Berry Paradox

There are several versions of the Berry paradox, the original version of which was published by Bertrand Russell and attributed to Oxford University librarian Mr. G. Berry. In the form stated by Russell (1908), the paradox notes that, "'The least integer not nameable in fewer than nineteen syllables' is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction."

REFERENCES

Chaitin, G. J. "The Berry Paradox." Complexity 1, 26-30, 1995.

Curry, H. B. Foundations of Mathematical Logic. New York: Dover, p. 6, 1977

.Erickson, G. W. and Fossa, J. A. Dictionary of Paradox. Lanham, MD: University Press of America, pp. 20-21, 1998.

Russell, B. "Mathematical Logic Is Based on the Theory of Types." Amer. J. Math. 30, 223, 1908.

Whitehead, A. N. and Russell, B. Principia Mathematica. New York: Cambridge University Press, p. 60, 1927.