A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth such as two true sentences which put together seem incompatible as both being true. Typically however, quoted paradoxical statements do not imply a real contradiction and the puzzling results can be rectified by demonstrating that one or more of the premises themselves are not really true, a play on words, faulty and/or cannot all be true together.
- Paradox is the sharpest scalpel in the satchel of science. Nothing concentrates the mind as effectively, regardless of whether it pits two competing theories against each other, or theory against observation, or a compelling mathematical deduction against ordinary common sense.
- Hans Christian von Baeyer, Information, The new Language of Science, Chapter 23, p. 204.
- It seems a little paradoxical to construct a configuration space with the coordinates of points which do not exist.
- In the matter of reforming things, as distinct from deforming them, there is one plain and simple principle; a principle which will probably be called a paradox. There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it and says, "I don't see the use of this; let us clear it away." To which the more intelligent type of reformer will do well to answer: "If you don't see the use of it, I certainly won't let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it."
This paradox rests on the most elementary common sense. The gate or fence did not grow there. It was not set up by somnambulists who built it in their sleep. It is highly improbable that it was put there by escaped lunatics who were for some reason loose in the street. Some person had some reason for thinking it would be a good thing for somebody. And until we know what the reason was, we really cannot judge whether the reason was reasonable.
- G. K. Chesterton, in The Thing : Why I Am A Catholic (1929), Ch. IV : The Drift From Domesticity
- Since the beginning of time tricksters (the mythological origin of all clowns) have embraced life's paradoxes, creating coherence through confusion — adding disorder to the world in order to expose its lies and speak the truth.
- The test of a first-rate intelligence is the ability to hold two opposing ideas in mind at the same time and still retain the ability to function.
- The Greeks observed a paradox about the dyad: While it appears separate from unity, its opposite poles remember their source and attract each other in an attempt to merge and return to the state of unity. The dyad simultaneously divides and unites, repels and attracts, separates and returns.
- Priya Hemenway in Divine Proportion : Φ (Phi) In Art, Nature, and Science (2005), Ch. 2 : Pythagoras and the Mystery of Numbers, p. 52.
- The best paradoxes raise questions about what kinds of contradictions can occur — what species of impossibilities are possible.
- William Poundstone, Labyrinths of Reason (1988), chapter 1, p. 19.
- Paradox is thus a much deeper and universal concept than the ancients would have dreamed. Rather than an oddity, it is a mainstay of the philosophy of science.
- William Poundstone, Labyrinths of Reason, chapter 1, p. 23.
- The assumption that anything true is knowable is the grandfather of paradoxes.
- William Poundstone, Labyrinths of Reason, chapter 12, p. 260.
- A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.
- These are old fond paradoxes to make fools laugh i' the alehouse.
- You undergo too strict a paradox,
Striving to make an ugly deed look fair.
- More than any other Hellenic thinker, Julian insisted on the virtue of paradox and on the importance of the search for religious truth.
- Gedaliahu A. G. Stroumsa, in Hidden Wisdom: Esoteric Traditions and the Roots of Christian Mysticism (2005).
- PARADOX: A statement that reduces the matter at hand to complete obscurity while clarifying it. ... Paradoxes are sensitive and can be routed by sneering.
- Gene Wolfe, "Words Weird and Wonderful", Castle of Days (1992), p. 237
- Paradoxes explain everything. Since they do, they cannot be explained.
- Gene Wolfe, The Book of the Short Sun, Volume 1: On Blue's Waters (1999), Ch. 9.
Hoyt's New Cyclopedia Of Practical Quotations 
- Quotes reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 579.
- For thence, — a paradox
Which comforts while it mocks, —
Shall life succeed in that it seems to fail:
What I aspired to be,
And was not, comforts me:
A brute I might have been, but would not sink i' the scale.
- Robert Browning, Rabbi-Ben-Ezra, Stanza 7.
- Then there is that glorious Epicurean paradox, uttered by my friend, the Historian, in one of his flashing moments: "Give us the luxuries of life, and we will dispense with its necessaries."
- Oliver Wendell Holmes, Sr., The Autocrat of the Breakfast Table (1858), VI.
- The mind begins to boggle at unnatural substances as things paradoxical and incomprehensible.
- Bishop South, Sermons.