A line is not made up of points. … In the same way, time is not made up parts considered as indivisible 'nows.'
Part of Aristotle's reply to Zeno's paradox concerning continuity.

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

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.

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.

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 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 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 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 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.

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.