It's not hard to follow, if you just reason it through. Maybe the tricky part is realizing there are finitely many 60 letter or less combinations of letters, a subset of which are meaningful and define a positive integer (rest are gibberish as far as we're concerned). This can only refer to a finite set of numbers, so there are ones not defined. The least of these satisfies above short sentence. Contradiction.

Its a novel twist on a typical flavor of paradox, to me anyway. Neat