'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
Contrary to popular belief these style of statements are not paradoxes (e.g. This statement is false). But are in fact meaningless. There is no possible truth-value that can be assigned to them, and so they remain un-verifieable (cf. A.J.Ayer) I cannot see the fascination. It is relatively easy to construct a logical inconsistency, and most people realise that they are nonsense. Is it me or are these statements of interest only the pedants, and as such, perfect for weeding out the non-actuaries amongst us?