Oh it's much worse for set theory than an actual antimony. For most of those are mere word-games of the "does not compute" variety, whereas Skolem's Paradox st

Oh it's much worse for set theory than an actual antimony. For most of those are mere word-games of the "does not compute" variety, whereas Skolem's Paradox states plainly, and uncontrovertibly, that there's no such thing as an absolutely uncountable infinite set. All sets have countable models, however uncountably vast they may be. It thus completely explodes all of Cantor's work on "countable" and "uncountable" infinities, rendering all infinite sets countable and equal. (As should have been intuitively obvious to begin with.) And it's ignored because people still find the nesting hierarchies of set theory useful, on occasion, even though what they now mean is very much open to question. Most of the people who have famously disparaged set theory as a theoretical foundation for mathematics -- like Wittgenstein -- have done so because, after Skolem, the whole thing is quite uncertain.