (2005), 220.
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The point of philosophy is to start with something so simple as not to seem worth stating and to end with something so paradoxical that no one will believe it
The Philosophy of Logical Atomism (1959), 10.
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The second [argument about motion] is the so-called Achilles, and it amounts to this, that in a race the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.
Statement of the Achilles and the Tortoise paradox in the relation of the discrete to the continuous.; perhaps the earliest example of the reductio ad absurdum method of proof.
Aristotle, Physics, 239b, 14-6. In Jonathan Barnes (ed.), The Complete Works of Aristotle (1984), Vol. 1, 404.
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The study of economics does not seem to require any specialised gifts of an unusually high order. Is it not, intellectually regarded, a very easy subject compared with the higher branches of philosophy and pure science? Yet good, or even competent, economists are the rarest of birds. An easy subject, at which very few excel! The paradox finds its explanation, perhaps, in that the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher—in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must lie entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood; as aloof and incorruptible as an artist, yet sometimes as near the earth as a politician.
'Alfred Marshall: 1842-1924' (1924). In Geoffrey Keynes (ed.), Essays in Biography (1933), 170.
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The [first] argument asserts the non-existence of notion on the ground that that which is in locomotion must arrive at the half-way stage before it arrives at the goal.
Dichotomy paradox
Aristotle, Physics, 239b10 11. In Reginald E. Allen, Greek Philosophy: Thales to Aristotle? (1991), 46.
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Unconscious, perhaps, of the remote tendency of his own labours, he [Joseph Black] undermined that doctrine of material heat, which he seemed to support. For, by his advocacy of latent heat, he taught that its movements constantly battle, not only some of our senses, but all of them; and that, while our feelings make us believe that heat is lost, our intellect makes us believe that it is not lost. Here, we have apparent destructability, and real indestructibility. To assert that a body received heat without its temperature rising, was to make the understanding correct the touch, and defy its dictates. It was a bold and beautiful paradox, which required courage as well as insight to broach, and the reception of which marks an epoch in the human mind, because it was an immense step towards idealizing matter into force.
History of Civilization in England (1861), Vol. 2, 494.
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Wheeler’s First Moral Principle: Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case life as a spacetime expert, however long, is more fun!
In E.F. Taylor and J.A. Wheeler, Spacetime Physics (1992), 20.
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When the mathematician says that such and such a proposition is true of one thing, it may be interesting, and it is surely safe. But when he tries to extend his proposition to everything, though it is much more interesting, it is also much more dangerous. In the transition from one to all, from the specific to the general, mathematics has made its greatest progress, and suffered its most serious setbacks, of which the logical paradoxes constitute the most important part. For, if mathematics is to advance securely and confidently, it must first set its affairs in order at home. [Coauthor with James R. Newman]
In Edward Kasner and James Newman, Mathematics and the Imagination (1940, 1949), 219.
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Whenever the essential nature of things is analysed by the intellect, it must seem absurd or paradoxical. This has always been recognized by the mystics, but has become a problem in science only very recently.
In The Tao of Physics (1975), 50.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton

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