ABSTRACT
We could avoid the contradiction by distinguishing between levels of description, in line with some treatments of semantic paradoxes like The Liar and of logical paradoxes like Russell’s. At level 0, integers would never be specified in terms of descriptions of the form ‘the least integer describable in such-and-such a way’; only at higher levels would such descriptions be admitted, and they would only refer to descriptions at the level one below. So the description ‘the least integer describable in fewer than twenty syllables’ would not be admitted at level 0. At level 1 this phrase would be interpreted as meaning ‘the least integer not describable at level 0 in fewer than twenty syllables’. Since it would not be a level-0 description itself, it would not be self-refuting.
