BERRY'S PARADOX

The phrases of a language that refer to numbers can be ordered, alphabetically and according to length. There will be a definite set of integers named by those phrases of less than any given length. In particular there will be some integer which is the least integer not nameable in fewer than nineteen syllables. But this phrase ‘the least integer not nameable in fewer than nineteen syllables’ then names this number, yet itself contains fewer than nineteen syllables. Berry's paradox is of the same family as the liar and other semantic paradoxes.