 No contradictions are known to follow from NF, but some uncomfortable consequences do follow. The Axiom of Choice is known to fail in NF: Specker (1953) proved that the universe cannot be well-ordered. (Since the universe cannot be well-ordered, it follows that the “Axiom” of Infinity is a theorem of NF: if the universe were finite, it could be well-ordered.) This might be thought to be what one would expect on adopting such a dangerous comprehension scheme, but this turns out not to be the problem. The problem is with extensionality.