# Berry's paradox

Berry's paradox is a paradox, devised by G.
G. Berry of the Bodleian Library at Oxford University in 1906, that involves
statements of the form: "The smallest number not nameable in under ten words."
At first sight, there doesn't seem anything particularly mysterious about
this sentence. After all, there are only so many sentences that have less
than ten words, and only a set *S* of these specify unique numbers;
so there is clearly some number *N* that is the smallest integer
not in *S*. The trouble is, the Berry sentence itself is a specification
for that number in only nine words! Berry's paradox shows that the concept
of nameability is inherently ambiguous and a dangerous concept to be used
without qualification. A similar air of the paradoxical swirls around the
notion of interesting numbers.

### Reference

1. Chaitin, G. J. "The Berry Paradox." *Complexity*, 1: 26-30
(1995).