  On the other hand, we could start, not with the formula Ω(x), but with the ordinary English sentence “x is uncountable.” If asked what this sentence means, a set theorist will say something about the lack of a bijection between x and the natural  numbers.[16]  If asked about the phrase “is a bijection,” she will go on to talk about collections of ordered pairs satisfying certain nice properties, and if asked about the term “ordered pair,” she will say something about the ways one can identify ordered pairs with particular sets. If she takes this process far enough—and if she saves herself some time by using symbols like ¬ and ∃y as abbreviations for “not” and “there exists a set y such that”—then she will eventually obtain a detailed explication of “x is uncountable” which looks just like the formula Ω(x). That is, if we simply compare the syntax of her explication of “x is uncountable” with the syntax of Ω(x), then we will find that these two expressions contain exactly the same symbols in exactly the same  order.[17]  Once again, therefore, we find that there's a real, if a somewhat superficial, similarity between Ω(x) and “x is uncountable”—a similarity which remains even after we stop using “x is uncountable” as a straightforward abbreviation for Ω(x), and a similarity which explains why even a perspicuously formulated version of Skolem's Paradox may continue to look somewhat puzzling.