The paradox of a man who states "I am lying." If he is lying, then he is telling the truth, and vice versa. Another version of this paradox is the Epimenides paradox. Such paradoxes are often analyzed
by creating so-called "metalanguages" to separate statements into different
levels on which truth and falsity can be assessed independently. For example, Bertrand
Russell noted that, "The man who says, 'I am telling a lie of order 
' is telling a lie, but a lie of order 
" (Gardner 1984, p. 222).
Liar's Paradox
See also
Epimenides Paradox, Eubulides ParadoxExplore with Wolfram|Alpha
References
Beth, E. W. The Foundations of Mathematics. Amsterdam, Netherlands: North-Holland, p. 485, 1959.Bocheński, I. M. §23 and 25 in Formale Logik. Munich, Germany: Alber, 1956.Church, A. "Paradoxes, Logical." In The Dictionary of Philosophy, rev. enl. ed. (Ed. D. D. Runes). New York: Rowman and Littlefield, p. 224, 1984.Curry, H. B. Foundations of Mathematical Logic. New York: Dover, pp. 5-6, 1977.Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 108-111, 1998.Fraenkel, A. A. and Bar-Hillel, Y. Foundations of Set Theory. Amsterdam, Netherlands, p. 11, 1958.Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, p. 222, 1984.Kleene, S. C. Introduction to Metamathematics. Princeton, NJ: Van Nostrand, p. 39, 1964.Prior, A. N. "Epimenides the Cretan." J. Symb. Logic 23, 261-266, 1958.Tarski, A. "The Semantic Conception of Truth and the Foundations of Semantics." Philos. Phenomenol. Res. 4, 341-376, 1944.Tarski, A. "Der Wahrheitsbegriff in den formalisierten Sprachen." Studia Philos. 1, 261-405, 1936.Weyl, H. Philosophy of Mathematics and Natural Science. Princeton, NJ, p. 228, 1949.Referenced on Wolfram|Alpha
Liar's ParadoxCite this as:
Weisstein, Eric W. "Liar's Paradox." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LiarsParadox.html