I think I can
explain this one better, or more
formally maybe.
Consider 'the least integer not nameable in fewer than nineteen syllables'. This expression appears to name a number (one hundred and eleven thousand, seven hundred and seventy seven, 111777), but it is also an expression of eighteen syllables that is itself a name of a number. So the least integer not nameable in fewer than 19 syllables is nameable by an expression containing fewer than nineteen syllables, which is a contradiction.
This is my favourite paradox, stated by G.G. Berry in 1906.