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A statement which appears self-contradictory or contrary to expectations, also known as an Antinomy.
Bertrand Russell 
classified known logical paradoxes into seven categories.
Ball and Coxeter (1987) give several examples of geometrical paradoxes.
See also Allais Paradox, Aristotle's Wheel Paradox, Arrow's Paradox, Banach-Tarski Paradox, Barber Paradox, Bernoulli's Paradox, Berry Paradox, Bertrand's Paradox, Cantor's Paradox, Coastline Paradox, Coin Paradox, Elevator Paradox, Epimenides Paradox, Eubulides Paradox, Grelling's Paradox, Hausdorff Paradox, Hempel's Paradox, Heterological Paradox, Leonardo's Paradox, Liar's Paradox, Logical Paradox, Potato Paradox, Richard's Paradox, Russell's Paradox, Saint Petersburg Paradox, Siegel's Paradox, Simpson's Paradox, Skolem Paradox, Smarandache Paradox, Socrates' Paradox, Sorites Paradox, Thomson Lamp Paradox, Unexpected Hanging Paradox, Zeeman's Paradox, Zeno's Paradoxes
References
Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed.
New York: Dover, pp. 84-86, 1987.
Bunch, B. Mathematical Fallacies and Paradoxes. New York: Dover, 1982.
Carnap, R. Introduction to Symbolic Logic and Its Applications. New York: Dover, 1958.
Curry, H. B. Foundations of Mathematical Logic. New York: Dover, 1977.
Kasner, E. and Newman, J. R. ``Paradox Lost and Paradox Regained.'' In Mathematics and the Imagination.
Redmond, WA: Tempus Books, pp. 193-222, 1989.
Northrop, E. P. Riddles in Mathematics: A Book of Paradoxes. Princeton, NJ: Van Nostrand, 1944.
O'Beirne, T. H. Puzzles and Paradoxes. New York: Oxford University Press, 1965.
Quine, W. V. ``Paradox.'' Sci. Amer. 206, 84-96, Apr. 1962.