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.

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.

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.

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.

Albert Einstein called the intuitive or metaphoric mind a sacred gift. He added that the rational mind is a faithful servant. It it paradoxical that in the context of modern life we have begun to worship the servant and defile the divine.

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.

Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in infering that he is an inexact man. Every careful measurement in science is always given with the probable error ... every observer admits that he is likely wrong, and knows about how much wrong he is likely to be.

And so the great truth, now a paradox, may become a commonplace, that man is greater than his surroundings, and that the production of a breed of men and women, even in our great cities, less prone to disease, and pain, more noble in aspect, more rational in habits, more exultant in the pure joy of living, is not only scientifically possible, but that even the partial fulfillment of this dream, if dream it be, is the most worthy object towards which the lover of his kind can devote the best energies of his life.

As lightning clears the air of impalpable vapours, so an incisive paradox frees the human intelligence from the lethargic influence of latent and unsuspected assumptions. Paradox is the slayer of Prejudice.

By denying scientific principles, one may maintain any paradox.

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.

During the eighteenth and nineteenth centuries we can see the emergence of a tension that has yet to be resolved, concerning the attitude of scientists towards the usefulness of science. During this time, scientists were careful not to stress too much their relationships with industry or the military. They were seeking autonomy for their activities. On the other hand, to get social support there had to be some perception that the fruits of scientific activity could have useful results. One resolution of this dilemma was to assert that science only contributed at the discovery stage; others, industrialists for example, could apply the results. ... Few noted the ... obvious paradox of this position; that, if scientists were to be distanced from the 'evil' effects of the applications of scientific ideas, so too should they receive no credit for the 'good' or socially beneficial, effects of their activities.
Co-author with Philip Gummett (1947- ), -British social scientist

Ever since I was a boy, I’ve been fascinated by crazy science and such things as perpetual motion machines and logical paradoxes. I’ve always enjoyed keeping up with those ideas. I suppose I didn’t get into it seriously until I wrote my first book, Fads and Fallacies in the Name of Science. I was influenced by the Dianetics movement, now called Scientology, which was then promoted by John Campbell in Astounding Science Fiction. I was astonished at how rapidly the thing had become a cult.

Goethe said that he who cannot draw on 3,000 years of learning is living hand to mouth. It could just as well be said that individuals who do tap deeply into this rich cultural legacy are wealthy indeed. Yet the paradox is that much of this wisdom is buried in a sea of lesser books or like lost treasure beneath an ocean of online ignorance and trivia. That doesn’t mean that with a little bit of diligence you can’t tap into it. Yet many people, perhaps most, never take advantage of all this human experience. They aren’t obtaining knowledge beyond what they need to know for work or to get by. As a result, their view of our amazing world is diminished and their lives greatly circumscribed.

How quaint the way of paradox—
At common sense she gaily mocks.

How wonderful that we have met this paradox. Now we have some hope of making progress.

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.

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.

If an ancient city survives to become a modern city, like Naples, its readability in archaeological terms is enormously reduced. It’s a paradox of archaeology: you read the past best in its moments of trauma.

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.

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.

It is no paradox to say that in our most theoretical moods we may be nearest to our most practical applications.

It is the individual only who is timeless. Societies, cultures, and civilizations - past and present - are often incomprehensible to outsiders, but the individual’s hunger, anxieties, dreams, and preoccupations have remained unchanged through the millennia. Thus, we are up against the paradox that the individual who is more complex, unpredictable, and mysterious than any communal entity is the one nearest to our understanding; so near that even the interval of millennia cannot weaken our feeling of kinshiIf in some manner the voice of an individual reaches us from the remotest distance of time, it is a timeless voice speaking about ourselves.

It is the reciprocity of these appearances—that each party should think the other has contracted—that is so difficult to realise. Here is a paradox beyond even the imagination of Dean Swift. Gulliver regarded the Lilliputians as a race of dwarfs; and the Lilliputians regarded Gulliver as a giant. That is natural. If the Lilliputians had appeared dwarfs to Gulliver, and Gulliver had appeared a dwarf to the Lilliputians—but no! that is too absurd for fiction, and is an idea only to be found in the sober pages of science. …It is not only in space but in time that these strange variations occur. If we observed the aviator carefully we should infer that he was unusually slow in his movements; and events in the conveyance moving with him would be similarly retarded—as though time had forgotten to go on. His cigar lasts twice as long as one of ours. …But here again reciprocity comes in, because in the aviator’s opinion it is we who are travelling at 161,000 miles a second past him; and when he has made all allowances, he finds that it is we who are sluggish. Our cigar lasts twice as long as his.

It was the failures who had always won, but by the time they won they had come to be called successes. This is the final paradox, which men call evolution.

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.

One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.

Paradox has been defined as “Truth standing on her head to get attention.”

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.

Perhaps the greatest paradox of all is that there are paradoxes in mathematics.

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.

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].

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.

The ‘paradox’ is only a conflict between reality and your feeling of what reality ‘ought to be’.

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

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.

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.

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.

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.

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 process of mutation is the only known source of the raw materials of genetic variability, and hence of evolution. It is subject to experimental study, and considerable progress has been accomplished in this study in recent years. An apparent paradox has been disclosed. Although the living matter becomes adapted to its environment through formation of superior genetic patterns from mutational components, the process of mutation itself is not adaptive. On the contrary, the mutants which arise are, with rare exceptions, deleterious to their carriers, at least in the environments which the species normally encounters. Some of them are deleterious apparently in all environments. Therefore, the mutation process alone, not corrected and guided by natural selection, would result in degeneration and extinction rather than in improved adaptedness.

The progress of science is an excellent illustration of the truth of the paradox that man must lose his soul before he can find it.

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.

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.

The third [argument of motion is] to the effect that the flying arrow is at rest, which result follows from the assumption that time is composed of moments: if this assumption is not granted, the conclusion will not follow.Arrow paradox

The world is a contradiction; the universe a paradox.

Then I have more than an impression—it amounts to a certainty—that algebra is made repellent by the unwillingness or inability of teachers to explain why we suddenly start using a and b, what exponents mean apart from their handling, and how the paradoxical behavior of + and — came into being. There is no sense of history behind the teaching, so the feeling is given that the whole system dropped down readymade from the skies, to be used only by born jugglers. This is what paralyzes—with few exceptions—the infant, the adolescent, or the adult who is not a juggler himself.

To build a road is so much simpler than to think of what the country really needs. A roadless marsh is seemingly as worthless to the alphabetical conservationist as an undrained one was to the empire-builders. Solitude, the one natural resource still undowered of alphabets, is so far recognized as valuable only by ornithologists and cranes. Thus always does history, whether or marsh or market place, end in paradox. The ultimate value in these marshes is wildness, and the crane is wildness incarnate.

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.

What a curious picture it is to find man, homo sapiens, of divine origin, we are told, seriously considering going underground to escape the consequences of his own folly. With a little wisdom and foresight, surely it is not yet necessary to forsake life in the fresh air and in the warmth of sunlight. What a paradox if our own cleverness in science should force us to live underground with the moles.

What happens when you place an insupportable strain on a mass, such that it cannot remain where it is? While leaving it nowhere to go? This is … the oldest proto-paradox, the one about the irresistible force and the immovable body. The mass implodes. It is squeezed out of its own world into some other.

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!

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.

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.